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PAGE 1 1 MANAGING RISK AND UNCERTAINTY IN AGRICULTURAL PRODUCTION By SERHAT ASCI A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2013 PAGE 2 2 2013 Serhat Asci PAGE 3 3 To my father PAGE 4 4 ACKNOWLEDGMENTS I would like to thank to Dr. VanSickle, chairman of my doctoral committee, for the support, supervision and enco uragement he has provided me throughout my graduate studies. I would also like to express my appreciation to my other members of my committee Dr. Borisov a, Dr. Seale and Dr. Cantliffe for their recommendations and constructive criticism during the prep aration of this dissertation. patience and understanding during these three past years of stressful graduate studies and work. Finally, I would like to recognize the invaluable c ontribution of my mother and brother to my past and present accomplishments. PAGE 5 5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF FIGURES ................................ ................................ ................................ ........ 10 ABSTRACT ................................ ................................ ................................ ................... 11 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 13 2 THE PERCEPTION OF U.S. AND MEXICAN GREENHOUSE TOMATOES IN THE U.S. MARKET ................................ ................................ ................................ 16 Introductory Remarks ................................ ................................ .............................. 16 Import Demand Model ................................ ................................ ............................ 19 Data ................................ ................................ ................................ ........................ 23 Results ................................ ................................ ................................ .................... 24 Tomato Import Demand ................................ ................................ .................... 24 Parame ter estimation ................................ ................................ ................. 26 Elasticity estimation ................................ ................................ ................... 26 Disaggregated Tomato Import Demand ................................ ........................... 28 Parameter estimation ................................ ................................ ................. 30 Elasticity estimation ................................ ................................ ................... 31 Summary and Discussion ................................ ................................ ....................... 32 3 THE POTENTIAL FOR GREENHOUSE TOMATO PRODUCTION EXPANSION IN FLORIDA ................................ ................................ ................................ ............ 60 Introductory Remarks ................................ ................................ .............................. 60 Tom ato Production in the US ................................ ................................ .................. 62 Literature Review: Risk in Investment Decision Making ................................ .......... 64 Data and Models ................................ ................................ ................................ ..... 66 Simulation model ................................ ................................ .............................. 69 Ranking risky assets ................................ ................................ ........................ 72 Real option approach ................................ ................................ ....................... 73 Results ................................ ................................ ................................ .................... 74 Discussion ................................ ................................ ................................ .............. 79 4 APPROACH TO DEVELOP FERTILIZER BEST MANAGEMENT PRACTICE ...... 91 Introductory Remarks ................................ ................................ .............................. 91 PAGE 6 6 Water Quality Policies to Address Agricultura l Water Pollution Issues ................... 95 Study Area ................................ ................................ ................................ .............. 98 Data ................................ ................................ ................................ ...................... 100 Methodology ................................ ................................ ................................ ......... 102 Production Functions ................................ ................................ ...................... 103 Linear stochastic plateau production function ................................ .......... 105 Quadratic stochastic plateau production function ................................ ..... 108 Maximum likelihood estimation of linear and quadratic plateau production functions ................................ ................................ .............. 110 Maximization of Expected Profit ................................ ................................ ..... 111 Financial Analysis Model ................................ ................................ ................ 112 Financial sheet model ................................ ................................ .............. 112 Simulations ................................ ................................ .............................. 114 Simulation scenarios ................................ ................................ ................ 117 Decision criteria used in scenario ranking ................................ ................ 118 Results ................................ ................................ ................................ .................. 119 Production Functions ................................ ................................ ...................... 120 Sensitivity An alysis ................................ ................................ ......................... 121 Financial Analysis Results ................................ ................................ .............. 121 Scenario Analysis: Alternative Fertilizer Application Rates ............................ 122 Scenario Analysis: Shifts in the Output Price Distributions ............................. 124 Summary and Discussion ................................ ................................ ..................... 125 5 CONCLUSION ................................ ................................ ................................ ...... 139 APPENDIX A DERIVATION OF CONSUMPTION MODEL ................................ ........................ 143 B BUDGET TABLES FOR ALTERNATIVE TOMATO PRODUCTION TECHNOLOG IES ................................ ................................ ................................ 147 C POTATO PRODUCTION EXPENSES FOR AN ACRE ................................ ........ 152 D SAS CODES FOR ESTIMATING PLATEAU FUNCTIONS ................................ .. 153 E FINANCIAL SHEET FORMULATIONS ................................ ................................ 154 LIST OF REFERENCES ................................ ................................ ............................. 155 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 163 PAGE 7 7 LIST OF TABLES Table page 2 1 The log likelihood ratio tests for homogeneity and symmetry a ........................... 35 2 2 Test results for the log likelihood ratio tests a ................................ ..................... 36 2 3 Parameter estimation of import demand, synthetic model, 1989 2012. ........... 37 2 4 Parameter estimation of import demand, Rotterdam model, 1989 2012. ........ 38 2 5 Parameter estimation of import demand, CBS model, 1989 2012. .................. 39 2 6 Parameter estimation of import demand, AIDS model, 1989 2012. ................. 40 2 7 Parameter estimation of import demand, NBR model, 1989 2012. .................. 41 2 8 Conditional expenditure and Slutsky price elasticities of import demand, synthetic model, 1989 2012. ................................ ................................ ............ 42 2 9 Conditional expenditure and Slutsky pr ice elasticities of import demand, Rotterdam model, 1989 2012. ................................ ................................ ......... 43 2 10 Conditional expenditure and Slutsky price elasticities of import demand, CBS model, 1989 2012. ................................ ................................ ........................... 44 2 11 Conditional expenditure and Slutsky price elasticities of import demand, AIDS model, 1989 2012. ................................ ................................ ................. 45 2 12 Conditional expenditure and Slutsky price elasticities of import demand, NBR model, 1989 2012. ................................ ................................ ........................... 46 2 13 The log likelihood ratio tests for homogeneity and symmetry a .......................... 47 2 14 Test results for the log likelihood ratio tests a ................................ ..................... 48 2 15 Parameter estimation of disaggregated import demand, synthetic model, 2004 2012. ................................ ................................ ................................ ....... 49 2 16 Parameter estimation of disaggregated import demand, Rotterdam model, 2004 2012. ................................ ................................ ................................ ....... 50 2 17 Parameter estimation of disaggregated import demand, CBS model, 2004 2012. ................................ ................................ ................................ .................. 51 2 18 Parameter estimation of disaggregated import demand, AIDS model, 2004 2012. ................................ ................................ ................................ .................. 52 PAGE 8 8 2 19 Parameter estimation of di saggregated import demand, NBR model, 2004 2012. ................................ ................................ ................................ .................. 53 2 20 Conditional expenditure and Slutsky price elasticities of disaggregated import demand, synthetic model, 2004 2012. ................................ ............................. 54 2 21 Conditional expenditure and Slutsky price elasticities of disaggregated import demand, Rotterdam model, 2004 2012. ................................ .......................... 55 2 22 Conditional expenditure and Slutsky price elasticities of disaggregated import demand, CBS model, 2004 2012. ................................ ................................ .... 56 2 23 Conditional expenditure and Slutsky price elasticities of disaggregated import deman d, AIDS model, 2004 2012. ................................ ................................ ... 57 2 24 Conditional expenditure and Slutsky price elasticities of disaggregated import demand, NBR model, 2004 2012. ................................ ................................ ... 58 3 1 Risk identification for greenhouse and field grown tomato productions .............. 81 3 2 Key assumptions used in g reenhouse t omato f inancial model ........................... 81 3 3 Tomato budget for three production technologies (in dollars per acre) ............... 82 3 4 Net income statements for alternative tomato production technologies, 2014 ($/acre) ................................ ................................ ................................ ............... 82 3 5 Stochastic variables used in financial model of tomato production investment decision ................................ ................................ ................................ .............. 83 3 6 Forecasted present values and net incomes for field grown and greenhouse tomato productions ($/acre) ................................ ................................ ................ 83 3 7 Net present values per acre field grown and greenhouse tomato productions ... 83 3 8 Summary statistics of Monte Carlo simulation for alternative technologies ........ 84 3 9 First and second order stochastic dominance results for alternative t echnologies ................................ ................................ ................................ ....... 84 3 10 Stochastic dominance with respect to a function results ................................ .... 85 3 11 Net present values with option value for fie ld grown and greenhouse tomato production ($/acre) ................................ ................................ ............................. 85 4 1 Descriptive statistics summary for TCAA potato production, 1952 2010 .......... 129 4 2 Stochastic variables and financial model assumptions ................................ ..... 129 PAGE 9 9 4 3 Sets of scenarios ................................ ................................ .............................. 130 4 4 Production functions and the optim um nitrogen levels ................................ ..... 130 4 5 Sensitivity analysis of optimum nitrogen level for linear function (in pounds of nitrogen per acre) ................................ ................................ ............................. 131 4 6 Sensitivity analysis of optimum nitrogen level for quadratic function (in pounds of nitrogen per acre) ................................ ................................ ............ 131 4 7 Summary statistics for 10 year NPV simulations for various fertilizer rate s ...... 131 4 8 First and second order stochastic dominance results for alternative fertilizer uses ................................ ................................ ................................ .................. 132 4 9 Analysis of Stochastic Dom inance with Respect to a Function (SDRF) ........... 132 4 10 Summary statistics for 10 year NPV simulations for various output prices ....... 132 4 11 Simulated NPV of a strict fertilizer level determined at the $12/cwt sale price 133 B 1 High technology greenhouse production expenses ................................ .......... 147 B 2 Regular Florida greenhouse production expenses ................................ ........... 148 B 3 Field grown tomato production expenses ................................ ......................... 149 B 4 High te chnology greenhouse construction cost ................................ ................ 150 B 5 Regular Florida greenhouse construction cost ................................ ................. 151 C 1 Potato production expenses in TCAA ($/acre) ................................ .................. 152 PAGE 10 10 LIST OF FIGURES Figure page 2 1 Field grown and protected culture fresh market tomato shipments by month. ... 59 2 2 U.S. share of winter (December April) and total tomato expenditure in the last 5 years, 2007 2012 ................................ ................................ ............................ 59 3 1 Tomato imports from Mexico by techno logy ................................ ....................... 86 3 2 Fresh tomato supply in the U.S. market ................................ ............................. 86 3 3 Domestic fresh tomato market in the U.S. ................................ .......................... 87 3 4 Risk modeling in the net present value analysis ................................ ................. 87 3 5 CDFs of simulated NPVs for alternative technologies ................................ ........ 88 3 6 Stochastic efficiency with respect to a function under a negative exponential utility function ................................ ................................ ................................ ...... 88 3 7 Present value binomial tree for field grown tomato production ........................... 89 3 8 Real option calculation for greenhouse tomato investment ................................ 90 4 1 The counties of Tri County Agricultural Area and agricult ural areas ................. 134 4 2 Potato yield and nitrogen use data (per acre) for Tri County Agricultural Area 135 4 3 Potato acreage and tot al production in Tri County Agricultural Area ................ 135 4 4 Plateau shift for the stochastic function due to weather effect .......................... 136 4 5 Pr edicted and actual yields given historic weather conditions and fertilizer use ................................ ................................ ................................ .................... 136 4 6 Predicted, actual and forecasted yields ................................ ............................ 137 4 7 CDFs of simulated net present values for various fertilizer use decisions ........ 137 4 8 PDF approximations of simulated net present values of optimum nitrogen levels at various output prices ................................ ................................ .......... 138 PAGE 11 11 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy MANAGING RISK AND UNCERTAINTY I N AGRICULTURAL PRODUCTION By Serhat Asci December 2013 Chair: John J VanSickle Co chair: Tatiana Borisova Major: Food and Resource Economics This dissertation includes three essa ys on the general topic of risk in agricultural production under global com petition, trade negotiations, and environmental policies The studies address the need for developing a more comprehensive methodology to examine viable options for agricultural production given competitive / regulatory pressures. Investment production a nd/or institutional risks are examined for two important Florida vegetable crops winter tomato and potato. T he first essay focuses on market risk and analy zes the consumer perception s of imported and domestic greenhouse tomatoes. D ifferential demand mode ls are estimated The results indicate a boom phase of growth in the U.S. greenhouse tomato market leading to the increase in sales of both U.S. and Mexico produced tomato T he second essay comprehensively identifies and characterizes the risks involved in greenhouse tomato investment decisions. In addition to market risks, the outcomes of the investments are affected by the uncertainty in cost and yield. To examine the risks, n et present value models with Monte Carlo simulation are used to analyze the vi ability of greenhouse investment decisions The analysis is further extended by utilizing real option method The results indicate that a grower would PAGE 12 12 choose to continue with field grown tomato production due to high option value and risk aversion. These r esults are consistent with what has been witnessed in tomato production in Florida. However, policies or market conditions such increase credit availability, increase interest rates, decrease energy prices, stabilize high tomato prices would make the green house production more preferable. Finally, the third essay examines the production risk and the choices of fertilizer application rates by Florida potato producers. Nitrogen fertilizer is commonly used as a strategy to manage production risks; however, exc essive nitrogen application has the potential to impact surface water quality. Using county level data, the study explores the economically optimal nitrogen fertilizer rate by explicitly considering the production risks The results show that no single fertilizer BMP can be recommended for all growers and all market conditions Overall, the three essays contribute to the economic literature on agricultural risk management, and generate information to assist agricultural produ cers and policy makers. PAGE 13 13 CHAPTER 1 INTRODUCTION The weather conditions, fluctuation in yields and prices, the change in government policies, severity of international competition, and new trade agreements have significant impact on agribusiness profit s (Ha rwood et al. 1999). All these factors are combined in the notions of risk and uncertainty. Risk management is a critical component in the agricultural management. Farmers make decisions by selecting one among many alternatives to diminish the negative econ omic effects of risk factors. R isk usually refers to the situation when alternative outcomes or conditions have known probabilities. In turn, uncertainty refers to the outcomes and conditions with unknown probability distribution However, these terms are often used interchangeably (Roberts, Osteen and Soule, 2004). All risk factors are categorized in literature as production risk, price risk, financial risk, institutional risk, and human risk (Moss, 2010) Uncertainty in weather and climate, disease and p ests create production risk by affecting both the yield and quality of commodities produced (i.e., production risks) Output p rice s received by farmers or input prices can fluctuate unpredictably for agricultural producers (i.e., price risks). P rice risk a nd production risks can be related, since prices can depend on total yield and quality of the produce. However, prices depend on many other variables like global market and competition. In turn, f inancial risk is caused by credit availability and the chang e in interest rate that affect the farm business borrowing money. Institutional risk is related with the government policies on taxes, environmental regulations, and agricultural subsidies that can have a crucial impact both on the agricultural firm and th e environment (Roberts, Osteen and Soule, PAGE 14 14 2004). At last, human factors such as accidents and illness can also create unpredictable situations and risks affecting the agricultural enterprises. Additional information about uncertain factors and effective r isk management strategies help producers to make better decisions. R isk management tools include enterprise diversification, vertical integration, contacts, hedging, options, liquidity insurance, and off farm employment (Harwood et al. 1999). The use of a lternative risk and government farm programs. The three essays in this dissertation focus on risk management in agricultural production given global competition and ch anging environmental regulations The first and second essays focus on the diversification of production practices as a risk management strategy. Specifically, t he study examines the adopti o n of greenhouse technology to mitigate Florida tomato producers rofit losses associated with the increasing competition with Mexican tomato imports. Tomato sales from Florida have dropped almost 50% in the last decade, from as much as $500 million /year to $250 million /year in market value. At the same time, the Mexican import (and primarily, greenhouse tomatoes ) increased significantly in the last years. Florida producers have begun to consider greenhouse tomato production as a way to regain competitiveness However, the adoption rate of this new production technology i s still low, offering a good opportunity for researchers to analyze the risks and opportunities associated with potential expansion in Florida greenhouse tomato production. Since the viability of new investment depends on the consumer perceptions of greenh ouse tomato and the market risk in the first essay, consumer demand for greenhouse tomatoes is examined PAGE 15 15 by using differential models. T he second essay aims at investigat ing the viability of greenhouse investment decisions, taking energy use as a price (co st) risk component for decision making, and using net present value and real option approach. The third essay focuses on institutional risk and examines the of fertilizer rate given changing water quality regulations. Specifically, the d evelopment of nitrogen fertilizer best management practice (BMP) is examined for Florida potato production. BMPs are being developed to improve and protect water quality in Florida ; however, the economic factors affecting the adoption of these BMP by the p roducers have not yet been examined The nitrogen fertilizer use decisions are commonly made by farmers to address production risks, including the risks associated with adverse weather events. At the same time, nutrient leaching from agricultural fields ha s the potential to impact surface water quality. In Florida, mandatory limits on nitrogen fertilizer application rates are proposed as a strategy to address water quality issues in several regions, including the northern potato producing region of Florida. This study explores the economic viability of the proposed nitrogen BMPs C ounty level data are used and stochastic production function s are estimated. F fertilizer use choices are examined using Monte Carlo simulations expected profit maximizati on, and stochastic ranking methods Overall, the three essays contribute to the economic literature on agricultural risk management and environmental policy, and generate information to assist agricultural producers and policy makers. PAGE 16 16 CHAPTER 2 THE PERCEP TION OF U.S. AND MEXICAN GREENHOUSE TOMATOES IN THE U.S. MA RKET Introductory Remarks The United States (U.S.) winter fresh tomato industry, especially from the beginning of December to the end of April in Figure 2 1, consists predominantly of Florida field grown (24%), Mexican field grown (27%) and Mexican greenhouse tomatoes (27%) Mexican and Floridian producers have engaged in a trade conflict since the early 1970s (Bredahl, Schmitz and Hillman, 1987; Vansickle, Evans and Emerson, 2003). Many U.S. produ cers believe that their industry is vulnerable to excessive imports and low prices. Further, some states in the U.S., such as California and Arizona, have started producing greenhouse tomatoes during the winter season. This response puts downward pressure on winter tomato prices and also makes the market more prone to new conflicts b etween the Mexican and Florida producers. Therefore, it is important to assess both import and domestic greenhouse production to address potential trade conflicts. We start the analysis by stu d y ing the substitution and complimentary relationships between imported and domestically produced tomatoes These relationships are referred to as consumer perception of the product For example, if two goods are substitutes, consumers perce ive them as similar products, whereas, two compliments are perceived as non competitive consumption goods. The U.S. is the second largest fresh tomato producer in the world with 33.5 million cwt in 2010, and the fresh tomato industry is the highest valued fresh vegetable industry in the na tion (FAOSTAT, 2013 ; USDA ERS, 2013b). Florida (12.3 million cwt) and California (10.4 million cwt) are the largest tomato producing states in the U.S. (USDA ERS, 2012c). Fresh field grown tomatoes are harvested in Califor nia PAGE 17 17 during all seasons except winter, while in Florida they are harvested from October to June with peak production from November to January. Recently, however, California and Arizona have become key states for U.S. greenhouse production transforming Calif ornia and Arizona into winter tomato producers when prices are at peak levels. provides fresh tomatoes more for the western part (VanSickle, Evans and Emerson, 2003). More th an half of the fresh tomatoes consumed in the U.S. are imported from Mexico and Canada, and half of these tomatoes come from greenhouse production ( Figure 2 2). The U.S. imported nearly 35 million cwt of fresh tomatoes in 2011, of which Mexico accounted fo r 11.5 million cwt with greenhouse tomatoes and Canada accounted for 3 million cwt with greenhouse tomatoes (USDA FAS, 2013). Other countries like the Netherlands and Spain also export greenhouse tomatoes to the U.S. but in much smaller quantities. U.S. gr eenhouse tomato production was 5.4 million cwt in 2011, a 16 % share of total U.S. fresh tomato production. G rowth trend s indicate there is still potential to expand this industry (USDA ERS, 2013a). F lorida producers historically go t higher prices for thei r tomatoes. The average average price in California was $33.10 per cwt (USDA ERS, 2013c). However, with the growth in the U.S. greenhouse industry and increased imports in th e winter market, average U.S. grower prices fell from $48.4 in 2010 to $31.3 in 2012 (USDA ERS, 2013a). Yield per acre of greenhouse tomatoes can be up to twenty fold that of field grown tomato es and this helps imported greenhouse tomatoes have opportuniti es to PAGE 18 18 increase their share in the U.S. by offering lower prices and better quality product (Cantliffe and VanSickle, 2009). In this paper, we analyze U.S. demand for domestic and imported tomatoes, and evaluate consumer preferences for the greenhouse and field grown tomatoes as well as cross price effects on demand for those commodities (i.e., consumer perceptions) To do so, tomato demand can be estimated by four differential demand systems (Rotterdam, AIDS, CBS and NBR) and a synthetic model that nests t he four demand systems (Barten, 1993). The domestic demand includes the shipments of U.S. products and the imported fresh tomatoes because the tomato market in the nation is assumed to be inseparable in this study (Winters, 1984). The demand analysis is co mpleted in two parts. The first aggregated part provides us a general perspective of the tomato market in the U.S. while the disaggregated data in the second part enable the comparison among the U.S. and Mexican tomato categories. In the aggregated analysi s, none of the four tested demand systems fits the data as well as the synthetic one. In the second analysis, the Rotterdam model fits the data best for evaluating domestic and import demand. The expenditure elasticity of aggregated U.S. tomatoes is greate r than unity in the aggregated analysis while those of other imported tomatoes are less than unity. The results from the disaggregated analysis show that Mexican greenhouse tomatoes also have a conditional expenditure elasticity greater than unity. The own price elasticities indicate that tomato demand is inelastic. Results also signify that U.S. tomatoes are substitutes with the imported tomatoes at the aggregate level. This indicates that imported and domestic tomatoes are perceived as a similar product. However, results for the disaggregated analysis PAGE 19 19 indicates that U.S. field grown and other tomatoes compete with both U.S. and Mexican greenhouse tomatoes, but that U.S. greenhouse tomatoes do not compete with Mexican greenhouse tomatoes. As fresh tomatoes are the highest valued fresh vegetable in the U.S., the fresh tomato market in the U.S. is an open market for rent seeking actions of importers and domestic producers. While importers try to increase their shares in this market by low ering their prices, do mestic producers want to keep it a high valued market and avoid any costly investment in production practices ( such as investment in greenhouse production ) The results of this study are exceptional for those interested in international trade and for polic y makers. Finding out how Mexican greenhouse tomatoes are perceived is a helpful tool for designing future policies for dealing with potential trade conflicts. Overall, the main goal of this study is to examine tomato demand in the U.S. and to evaluate con sumer preferences for the domestic greenhouse, domestic field grown, imported, and Mexican greenhouse tomatoes and as well as cross price effects on demand for these goods. The paper is organized as follows. The next section presents and discusses the diff erential demand systems. A later section describes the data sources and discusses the data used in this study. The third section demonstrates the results of tomato demand in the U.S. and wraps up the results for disaggregated tomato demand analysis, partic ularly for the greenhouse tomatoes. Finally, we summarize the findings and indicate possible future direction for study. Import Demand Model The first differential demand system known as the Rotterdam model was developed by Barten (1964) and Theil (1965). In 1980, Deaton and Muellbauer (1980) developed the Almost Ideal Demand System (AIDS). Later, Keller and Van Driel (1985), PAGE 20 20 and Clements (1987) developed the Central Bureau of Statistics (CBS) model, combining these two parameterizations. The contribution o f the CBS is that its marginal shares are not constant as they are in the Rotterdam model. Neves (1987) developed a fo u rth model, called the National Bureau of Research (NBR) model. Finally, Barten (1993) developed a synthetic model that nested all four di fferential systems. One of the first applications of these demand systems to import demand was for an agricultural commodity by Seale, Sparks and Buxton (1992) who applied the differential demand systems to the imports of U.S. fresh apple s More recently, Schmitz and Seale (2002) used this methodology to estimate the demand for fresh fruit imports into Japan. Our analysis utilizes the methodologies above. We extend the methodology to demand for imported tomatoes, both greenhouse and field grown. We also fi t the models to monthly data, not previously used in other studies. Let the utility function take the general form of of a finite number of commodities. We assume twice differentiability and non saturation so that The generalized diminishing marginal utility requires that the Hessian matrix of the utility function, is negative definite and symmetric matrix. We can derive demand equations by maximizing the utility function subject to the where is the price, is quantity, and M is the total budget so that and (2 1) PAGE 21 21 Differentiating equation (2 1) proportionality with respect to and M and demand equation. The well known parameterization of this equation gives us the Rotterdam demand system: (2 2) In this equation, represents the average budget share of good i while the parameter is the margin al budget share of good i and is a compensated price effect for commodity i with respect to the price of commodity j There are three constraints for demand theory : adding up ( ) ; homogeneity ( ) ; and Slutsky symmetry ( ) The expenditure elasticity ( i ) of import demand for good i and the S lutsky price elasticity ( ij ) and C ournot 1 price elasticity ( c ij ) of good i with respect to price j respectively, are calculated by the following equations: ; (2 3) ; and (2 4 ) (2 5 ) 1 Cournot price elasticities are calculated but the results are not included in this study. These elasticities reflect both price and income effects of the demand with respect to a change in the prices of the goods. In theory, cournot own price elasticies are lower than the slutsky own price elasticies. PAGE 22 22 Replacing with in the equation (2 2) and rearranging the terms lead us to the CBS model (Keller and Van Driel, 1985): ( 2 6 ) Substituting by in the equation (2 6) gives us the (differential) AIDS equation (Barten, 1993): (2 7 ) Additionally, the NBR is generated by replacing w ith in the equation (2 7) (Neves, 1987). (2 8 ) The synthetic or general model, proposed by Barten (1993), is shown in equation (2 9) below and has two additional parameters, and : (2 9 ) where and The constraints on the model are: adding up ; homogeneity ; and Slutsky symmetry The expenditure elasticity, the Slutsky price elasticity and Cournot price elasticities are found respectively by ; ; and where represents Kronecker delta equal to u nity if i=j and zero otherwise. The parameters, and give us the information about PAGE 23 23 the best demand system that fits the data. Equation (2 9) becomes Rotterdam when and CBS when and AIDS when and and NBR when and Data Monthly imports and domestic fresh tomato shipments data are used in this study. The tomato import data are found at Global Agricultural Trade Systems (GATS) of Foreign Agricultural Service, United States Department of Agriculture (USDA FAS, 2013). The Harmonized Commodity Description and Coding System (HS) is used at the 10 digits level. Import values and quantity data are collected for Mexico (field grown and greenhouse tomatoes), Canada (almost all greenhouse tomatoes), Netherland (all greenhouse tomatoes) and other countries (mainly greenhouse tomatoes) from Jan uary 1989 to June 2012 (USDA FAS, 2013). Expenditure on U.S. tomatoes is Economic Research Service (USDA ERS, 2013c). The monthly movement data and shipping prices are coll ected from January 1978 to June 2010 from an ERS dataset (USDA ERS 2013c). The monthly data are extended to August 2012 by using the summation of daily movements and the average of daily shipping point prices reported by Agricultural Marketing Service (AMS ), U.S. Department of Agriculture (USDA AMS, 2013). Therefore, the time frame of the analysis is from January 1989 to August 2012 with 270 observations. Disaggregated data that allow us to compare field grown and greenhouse produced tomatoes of the U.S. an d Mexico are collected from the daily AMS reports for quantity movements from shipping points, shipping point prices and terminal point PAGE 24 24 prices that cover the time period from October 2004 to August 2012 with 94 total observations (USDA AMS, 2013). Monthly prices from daily reports are calculated from the simple average of the daily shipping point prices. The weighted average cannot be calculated since the price data are not reported with the quantity sold. Monthly quantities are found at daily movements re ported from the shipping points for each tomato category: field grown, greenhouse, plum, cherry and grape tomatoes. The greenhouse tomatoes category does not include plum, cherry and grape tomatoes produced in greenhouses. U.S. greenhouse tomato prices are only found at the terminal points. Therefore, the terminal point prices for greenhouse tomatoes are scaled by the ratio of the shipping point to the terminal point prices for field grown tomatoes. Results Tomato Import Demand The parameters are calculated using Time Series Processor (TSP version 5.0). The equations are estimated by iterative seemingly unrelated regressions (SUR). One equation is dropped during estimation to comply with the adding up condition (Barten, 1993). Log differences and average s hares are calculated by taking a 12 month difference to account for seasonality. The Hildreth Lu procedure is applied to test for autocorrelation of the system of equations and GARCH is used to test for homoscedasticity. The parameter rho, the autocorrelat ion parameter as a fraction, is chosen by transforming both dependent and independent variables by and for ( i likelihood level of the multivariate regression. When the model without rho is taken as a base model, the PAGE 25 25 log likelihood ratio (LR) test rejects that rho is equal to zero at the 5% level. When the GARCH parameters are tested for homoscedasticity, they are not found different from zero at the 5% level. Therefore, we reject the null hypothesis of homoscedasticity. The robust (White) standard errors are calculated and given in parenthesis for each coefficient and elasticity. Homogeneity and symmetry are imposed on the unrestricted demand systems and these restrictions are tested with LR tests. Table 2 1 illustrate s the results of the LR R U is the vector of parameter estimates of the unrestricted model, and L(.) is the log likelihood value. When the homogeneity restriction is compared with the critical value of a 2 distribution at 5% significance level, we fail to reject the homogeneity hypothesis in CBS demand system and the symmetry in Rotterdam, AIDS and NBR. Therefore, the augmented chi square described by Laitenen (1978), is used for the homogeneity restriction. Since the symmetry restriction is barely rejected, we accept the restriction by referring to Meisner (1979) who showed the sad fate of symmetry test. The augmented chi square (T 2 ) is calculated by where n is the number of commodities in the equations, and N is the number of observations. F values are found for homogeneity as Thus, we fail to reject homogeneity hypothesis at the 5% significance level. Estimating the synthetic mode l allows us to select among the four demand systems of this analysis. We find that and coefficients are respectively 0.441 and 0.317 and statistically significant at the 1% level. Since both of the values are c lose to be 0.5, we could not detect the best demand system that fits the data for tomato import PAGE 26 26 demand analysis. Additionally, LR tests are conducted for the same purpose. Table 2 2 shows the comparison of the four demand systems to the synthetic model wit h homogeneity and symmetry imposed. In all cases, we reject the four models in comparison to the synthetic model at the 5% significance level. Accordingly, we only discuss the results of the synthetic model. Parameter estimation Parameter estimates with ho mogeneity and symmetry restrictions are provided for all the parameterizations in Table 2 3, Table 2 4, Table 2 5, Table 2 6 and Table 2 7. All the expenditure coefficients for the synthetic model, used since the other models are rejected, are positive but only the coefficients for the U.S. and the Rest of the World (ROW) are statistically significant at the 5% level. The own price coefficients for all the goods are negative and statistically significant at the 1% level except for the U.S. and Mexican toma to price coefficients. Three out of ten cross price coefficients are statistically significant at the 10% level. It is important to note that the expenditure and price coefficients of the synthetic model do not give any information on the income elasticity or on the substitution effect like the other demand systems. Elasticity estimation The conditional expenditure and Slutsky price elasticities for the U.S and each importer country are presented in Table 2 8, Table 2 9, Table 2 10, Table 2 11 and Table 2 1 2 All the elasticity values are calculated at the sample mean from 1990:1 to 2012:08. The individual parameter estimates, showed in previous tables, are used to calculate the elasticities. All of the expenditure elasticities are statistically significant at the 5% level. The point estimates of the expenditure elasticities of U.S. tomatoes and ROW tomatoes are PAGE 27 27 greater than unity. This indicates that if the expenditure on tomatoes increases by 1%, the expenditure on these products increase by more than 1%. The results show that a 1% increase in the expenditure for tomato creates a 1.32% increase in U.S. and a 1.16% increase in the ROW tomatoes, respectively, while the demand for Mexican, Canadian and Dutch tomatoes only increases 0.56%, 0.55% and 0.58%, resp ectively. These results indicate that U.S. consumers prefer U.S. and ROW tomatoes as total expenditure for fresh tomatoes increase allowing for no price changes. The Slutsky own price elasticity designates the percentage change in quantity demanded resulti ng from a percentage change in price, holding real expenditure constant. All own price elasticities are negative and significant at the 1% level except for ROW. Results indicate that the demand for tomatoes is inelastic since all estimated own price e lasti cities are less than unity in absolute terms. The own price elasticity of U.S. tomatoes is one of the lowest elasticities followed by Mexican tomatoes, and then by Canadian tomatoes. The results also indicate that these products have relative competitivene ss power in the market. For instance, a 1% increase in the price of U.S. tomatoes decreases, the quantity demanded only by 0.16%, whereas, the same increase in Mexican tomato price decreases the demand by 0.24% ce teris paribus Although the difference is not large, it still shows that U.S. tomatoes have a price advantage in the market if prices rise. However, a 1% decrease in Mexican tomato price increases the demand for Mexican tomatoes more than the same price decrease on U.S. tomatoes would increase dem and for U.S. tomatoes. Cross price elasticity shows the response i n demanded quantity to price changes of other tomatoes. For example, the cross price elasticity of U.S. tomatoes with respect PAGE 28 28 to Mexican tomatoes reveals the percentage change in the quantit y demanded for U.S. tomatoes resulting from a percentage change in the Mexican tomatoes price. A positive and statistically significant cross price elasticity indicates substitute goods while the negative price elasticity indicates complement goods. The an alysis shows that 16 out of 20 cross price elasticities are statistically significant at the 10% level and all the U.S. cross price elasticities are positive and statistically significant at the 1% level. U.S. tomatoes are substitutes with the all importe d tomatoes. The largest cross price elasticity is for U.S. tomatoes relative to Mexican tomatoes with a value of 0.12. The other cross price elasticities of the U.S. with respect to the other tomatoes are 0.03, 0.01 and 0.01, respectively, for Canadian, Du tch and ROW tomatoes. These elasticities indicate the percentage change in the quantity demanded for U.S. tomatoes resulting from a percentage change in the other tomatoes prices. In turn, a 1% increase in the price of U.S. tomatoes increases, ceteris pari bus, the quantity demanded for Mexican, Canadian, Dutch and ROW tomatoes by 0.21%, 0.23%, 0.25% and 0.48%, respectively. Moreover, a price change in Mexican tomatoes strongly affects the quantity demanded for the U.S. tomatoes, and a price increase in the U.S. tomatoes has a large effect on the quantity demanded for the other tomatoes. Disaggregated Tomato Import Demand The analysis is further expanded to evaluate disaggregated tomato product categories according to production techniques and the types of to matoes. The aim of the disaggregation is to explore the consumption preferences of U.S. consumers and to analyze the demand for U.S. greenhouse tomatoes. Since we aim to compare field grown and greenhouse produced tomatoes of the U.S. and Mexico, we aggreg ated plum, cherry and grape tomatoes as U.S. other tomatoes, and all the other tomato PAGE 29 29 importers (i.e. Canada, the Netherland, Spain) as ROW while keeping the total tomato expenditure the same as in the previous section. All the statistical tests described in the previous section for import demand are applied in this analysis. We reject the hypothesis of autocorrelation by using log likelihood test for the rho obtained from Hildreth Lu procedure. Homoscedasticity is tested by GARCH and we reject the null hyp othesis of homoscedasticity at the 5% significance level. The robust (White) standard errors are used to control for heteroscedasticity. Homogeneity and symmetry restrictions are tested by the lo g likelihood ratio test. Table 2 13 indicates that homogenei ty restrictions are rejected for CBS, AIDS and NBR models at the 5% significance level. We fail to reject the symmetry hypothesis at the 5% significance level for all the demand systems. The augmented chi square (T 2 ) is calculated for F values of F ( 83,5 ) =4 .42 for homogeneity. The results showed that we fail to reject homogeneity at the 5% significance level for all of the demand systems except barely for AIDS model. The coefficients of the synthetic model are estimated and the two coefficients that can rest rict the synthetic model to the other four demand systems are and Neither is statistically different from zero. These coefficients indicate that the Rotterdam demand system fits the data better than the other d emand systems for the disaggregated tomato analysis. LR tests a lso confirm our finding. Table 2 14 shows that we can only fail to reject the Rotterdam model at the 5% significance level when the four demand systems are compared with the synthetic model wit h PAGE 30 30 homogeneity and symmetry imposed results. Therefore, the results are presented only for the Rotterdam demand system for this section. Parameter estimation The Rotterdam estimates for parameters with homogeneity and symmetry restrictions a re presented in Table 2 15, Table 2 16, Table 2 17, Table 2 18 and Table 2 19 Estimated expenditure coefficients are all positive and statistically significant at the 1% level except for Mexico field grown greenhouse and ROW tomatoes. All the statistically significant S lutsky own price coefficients are negative. The U.S. and the Mexican greenhouse tomato own price coefficient s are not statistically different than zero while the others are statistically significant at the 5% level. Nine out of 15 cross price coefficients are statistically significant at the 10% level. The results signify that U.S. field grown tomatoes are substitute with Mexican field grown and greenhouse tomatoes as well as U.S. other tomatoes. For instance, a 1% increase (decrease) in the U.S. field grow n tomato price raises (diminishes) the quantity demanded for Mexican field grown and greenhouse tomatoes 0.05% and 0.03%, respectively. Interestingly, we find that U.S. greenhouse tomatoes are complementary with Mexican greenhouse tomatoes. U.S. consumers seemingly do not differentiate between U.S. and Mexican greenhouse tomatoes would increase the demand of U.S. greenhouse tomatoes. Mexican field tomatoes are also complements w ith Mexican greenhouse tomatoes. It signifies that these goods would benefit from a n increase of for other Mexican tomatoes. For instance, a price decrease in Mexican field grown or greenhouse tomatoes raises the quantity demanded of both goods. PAGE 31 31 Elasticity estimation Conditional e xpenditure and Slutsky price elasticities of disaggregated tomato demand are provided in Table 2 20, Table 2 21, Table 2 22, Table 2 23 and Table 2 24 All the elasticity values for the Rotterdam demand syste ms are calculated at the sample mean from 2005:10 to 2012:08 E lasticities are calculated from individual parameter estimates presented in previous tables The expenditure elasticities of U.S. field grown, U.S. greenhouse, U.S. others and Mexican greenhous e tomatoes are greater than unity and statistically significant at the 1% level. Thus, the disaggregated data analysis shows us that Mexican greenhouse tomato demand response is also similarly to that of U.S. tomatoes in the market when total expenditure f or fresh tomatoes changes. The expenditure elasticity for Mexican field grown and ROW are not statistically different from zero. The statistically significant own price elasticities are all negative and less than unity in absolute terms similar to the resu lts in the previous section. Four out of six own price elasticies are statistically significant at the 5% level in the Rotterdam demand system. The largest ( .09) is that of U.S. field grown tomatoes while those of U.S. others, Mexican field grown, and Mex ican greenhouse tomatoes are of similar size of around .03. The interpretation of cross price elasticities shows us essentially the substitution effect of U.S. tomatoes by categories. We find that U.S. field grown and U.S. other tomatoes are substitutes w ith Mexican field grown and Mexican greenhouse tomatoes. A 1% increase in the price of Mexican field grown (greenhouse) tomatoes, ceteris paribus, increases the demand of U.S. field grown tomatoes by 0.12% (0.11%). However, a 1% increase in the price of U. S. field grown tomatoes increases the PAGE 32 32 Mexican field grown or greenhouse tomato demand by 0.17% and 0.22%, respectively. Accordingly, the quantity demanded of U.S. field grown tomatoes is more sensitive to the price changes of imported tomatoes than the qua ntity demanded of imported tomatoes is to price changes in U.S. field grown tomatoes. U.S. other tomatoes are found to be less sensitive to the price change in the Mexican tomatoes because a 1% increase in the U.S. other tomatoes increases the demand for t he Mexican field grown or greenhouse tomatoes demand by 0.07% and 0.11%, respectively, while this price increase in the Mexican field grown or greenhouse tomatoes will result in a 0.15% and 0.16% increases in U.S. other tomatoes demand. We conclude that the demand of tomatoes is significantly affected by the price change of the U.S. and Mexican tomatoes. Surprisingly, the cross price elasticity between the U.S. and Mexican greenhouse tomatoes is negative and statistically significant at the 5% level indic ating they are complements. This result supports our discussion in the introduction that imports of Mexican greenhouse tomatoes stimulate investment in U.S. greenhouse tomatoes. Results also show that the Mexican field tomatoes are complements with Mexican greenhouse tomatoes. The findings in this section suggest that the growth of greenhouse tomatoes will continue unti l their market share reaches a maturation stage. Summary and Discussion The trade conflict bet ween the U.S. and Mexico tomato producer s is s till a great concern for the winter tomato market. In 1996, the U.S. established a fixed entrance price for Mexican tomatoes as part of a complex arrangement in 1996. Nevertheless, the Executive Vice President of the Florida Tomato Exchange pointed out tha PAGE 33 33 conflict is often mentioned by producer and importer groups as farmers and polic y makers continue searching for alternative ways to deal with this issue (Malkin, 2012). The renegotiated suspension agreement for the antidumping investigation raises the reference prices of Mexican tomatoes ranging from 50% to 300% from the previous agr eement depending on their category (US DC, 2013). This agreement distinctively covers four different tomato categories including open area, controlled environment, specialty loose and specialty packed categories Although this study confirm s the importance of categorizing tomatoes, it also emphases the significant effect of the substitution and complementary linkage between these categories. The analysis of these linkages between the U.S. and Mexican tomatoes helps policy makers to understand the market and to choose the right policies. The results suggest that demand for U.S. tomatoes is more sensitive to change in total expenditure for field grown tomatoes than the demand for imported tomatoes. However, the disaggregated analysis shows that the demand for Mexican greenhouse tomatoes responds similarly to that of U.S. field grown tomatoes. We find that U.S. tomatoes are perceived as a similar product to imported tomatoes by consumers, which indicates the strong competition among these goods in the market. Fu rthermore, the tomato demand is not sensitive to the price changes in U.S. greenhouse tomatoes while the price changes in U.S. field grown and other tomatoes affects the demand significantly. Although U.S. field grown tomatoes compete with Mexican field g rown tomatoes and all sources of greenhouse tomatoes, there is a synergistic relationship between PAGE 34 34 imported and domestically grown greenhouse tomatoes. Since the beginning of the 21st century, we have witnessed a large increase in the production and marketi ng of greenhouse tomatoes, taking market share away from field grown tomato producers. Mexican greenhouse tomatoes are competing with and taking market share from U.S. field grown tomatoes but have led to a growth in production of U.S. greenhouse tomatoes. When a sector is in a boom phase of growth (as has been the greenhouse tomato market), it appears that competitive produc t s are complimentary in the market. This will in fact continue until the market matures and it moves into the bust side of the boom bu st business cycle in sector analysis (Schmitz 1995). When the market matures we hypothesize U.S. and imported greenhouse tomatoes will shift from complementary products to substitutes in the market. Until then, the investment of greenhouse tomatoes will co ntinue to grow in the U.S. while demand for field grown tomatoes continues to shrink. PAGE 35 35 Table 2 1. The log likelihood ratio tests for homogeneity and symmetry a Log likelihoods R ) U )] 2 (0.05) T 2 (0.05) Synthetic Model Unrestricted Model (26) 2883.43 Homogeneity (22) 2878.42 10.02 9.49 22.77 Homogeneity + Symmetry (16) 2871.62 13.60 12.59 Rotterdam Unrestricted Model (24) 2858.71 Homogeneity (20) 28 51.96 13.50 9.49 22.77 Homogeneity + Symmetry (14) 2845.88 12.16 12.59 CBS Unrestricted Model (24) 2833.30 Homogeneity (20) 2828.99 8.62 9.49 22.77 Homogeneity + Symmetry (14) 2821.51 14.96 12.59 AIDS Unrestricted Model (24) 2854.43 Homogeneity (20) 2848.27 12.32 9.49 22.77 Homogeneity + Symmetry (14) 2842.58 11.38 12.59 NBR Unrestricted Model (24) 2827.90 Homogeneity (20) 2822.41 10.98 9.49 22.77 Homogeneity + Symmetry (14) 2817.57 9.68 12.59 Notes: a Number of param eters estimated is given in parenthesis. PAGE 36 36 Table 2 2 Test re sults for the log likelihood ratio tests a Log likelihoods R ) U )] 2 (0.05) Synthetic Model (16) 2871.62 Rotterdam (14) 2845.88 51.48 b 5.99 CBS (14) 2821.51 100.22 b 5.99 AIDS (14) 2842.58 58.08 b 5.99 NBR (14) 2817.57 108.10 b 5.99 Notes: a Number of parameters estimated is given in parenthesis. b LR values of tested model against synthetic model, homogeneity and symmetry imposed on both. PAGE 37 37 Table 2 3 Parameter estimation of impor t demand, synthetic model 1989 2012. Slutsky Price Coefficients (e ij ) Expenditure Coefficients (d i ) U S Mexico Canada Netherlands ROW 1 2 U S 0.017 0.011 0.003 0.001 0.002** 0.504*** 0.441*** 0.317*** (0.020) (0.020) (0.002) (0.001) (0.001) (0.128) (0.121) (0.061) Mexico 0.011 0.002 0.002 0.001 0.040 (0.020) (0.002) (0.002) (0.001) (0.089) Canada 0.008*** 0.006*** 0 .001 0.007 (0.003) (0.002) (0.001) (0.005) Netherlands 0.008*** 0.001* 0.002 (0.001) (0.001) (0.004) ROW 0.003*** 0.005** (0.001) (0.003) Notes: Asterisks (*, **, ***) represent significant at the 10%, 5% and 1 % level, respectively. ROW=rest of the world. PAGE 38 38 Table 2 4 Parameter estimation of import demand Rotterdam mo del, 1989 2012. ij ) Marginal Income Share i ) U S Mexico Canada Netherlands ROW U S 0.088*** 0.070*** 0.011*** 0.003*** 0.003*** 0.749*** (0.017) (0.017) (0.002) (0.001) (0.001) (0.083) Mexico 0.074*** 0.000 0.003 0.002* 0.205** (0.017) (0.003) (0.002) (0.001) (0.081) Canada 0.017*** 0.006*** 0.000 0.028*** (0.004) (0.002) (0.001) (0.008) Netherlands 0.010*** 0.002** 0.009** (0.001) (0.001) (0.005) ROW 0.004*** 0.009*** (0.001) (0.003) Notes: Asterisks (*, **, ***) represent significant at the 10%, 5% and 1% level, respectively. ROW=rest of the world. PAGE 39 39 Table 2 5 Parameter estimation of import demand CBS model 1989 2012. ij ) Marginal Income Share ( i ) U S Mexico Canada Netherlands ROW U S 0.084*** 0.066*** 0.012*** 0.003*** 0.003*** 0.185* (0.018) (0.018) (0.002) (0.001) (0.001) (0.097) Mexico 0.067*** 0.003 0.003 0.002 0.174* (0.019) (0.003) (0.002) (0.001) (0.100) Canada 0.015*** 0.005*** 0.001 0.010 (0.004) (0.002) (0.001) (0.008) Netherlands 0.009*** 0.002** 0.004 (0.001) (0.001) (0.005) ROW 0.004 *** 0.003 (0.001) (0.003) Notes: Asterisk s (*, **, ***) represent significant at the 10%, 5% and 1% level, respectively. ROW=rest of the world. PAGE 40 40 Table 2 6 Parameter estimation of import demand AIDS m odel, 1989 2012. Slutsky Price Coefficients ( ij ) Marginal Income Share ( i ) U S Mexico Canada Netherlands ROW U S 0.128*** 0.109*** 0.015*** 0.004*** 0.000 0.189** (0.017) (0.017) (0.003) (0.001) (0.001) (0.090) Mexico 0.118*** 0.006** 0.001 0.002 0.160* (0.017) (0.003) (0.002) (0.001) (0.090) Canada 0.011*** 0.007*** 0.0 02* 0.020** (0.004) (0.001) (0.001) (0.008) Netherlands 0.002 0.000 0.008** (0.001) (0.001) (0.004) ROW 0.000 0.001 (0.001) (0.003) Notes: Asterisks (*, **, ***) represent significant at the 10%, 5% and 1% level, respective ly. ROW=rest of the world. PAGE 41 41 Table 2 7 Parameter estimation of import demand NBR m odel, 1989 2012. Slutsky Price Coefficients ( ij ) Marginal Income Share i ) U S Mexico Canada Netherlands ROW U S 0.124*** 0.105*** 0.015*** 0.003*** 0.000 0. 753*** (0.016) (0.016) (0.004) (0.001) (0.001) (0.076) Mexico 0.111*** 0.003 0.001 0.001 0.219*** (0.017) (0.004) (0.002) (0.001) (0.072) Canada 0.009** 0.007* 0.002 0.018* (0.004) (0.002) (0.001) (0.010) Netherlands 0.003** 0.001 0. 005 (0.001) (0.001) (0.004) ROW 0.000 0.005* (0.001) (0.003) Notes: Asterisks (*, **, ***) represent significant at the 10%, 5% and 1% level, respectively. ROW=rest of the world. PAGE 42 42 Table 2 8 Conditional ex penditure and Slutsky price e lasticities of import demand, synthetic model, 1989 2012. U.S. Mexico Canada Netherlands ROW Expenditure Elasticity U.S. 0.16*** 0.12*** 0.03*** 0.01*** 0.01*** 1.32*** (0.03) (0.03) (0.004) (0.002) (0.002) (0.15) Mexico 0.21*** 0.24*** 0.02* 0.01 0.005 0.56** (0.05) (0.05) (0.009) (0.005) (0.003) (0.26) Canada 0.23*** 0.07* 0.41*** 0.09*** 0.02 0.55*** (0.03) (0.04) (0.06) (0.02) (0.02) (0.13) Netherlands 0.25*** 0.21** 0.42*** 0.80*** 0.08* 0.58** (0.07) (0.11) (0.10) (0.10) (0.05) (0 .28) ROW 0.48*** 0.21 0.18 0.18* 0.05 1.16*** (0.15) (0.15) (0.16) (0.11) (0.13) (0.40) Notes: Asterisks (*, **, ***) represent significant at the 10% 5% and 1% level, respectively. ROW=rest of the world. PAGE 43 43 Table 2 9 Conditional ex penditure and Sl utsky price elasticities of import demand Rotterdam model, 1989 2012. U.S. Mexico Canada Netherlands ROW Expenditure Elasticity U.S. 0.15*** 0.12*** 0.02*** 0.01*** 0.01*** 1.30*** (0.03) (0.03) (0.00) (0.00) (0.00) (0.14) Mexico 0.21*** 0.23*** 0.00 0.01 0.01* 0.62** (0.05) (0.05) (0.01) (0.01) (0.00) (0.24) Canada 0.16*** 0.00 0.24*** 0.08*** 0.00 0.39*** (0.03) (0.04) (0.05) (0.02) (0.02) (0.11) Netherlands 0.21*** 0.18 0.36*** 0.63*** 0.11** 0.60** (0.07) (0.12) (0.10) (0.09) (0.05) (0.29) ROW 0.47*** 0.28* 0.04 0.25** 0.55*** 1.25*** (0.16) (0.16) (0.16) (0.11) (0.13) (0.42) Notes: Asterisks (*, **, ***) represent significant at the 10% 5% and 1% level, respectively. ROW=rest of the world. PAGE 44 44 Table 2 10 Conditional expe nditu re and Slutsky price elasticities of import demand CBS model, 1989 2012. U.S. Mexico Canada Netherlands ROW Expenditure Elasticity U.S. 0.15*** 0.11*** 0.02*** 0.01*** 0.01*** 1.32*** (0.03) (0.03) (0.00) (0.00) (0.00) (0.17) Mexico 0.20*** 0.20* ** 0.01 0.01 0.01 0.47 (0.05) (0.06) (0.01) (0.01) (0.00) (0.30) Canada 0.17*** 0.04 0.22*** 0.08*** 0.01 0.86*** (0.03) (0.05) (0.06) (0.02) (0.02) (0.11) Netherlands 0.18*** 0.16 0.34*** 0.57*** 0.11** 0.77** (0.07) (0.11) (0.10) (0.09) (0.0 5) (0.31) ROW 0.44*** 0.24 0.11 0.25** 0.54*** 1.49*** (0.16) (0.15) (0.16) (0.11) (0.12) (0.38) Notes: Asterisks (*, **, ***) represent significant at the 10% 5% and 1% level, respectively. ROW=rest of the world. PAGE 45 45 Table 2 11 Conditional expenditu re and Slutsky price elasticities of import demand AIDS model, 1989 2012. U.S. Mexico Canada Netherlands ROW Expenditure Elasticity U.S. 0.20*** 0.14*** 0.05*** 0.01*** 0.01*** 1.33*** (0.03) (0.03) (0.01) (0.00) (0.00) (0.16) Mexico 0.25*** 0.31 *** 0.05*** 0.01** 0.00 0.52* (0.05) (0.05) (0.01) (0.00) (0.00) (0.27) Canada 0.37*** 0.25*** 0.78*** 0.12*** 0.04** 0.72*** (0.04) (0.04) (0.05) (0.02) (0.02) (0.11) Netherlands 0.33*** 0.25** 0.53*** 1.08*** 0.02 0.50** (0.07) (0.10) (0.09) ( 0.07) (0.04) (0.25) ROW 0.52*** 0.07 0.41** 0.05 0.95*** 0.85** (0.13) (0.17) (0.18) (0.09) (0.10) (0.37) Notes: Asterisks (*, **, ***) represent significant at the 10% 5% and 1% level, respectively. ROW=rest of the world. PAGE 46 46 Table 2 12 Conditional expenditure and Slutsky price elasticities of import demand NBR model, 1989 2012. U.S. Mexico Canada Netherlands ROW Expenditure Elasticity U.S. 0.21*** 0.15*** 0.05*** 0.01*** 0.01*** 1.31*** (0.03) (0.03) (0.01) (0.00) (0.00) (0.13) Mexico 0.26* ** 0.33*** 0.06*** 0.01** 0.00 0.66*** (0.05) (0.05) (0.01) (0.01) (0.00) (0.22) Canada 0.36*** 0.29*** 0.81*** 0.12*** 0.03* 0.25* (0.05) (0.05) (0.06) (0.02) (0.02) (0.14) Netherlands 0.36*** 0.26** 0.54*** 1.15*** 0.02 0.33 (0.07) (0.11) (0. 11) (0.07) (0.04) (0.27) ROW 0.56*** 0.12 0.34* 0.06 0.97*** 0.63* (0.13) (0.17) (0.18) (0.09) (0.10) (0.38) Notes: Asterisks (*, **, ***) represent significant at the 10% 5% and 1% level, respectively. ROW=rest of the world. PAGE 47 47 Table 2 13 The log likelihood ratio tests for homogeneity and symmetry a Log likelihoods R ) U )] 2 (0.05) T 2 (0.05) Rotterdam Unrestricted Model (35) 923.73 Homogeneity (30) 918.24 10.98 11.07 23.16 Homogeneity + Symmetry (20) 913.94 8.60 18.31 CBS Unrestricted Model (35) 915.10 Homogeneity (30) 908.90 12.40 11.0 7 23.16 Homogeneity + Symmetry (20) 904.38 14.96 18.31 AIDS Unrestricted Model (35) 890.61 Homogeneity (30) 878.10 25.02 11.07 23.16 Homogeneity + Symmetry (20) 874.92 6.36 18.31 NBR Unrestricted Model (35) 887.18 Homogeneity (30) 8 76.20 21.96 11.07 23.16 Homogeneity + Symmetry (20) 872.80 6.80 18.31 Notes: a Number of parameters estimated is given in parenthesis. PAGE 48 48 Table 2 14 Test re sults for the log likelihood ratio tests a Log likelihoods R ) U )] 2 (0.05) Synthetic Model (22) 914.18 Rotterdam (20) 913.94 0.46 b 5.99 CBS (20) 904.38 19.60 b 5.99 AIDS (20) 874.92 78.52 b 5.99 NBR (20) 872.80 82.76 b 5.99 Notes: a Number of parameters estimated is given in parenthesis. b LR values of tested model against synthetic model, homogeneity and symmetry imposed on both. PAGE 49 4 9 Table 2 15 Parameter estimation of disaggregated import demand, synthetic model 2004 2012. Slutsky Price Coefficients (e ij ) Marginal Income Share (d i ) U.S. Fie ld grown U.S. Greenhouse U.S. Others Mexico Field grown Mexico Greenhouse ROW 1 2 U.S. Field grown 0.081*** 0.005 0.007 0.049*** 0.028*** 0.007* 0.372*** 0.037 0.056 (0.021) (0.013) (0.007) (0.014) (0.010) (0.03) (0.129) (0.205) (0.084) U.S. Greenhouse 0.035 0.006 0.011 0.033* 0.010 0.128** (0.022) (0.010) (0.012) (0.019) (0.009) (0.050) U.S. Others 0.027** 0.015** 0.017** 0.007 0.144*** (0.010) (0.006) (0.008) (0.006) (0.049) Mexico Field grown 0.029 0.036*** 0.012** 0.128 (0.022) (0.011) (0.006) (0.099) Mexico Greenhouse 0.042** 0.017** 0.248*** (0.017) (0.008) (0.054) ROW 0.019 0.018 (0.009) (0.025) Notes: Asterisks (*, **, ***) represent significant at the 10%, 5% and 1% level, respectively. cherry and grape tomatoes. PAGE 50 50 Table 2 16. Parameter estimation of disaggregated import demand Rotterdam mo del, 2004 2012. ij ) Marginal Income Share i ) U.S. Field grown U.S. Greenhouse U.S. Others Mexico Field grown M exico Greenhouse ROW U.S. Field grown 0.092*** 0.006 0.005 0.053*** 0.030*** 0.008* 0.361*** (0.014) (0.013) (0.006) (0.012) (0.009) (0.004) (0.091) U.S. Greenhouse 0.030 0.005 0.010 0.032* 0.010 0.124** (0.022) (0.010) (0.011) (0.019) (0.009 ) (0.049) U.S. Others 0.032*** 0.016*** 0.018** 0.007 0.141*** (0.008) (0.005) (0.008) (0.006) (0.036) Mexico Field grown 0.039*** 0.033*** 0.013** 0.122 (0.016) (0.011) (0.006) (0.102) Mexico Greenhouse 0.035** 0.017** 0.240*** (0.016) (0.008) (0.048) ROW 0.021** 0.012 (0.009) (0.017) Notes: Asterisks (*, **, ***) represent significant at the 10%, 5% and 1% level, respectively. PAGE 51 51 Table 2 17. Parameter estimation of disaggregated import demand CBS m odel, 2004 2012. ij ) Marginal Income Share ( i ) U.S. Field grown U.S. Greenhouse U.S. Others Mexico Field grown Mexico Greenhouse ROW U.S. Field grown 0.091*** 0.006 0.005 0.052*** 0.031*** 0.007 0.041 (0.014) (0.013) (0.006) (0.013) ( 0.009) (0.005) (0.104) U.S. Greenhouse 0.028 0.003 0.010 0.031* 0.010 0.032 (0.022) (0.010) (0.011) (0.018) (0.010) (0.050) U.S. Others 0.033*** 0.017*** 0.017** 0.006 0.030 (0.008) (0.006) (0.008) (0.006) (0.038) Mexico Field grown 0. 042*** 0.030*** 0.014** 0.093 (0.016) (0.010) (0.006) (0.113) Mexico Greenhouse 0.024 0.011 0.077 (0.015) (0.009) (0.045) ROW 0.025** 0.087 *** (0.010) (0.022) Notes: Asterisks (*, **, ***) represent significant at the 10%, 5% and 1% level, respectively. PAGE 52 52 Table 2 18. Parameter estimation of disaggregated import demand AIDS m odel, 2004 2012. Slutsky Price Coefficients ( ij ) Marginal I ncome Share ( i ) U.S. Field grown U.S. Greenhouse U.S. Others Mexico Field grown Mexico Greenhouse ROW U.S. Field grown 0.110*** 0.025** 0.038*** 0.022 0.017** 0.008 0.037 (0.016) (0.012) (0.006) (0.013) (0.009) (0.006) (0.100) U.S. Greenhouse 0.107*** 0.008 0.031*** 0.051*** 0.007 0.040 (0.021) (0.012) (0.011) (0.017) (0.010) (0.051) U.S. Others 0.052*** 0.006 0.012 0.012* 0.014 (0.010) (0.006) (0.009) (0.007) (0.037) Mexico Field grown 0.130*** 0.069*** 0.001 0.117 (0.018) (0.012) (0.007) (0.106) Mexico Greenhouse 0.130*** 0.005 0.109** (0.016) (0.009) (0.045) ROW 0.020* 0.082*** (0.011) (0.025) Notes: Asterisks (*, **, ***) represent significant at the 10%, 5% and 1% level, respectiv ely. PAGE 53 53 Table 2 19. Parameter estimation of disaggregated import demand NBR m odel, 2004 2012. Slutsky Price Coefficients ( ij ) Marginal Income Share i ) U.S. Field grown U.S. Greenhouse U.S. Others Mexico Field grown Mexico Greenhouse ROW U.S. Field grown 0.107*** 0.025** 0.038*** 0.020 0.018* 0.006 0.346*** (0.015) (0.012) (0.006) (0.013) (0.010) (0.006) (0.091) U.S. Greenhouse 0.110*** 0.011 0.030*** 0.052 *** 0.008 0.128** (0.021) (0.012) (0.011) (0.018) (0.010) (0.051) U.S. Others 0.054*** 0.008 0.011 0.008 0.124*** (0.009) (0.006) (0.009) (0.007) (0.036) Mexico Field grown 0.134*** 0.072*** 0.004 0.095 (0.018) (0.013) (0.006) (0.099 ) Mexico Greenhouse 0.146*** 0.014 0.269*** (0.017) (0.009) (0.057) ROW 0.024** 0.038** (0.010) (0.023) Notes: Asterisks (*, **, ***) represent significant at the 10%, 5% and 1% level, respectively. S. PAGE 54 54 Table 2 20. Conditional expe nditure and Slutsky price elasticities of disaggregated import demand, synthetic model 2004 2012. U.S. Field grown U.S. Greenhouse U.S. Others Mexico Field grown Mexico Greenhouse ROW Expenditure Elasticity U.S. Field grown 0.30*** 0.02** 0.02* 0.17*** 0.10*** 0.03*** 1.16*** (0.06) (0.01) (0.01) (0.02) (0.01) (0.01) (0.21) U.S. Greenhouse 0.07** 0.32 0.05 0.10 0.34* 0.11 1.31** (0.03) (0.23) (0.10) (0.12) (0. 20) (0.17) (0.52) U.S. Others 0.05* 0.05 0.29*** 0.15*** 0.17** 0.07 1.28*** (0.03) (0.09) (0.07) (0.05) (0.08) (0.09) (0.33) Mexico Field grown 0.24*** 0.04 0.07*** 0.17** 0.15*** 0.06 0.54 (0.03) (0.05) (0.02) (0.07) (0.05) (0.06) (0.46) Mex ico Greenhouse 0.19*** 0.21* 0.12** 0.21*** 0.22** 0.11 1.54*** (0.03) (0.12) (0.05) (0.07) (0.11) (0.09) (0.31) ROW 0.08*** 0.10 0.07 0.13 0.16 0.13 0.13 (0.03) (0.15) (0.09) (0.13) (0.13) (0.29) (1.23) Notes: Asterisks (*, **, ***) represent significant at the 10%, 5% and 1% level, respectively. PAGE 55 55 Table 2 21. Conditional ex penditure and Slutsky price elasticities of disaggregated import demand Rotterdam mo del, 2 004 2012. U.S. Field grown U.S. Greenhouse U.S. Others Mexico Field grown Mexico Greenhouse ROW Expenditure Elasticity U.S. Field grown 0.30*** 0.02 0.02 0.17*** 0.10*** 0.03* 1.16*** (0.05) (0.04) (0.02) (0.04) (0.03) (0.01) (0.29 ) U.S. Greenhou se 0.07 0.32 0.05 0.10 0.34* 0.11 1.31** (0.14) (0.23) (0.10) (0.12) (0.20) (0.09) (0.52 ) U.S. Others 0.05 0.05 0.29*** 0.15*** 0.16** 0.07 1.29*** (0.06) (0.09) (0.07) (0.05) (0.07) (0.05) (0.33 ) Mexico Field grown 0.24*** 0.04 0.07*** 0.17* 0.15*** 0.06** 0.55 (0.05) (0.05) (0.02) (0.07) (0.05) (0.02) (0.46 ) Mexico Greenhouse 0.19*** 0.21* 0.11** 0.21*** 0.22** 0.11** 1.53*** (0.06) (0.12) (0.05) (0.07) (0.10) (0.05) (0.31) ROW 0.07* 0.10 0.07 0.12** 0.16** 0.20** 0.12 (0.04) (0.08) (0.05) (0.05) (0.08) (0.08) (0.16 ) Notes: Asterisks (*, **, ***) represent significant at the 10%, 5% and 1% level, respectively. PAGE 56 56 Table 2 22. Conditional expendit u re and Slutsky price elasticities of disaggregated import demand CBS mo del, 2004 2012. U.S. Field grown U.S. Greenhouse U.S. Others Mexico Field grown Mexico Greenhouse ROW Expenditure Elasticity U.S. Field grown 0.29*** 0.02 0.02 0.17*** 0.10*** 0 .02 1.13*** (0.05) (0.04) (0.02) (0.04) (0.03) (0.02) (0.34) U.S. Greenhouse 0.06 0.30 0.03 0.11 0.33* 0.11 1.34** (0.13) (0.23) (0.11) (0.12) (0.19) (0.10) (0.52) U.S. Others 0.04 0.03 0.30*** 0.16*** 0.16** 0.05 1.27*** (0.06) (0.09) (0.07) (0.05) (0.07) (0.06) (0.34) Mexico Field grown 0.23*** 0.05 0.08*** 0.19*** 0.14*** 0.06** 0.58 (0.06) (0.05) (0.02) (0.07) (0.04) (0.03) (0.51) Mexico Greenhouse 0.20*** 0.20* 0.11** 0.19*** 0.16 0.07 1.49*** (0.06) (0.12) (0.05) (0.06) (0.10 ) (0.06) (0.29) ROW 0.07 0.10 0.05 0.13** 0.11 0.24** 0.17 (0.04) (0.09) (0.06) (0.06) (0.08) (0.09) (0.21) Notes: Asterisks (*, **, ***) represent significant at the 10%, 5% and 1% level, respectively. lum, cherry and grape tomatoes. PAGE 57 57 Table 2 23. Conditional expenditure and Slutsky price elasticities of disaggregated import demand AIDS m odel, 2004 2012. U.S. Field grown U.S. Greenhouse U.S. Others Mexico Field grown Mexico Greenhouse ROW Expendi ture Elasticity U.S. Field grown 0.34*** 0.02 0.01 0.15*** 0.10*** 0.08*** 1.12*** (0.05) (0.04) (0.02) (0.04) (0.03) (0.02) (0.32) U.S. Greenhouse 0.05 0.23 0.02 0.10 0.38** 0.18* 1.42*** (0.12) (0.22) (0.13) (0.12) (0.18) (0.11) (0.54) U.S. Ot hers 0.03 0.02 0.41*** 0.17*** 0.26*** 0.01 1.13*** (0.06) (0.11) (0.09) (0.05) (0.08) (0.06) (0.34) Mexico Field grown 0.21*** 0.04 0.08*** 0.19** 0.21*** 0.10*** 0.48** (0.06) (0.05) (0.03) (0.08) (0.04) (0.03) (0.47) Mexico Greenhouse 0.20*** 0.23** 0.18*** 0.22*** 0.02 0.07 1.69*** (0.06) (0.11) (0.06) (0.08) (0.10) (0.06) (0.29) ROW 0.23*** 0.16* 0.01 0.21*** 0.11 0.72*** 0.22 (0.06) (0.10) (0.07) (0.06) (0.09) (0.07) (0.24) Notes: Asterisks (*, **, ***) represent significant at t he 10%, 5% and 1% level, respectively. PAGE 58 58 Table 2 24. Conditional expenditure and Slutsky price elasticities of disaggregated import demand, NBR model, 2004 2012. U.S. Fie ld grown U.S. Greenhouse U.S. Others Mexico Field grown Mexico Greenhouse ROW Expenditure Elasticity U.S. Field grown 0.34*** 0.02 0.01 0.16*** 0.10*** 0.09*** 1.11*** (0.05) (0.04) (0.02) (0.04) (0.03) (0.02) (0.29) U.S. Greenhouse 0.05 0.25 0.01 0.09 0.39** 0.19* 1.35** (0.12) (0.22) (0.12) (0.12) (0.19) (0.11) (0.54) U.S. Others 0.04 0.01 0.40*** 0.15*** 0.26*** 0.04 1.14*** (0.06) (0.11) (0.08) (0.05) (0.08) (0.06) (0.33) Mexico Field grown 0.22*** 0.04 0.07*** 0.17** 0.21*** 0.09*** 0.42 (0.06) (0.05) (0.02) (0.08) (0.04) (0.03) (0.44) Mexico Greenhouse 0.19*** 0.23** 0.18*** 0.24*** 0.09 0.01 1.71 (0.06) (0.11) (0.06) (0.09) (0.11) (0.06) (0.36) ROW 0.25*** 0.17* 0.04 0.19*** 0.02 0.69*** 0.36 (0.06) (0.10) (0.07) (0.06) (0.09) (0.07) (0.22) Notes: Asterisks (*, **, ***) represent significant at the 10%, 5% and 1% level, respectively. PAGE 59 59 Source: Adopted from USDA ERS North American Fresh Tom ato Market Report (USDA ERS 2013a) Figure 2 1. Field grown and protected culture fresh market tomato shipments by month Source: Calculated by Authors from Fresh Tomato Shipments (USDA AMS 2013) Figure 2 2. U.S. share of winter (December April) a nd total tomato expenditure in the last 5 years, 2007 2012 PAGE 60 60 CHAPTER 3 THE POTENTIAL FOR GREENHOUSE TOMATO PRODUCTION EXPANSION IN FLORIDA Introduct ory Remarks Among all the vegetable crops in the U.S., the total value of production is the highest for toma to production (USDA ERS 2013a). T omato demand in the U.S. is high during all 12 months of the year (USDA ERS 2013b). During the summer season most of U.S. states, Mexico and Canada produce tomatoes so the supply is high and prices are relatively low. Howev er, the dynamics are different during the winter season since the main tomato suppliers are the state of Florida and Mexico only Florida produces field grown tomatoes, while Mexico ships more greenhouse tomatoes every year to the U.S. Figure 3 1 shows the disaggregation of tomato import s from Mexico by field grown and greenhouse tomatoes. The composition of Mexican imports has been significantly enhanced by greenhouse production and it has been observe d that the increase in Mexican tomato imports is associ ated with the increase in greenhouse tomato import s specifically Due to the demand for high quality tomato by U.S. consumers and the reference price applied on Mexican tomato import (US DC, 2013) Mexican producers are increasingly able to offer greenhous e tomatoes with higher quality and lower prices than the Florida field grown winter tomatoes. Additionally, Mexico greenhouse production acreage increased to 30,000 acres in 2012 and 70% of th is acreage is devoted to tomato production (SAGARPA 2013). Tomat o production in Florida has fallen from 55,000 acres in 1990 to 30,000 acres in 2012 (USDA ERS 2013b). Overall, competition with Mexican producers affects the profits of Florida tomato producers that have traditionally benefited from high er prices in the w inter market. Figure 3 2 demonstrates PAGE 61 61 the last 10 years of domestic a nd import tomatoes in the U.S. m arket. D omestic fresh tomatoes supply went down 25% from the peak level in 2005. The supply of fresh tomatoes imported from Mexico almost doubled in the la st ten years surpassing US domestic tomatoes in the last two years. The increase in Mexican tomato imports created a trade conflict with the U.S. fresh winter tomato industry The international competition has been an issue in the industry since the early 1970s. Given that tomato es are the highest valued fresh vegetable crop the U.S. fresh tomato market is favored by importers and domestic producer s alike While importers try to increase their shares with low prices, domestic producers attempt to keep the ir share in the tomato market without any costly investment in production practices. However, the competition with Mexican greenhouse tomato producers push ed winter tomato producers (particularly, in Florida) to search for new investment opportunities like greenhouse tomato production. There are advantages and disadvantages to greenhouse production. For instance, the controlled environment of greenhouse production gives high and stable yields. It also enables farmers to perfect crop timing and to supply win ter markets when fresh market prices are at a premium On the other hand, the disadvantages are high initial investment cost s high operating cost s and energy intensive production practices This paper aims to incorporate risk into the net present value and real option analysis to investigate whether it is beneficial for Florida tomato producers to invest in greenhouse production methods. Feasibility of the greenhouse investment opportunities rent revenue and cost structure s of tomato production technologies Therefore, the study also investigate s PAGE 62 62 whether the investment in greenhouse technology can allow Florida producers to increase their per unit revenue or reduce the ir production costs and to keep their market share. Tomato Production in the US Fresh tomatoes are harvested in California during all seasons except winter, while in Florida tomatoes are harvested from October to June with peak production from November to January. Most of Florida Mexico provides fresh tomatoes for the western part of U.S. (VanSickle et al. 2003). Overall, almost one third of the total U.S. fresh tomato consumption is imported from Mexico and Canada during the off s eason period, and around 40% of Mexican and the large majority of Canadian tomatoes are produced in greenhouses (USDA FAS 2012). Other countries like the Netherlands and Spain also export greenhouse tomatoes to the U.S. in smaller quantities. In the last decade, U.S. greenhouse tomato production increased two fold (from 2.7 million cwt in 2000 to 5.4 million cwt in 2011), although its share in the total fresh tomato market is still relatively low at approximately 15 percent ( Figure 3 3). However, for the r etail market specifically, more than 40% of domestic tomatoes are produced using greenhouse technologies (USDA ERS 2013b). California and Arizona have become the key states for greenhouse production since the competition with Mexican greenhouse tomato prod ucers drove them to switch into their niche market during the winter season when the tomato price is at peak level. Florida supplies tomatoes largely for the winter market while California field grown production supplies in spring and summer. Florida produ cers get higher prices for their product because they produce in the off season, when lower winter supplies result PAGE 63 63 in higher prices. The average price of fresh tomatoes was $72.50 per cwt in 2010 in Florida, while the average price in California was $33.10 per cwt (USDA ERS, 2012b). However, fresh tomato prices are known to be sensitive to the instabilities of supply that Mexican greenhouse production has anywhere between three fold and twenty fold more yield (on per acre basis) than Florida field production. Although greenhouse production cost is high, it is competitive in revenue and the quality can be better than that of field grown tomatoes. Hence, imported greenhouse tomatoes have m ore opportunities to increase their market share in the U.S. (Cantliffe and VanSickle 2009). Overall, the increased interest in greenhouse tomato production in Southwestern states, as well as increasing competition from imported Mexican greenhouse tomatoe s can subsequently decrease winter tomato prices, and hence the profits of Florida producers. As mentioned above investment and operating costs for greenhouse tomato production are higher than those of field production, and as a result, greenhouse produc tion is often perceived by Florida producers as more risky (Cook and Calvin 2005). The main risk parameters for tomato production could be identified as market, yield, price and cost risks ( Table 3 1). The source of market risk is the perception of produ cts. For instance, greenhouse tomatoes might be perceived as a different product than field grown tomatoes influencing the demand and supply relationships. This type of risk is not considered in this study (see chapter 2 for the discussion about the consu mer perception) Controlled atmosphere almost eliminate s the yield risk in greenhouse production whereas yield risk is high for field grown production An industry survey indicates that PAGE 64 64 tomato es yield varies from 20 to 32 lbs (9 14.5 kg) per plant space p er year in the regular greenhouses while yield can range from 46 to 50 lbs (21 23 kg) per plant space under the best greenhouse technology (Pena 2005). Furthermore, a field grown trial showed that per plant tomato yield generally ranges from 6 to 15 lbs ( 3 7 kg) per plant space in Florida (UF IFAS, 2013). The source of price risk is the supply and demand relationship. Stabilized greenhouse production ( i.e. the ability to target harvesting time to the periods when the prices are high) reduces this price risk Moreover, low price d imported tomatoes increase price risk for domestic greenhouse and field grown producers. Finally, c ost risk comes from inputs, energy and labor expenses H igh operating cost s and energy intensive production process es increase the cha nces of negative profits for greenhouse production although there are some technological improvements to reduce this risk. However, cost risk is relatively low in field grown production. Nevertheless, the investment in greenhouse production systems may be a viable option for growers in Florida, since this technology results in much greater yields, higher quality products, and a more stable market demand and/or prices than the current field grown production technology. Literature Revie w : Risk in Investment D ecision Making To explore investment decisions made by growers, the risk based model is widely used by academics and business consultants. In this study, a comprehensive investment decision model is developed, and then a simulation approach for including r isk is employ ed to examine the decision to invest in the greenhouse production systems in Florida. Below, existing studies are reviewed focus ing on (a) agricultural PAGE 65 65 decision making under risk and uncertainty, and (b) application of simulation methods for r isk based analysis and (c) real option value for invest ing in a new technology. There are numerous empirical studies of risk and agricultural decision making. The risk analysis methodologies proposed in the studies can be summarized chronologically as fol lows. I nitially, risk programming was applied by Hazell (1971) to risk attitudes; further, an empirical analysis o f effective educational programs to facilitate risky decision making was provided by Nelson and Harris (1978). Then, Young (1984) improved the methods of measuring risk. More general efficiency criteria for ordering risky choices were introduced by King and Robison (1981), and stochastic simulation was propo sed by Mapp and Helmers (1984). More applications of risk analysis in production, marketing, and finance are also published by various researchers (Robison and Brake 1979; Sonka and Patrick 1984). Collins and Barry (1986) evaluated two approaches for usin g a single index model in portfolio analysis for agricultural firms. The single index model offers a summary measure of risk for individual assets or enterprises that accounts for the combined effects of the asset's own variance, as well as covariance with other assets. When used in portfolio analysis to derive risk efficient sets of decision choices, the single index model offers a computationally efficient way to use quadratic programming that accounts for a full constraint set and for the covariance rela tionships among the decision choices. Williams et al. (1990) examined risk based decisions in the context of stochastic dominance between two tillage systems, conventional tillage and no tillage, for five crop PAGE 66 66 rotations, wheat fallow, grain sorghum fallow continuous wheat, continuous grain sorghum, and wheat grain sorghum fallow. Their results showed that risk averse managers prefer a conventional tillage wheat sorghum fallow system. Simulation is a widely covered subject; however, most of the existing st udies are not written for agricultural economists and do not relate to agricultural firm level models. Simulation as a tool for analyzing risky decisions was suggested by Anderson et al. (1977). The various types of equations and identities used to constru ct the Farm Level Income and Policy Simulation Model in these studies described in Richardson and Nixon (1986; 1999); however, the methods for simulating the random variables were not discussed. Risk analysis for adopting any of four commonly used zero r unoff sub irrigation systems in greenhouse operations was described on different crop categories by Uva et al. (2000) with a Monte Carlo simulation approach. Richardson et al. (2000) developed a procedure for estimating and simulating probability distribut ions in farm level risk assessment and clearly describe the procedure on how to analyze risk by this method. Iwai and Emerson (2008) combin ed risk analysis with a Monte Carlo simulation by calculating NPV and the real options price to assess sugarcane mech anization investment in Florida. In lieu of previous studies, the goal of this paper is to examine agricultural decision making under risk and uncertainty, and to apply simulation methods for risk based analysis on greenhouse tomato investment decisions in Florida. Data and Model s The financial models to analyze tomato production in Florida are built on three different production budget s The first budget set is called the patriot model based on high technology greenhouse tomato production system (Greenhous e HT) which has PAGE 67 67 higher cost but in turn higher yield than the typical Florida greenhouse production (VanSickle, 2011). The second set is for the typical greenhouse tomato production in Florida (Greenhouse FL) ; this set relies on the enterprise budget infor mation from the 2006). T his budget was updated as of 2013 by UF extension agents. The last budget contains the field grown tomato production budget provided as inter active budget tables for Florida field grown tomato by University of Florida, Food and Resource Economics Department (UF FRED 2013). T he first two sets use different greenhouse sizes (patriot model is based on 120,000 sq uare m eters (29.7 acres) greenhouse area and the For this analysis, a ll the budget sets are adjusted to a one acre basis to make a relevant comparisons between field grown and greenhouse production systems The budget data are ins erted into pro forma financial statements, namely the income statement, cash flow statement and balance sheet, for each production technology. The financial model is constructed in Excel add in Simetar, a simulation and risk analysis software (Richardson, Schumann and Feldman, 2008). The data include expected yield, expected unit price, variable cost, fixed cost, construction cost, and durables expense. The i nitial equity (IE) requirement for field grown production (fg) is assumed to be zero while it is se t to $35,000.00/acre for greenhouse production. The operations are assumed to be owned by 100% equity holder (i.e., by the producer) Working capital loans are provided for 90% of the annual varia ble production at an interest r ate of 5%. PAGE 68 68 It is further assu med that 80% of the equipment and durables costs for greenhouse tomato production are funded with a seven year loan at 8% interest. The r ate of return to investment is assumed to be 10%, which is used as a discount rate for the Net Present Value (NPV) ana lysis. Financial model assumptions are presented in Table 3 2, and the budget summaries in Table 3 3. Table 3 3 indicates that greenhouse production requires approximately from 15 to 30 times more start up cash than the field production. The largest expens e for greenhouse production is growing cost since the high yield requires high seedlings and chemicals expenses. Labor cost for Florida greenhouse production accounts for the big portion of total expense. It is observe d that the higher yield in greenhouse production leads to lower per unit sales costs, as compared with the field grown production. The budget summaries reveal that greenhouse production is an energy intense technology because energy cost accounts for a significant portion of the total producti on cost. Table 3 4 presents the net income statements (NIs) of all three tomato production technologies for 2014. Revenue is found by multiplying production volume and product price at the expected level when the simulated variables are non stochastic We find that the break ev en production points are 22 lbs per plant ( or 26 kg per square meter assuming 10,650 plants per acre ) and 38 lbs per plant ( or 52 kg per square meter assuming 12,141 plants per acre ) for Florida greenhouse (fl) and high tech greenho use (ht) respectively. Therefore, these levels are used for the rest of the analysis. The tax rate on earnings before tax (EBT) is taken as 25% based on the average tax rate of agricultural production firms as calculated from corporate tax data PAGE 69 69 for the l ast ten years (IRS 2012). S traight line depreciation is applied for all equipment. Gross profit, earnings before tax (EBT) and net income are computed as follows: Gross Profit = Revenue Cost (3 1) EBT = Gross Profit Depreciation Administrati on Cost Interest (3 2) Net Income = EBT Tax (3 3) The n et present value (NPV) framework is commonly used to evaluate agricultural investment. In this analysis, expected present values (PV) of NI are calculated for the span of ten years and disc ounted to the starting period NPV was obtained by subtracting the initial investment amount from the present value of the enterprise. (3 4) where start up equity value is added manually t o prevent firms from running out of cash during the financial year PV is the present value at the time t for ten years of analysis, terminal value is the value of the firm at the end of ten years, and r is the after tax discount rate. Simulation model The objective of this study is to incorporat e yield, price and cost risks in the NPV analysis This objective is achieved by simulating the risk parameters for 10 years. A Monte Carlo simulation model of tomato production is based on the framework presented by Richardson, Lemmer and Outlaw (2007). R isk parameters are the correlated tomato yield and sale s price s used in t he financial statement analysis. Data were collected from USDA ERS annual field grown price and yield data from 1990 to 2012 for Florida and from USDA AMS monthly terminal point gree nhouse price s in the PAGE 70 70 eastern states from January 2004 to December 2012. Time series tomato price/yield data sets are used to assess price/yield correlation and volatility. Specifically, USDA ERS data are used to analyze the price/yield correlation of field grown methods ; the correlation is used in price simulations, which is then applied to all financial analysis. We assume no fluctuations in greenhouse tomato yield. Moreover, the USDA AMS data are used to calculate the premium received by greenhouse tomato es End user fuel prices are used for estimating the increase in the energy cost. The risk on cost is accounted for in the model by using the fuel/liquid petroleum gas and electricity price relationship. The gas and electricity price s data are collected fr om 1990 to 2011 (US EIA 2013). The price change in the simulated prices is inserted as the stochastic growth rate for annual fuel and electricity expenses, which is used to generate the stochastic energy cost. All simulated stochastic components are iterat ed simultaneously in the model and the key components of the financial model are simulated 500 times for each production technology to estimate the probability density functions (PDF) and c umulative distribution functions (CDF). T he distribution of yield, revenue, cost and net present value s (NPV) are obtain ed ( Figure 3 4). The NPV distributions are ranked using Simetar software tools such as mean variance method, first and second degree stochastic dominance, stochastic dominance with respect to a function (SDRF) and stochastic efficiency with respect to a function (SERF) to incorporate risk aversion (Hardaker et al. 2004). The stochastic variables are selected as the tomato yield sale prices fuel/lpg gas price and electricity price. The multivariate emp irical (MVE) probability distribution is used for the simulation of these variables (Richardson, Klose and Gray 2000) where PAGE 71 71 yield and sale prices correlation and, gas and electricity price correlation are utilized The methodology of MVE is summarized belo w. Non random components are found as a function of linear trend: (3 5) Then, random components are calculated by the difference of actual and predicted values ( ) (3 6) Relative variability of observations is measured as a fraction of random components to predicted values. (3 7) After the relative variability is sorted for each observation, correlation matrix is calculated b y the probabilities of occurrence for the se variables The intra temporal correlation matrix for price and yield variables is found as follows: (3 8) Correlated standard normal deviates (CSND ik ) are found by us ing this correlation matrix and independent standard normal deviates (R ik ) for ten year simulation time span (with years indexed by k). Thus, the empirical distribution for each variable is estimated using correlated uniform deviates : (3 9) PAGE 72 72 At last, stochastic simulation ( ) is found by the multiplication of predicted values and the MVE distribution. The relative risk expansion in the model is given as ( ) which is selected as unity in this analysis (3 10) The stochastic variables, summarized in Table 3 5, are inserted into financial models for the iteration of NPV to evaluate the economic risk for the tomato investment decision. Ranking risky assets Mean variance method, first and second degree stochastic dominance, SDRF and SERF are used to rank the risky production technology alternatives. Mean variance method simply looks for less variance and high er mean for ranking the risky alternatives. First degree stochastic dominance compares CDFs of the NPVs for the risky alternatives. If CDFs of two alternatives are represented as F ( x ) and G ( x ) and F ( x ) dominates G ( x ) then for all x CDFs of the two alternatives compared sho uld not cross each other (Richardson and Outlaw 2008). If they cross, one could use second degree stochastic dominance for ranking the risky alternatives. Using this criterion, if F ( x ) dominates G ( x ) when we obtain for all x Finally SDRF is applied to incorporate known risk aversion coefficients (RAC) into ranking of risky alternatives. SDRF can be described as follows: (3 11) where F ( x ) is preferred to G ( x ) under given risk aversion coefficient ( r i ( x )) of the decision maker where i refers to the upper and lower limits of risk aversion coefficients PAGE 73 73 (Richardson and Outlaw 2008). At last, SERF examines the risk aversion for which the certainty equivalent (CE) is calculated to determine t he ranking of risky alternatives (Hardaker et al. 2004). (3 12) where U 1 j risky alternatives between upper and lower limits of risk aversion coefficients, respectively, represented as ( r U ( x )) and ( r L ( x )). Real option approach The NPV analysis has the following limitations : (1) only current information available at the time of the decision is used, (2) after the initial investment decision is made, the futur e decisions cannot be analyzed; and (3) just a single discount rate is used to calculate NPV (as opposed to allowing the rate to change over time). Hence, the analysis of NPV using criteria discussed above may be incomplete, and it may not be sufficient to explain why U.S. growers still do not switch to the greenhouse tomato production. The next step in this research is to use real options approach (ROA) to evaluate viability of greenhouse tomato production in Florida. ROA has several advantages. First, ROA allows including the future value of agricultural investment into current investment decision analysis Second ly ROA controls for the irreversibility of investment in analysis. Third ly ROA allows modeling dynamic decision making process while NPV models for the current decision Fo u rth, ROA allows for the flexibility of agricultural investment by including the non linear distribution of the cash flow or the eventual risk profile changes. The main difference in the concept of NPV and ROA could be shown as follows: PAGE 74 74 (3 13 ) (3 14 ) where represents the comparison of the possible values to choose the best among the possible alternatives (Copeland and Antikarov, 2003 ) ROA uses exp ectation of maximum values where the decision is made after the information is revealed (maximize at t = T ). In contrast, NPV assign the decision for today by looking at the maximum of the expectations (maximize at t = 0 ). Real option value is calculated by us ing the binomial decision tree procedure expressed by Copeland and Antikarov (2003) and follow ed Iwai and Emerson (2008). The details of the calculation and the assumptions are summarized in the result section. Results The non stochastic NPVs can be comput ed when all assumptions are substituted into the financial model at the mean values. Table 3 6 presents forecasted present firm values and net incomes for field grown and greenhouse tomato production for ten year period s We use equation (3 4) to separatel y calculate NPVs for each technology Table 3 7 suggests that high tech greenhouse production is the most feasible investment opportunity Florida greenhouse technology is the second best investment (given the assumptions made) T he NPV result s presented in Table 3 7 are not sufficient to explain the greenhouse investment decision given by Florida tomato producers. Therefore, NPV values are simulat ed using Monte Carlo method applied to the financial model in Simetar add in to Excel Simulations are completed for the stochastic components which represents the risk associated with the tomato production technologies considered (i.e., yield, sale prices, PAGE 75 75 gas price and electricity price) The simulation results are summarized in Table 3 8. standard deviation. Therefore, we cannot rank the investment decision by using the mean variance method only The cumulative distribution function (CDF) of NPV values for alternative production technologies are illustrated in Figure 3 5. CDFs cross each other and hence, the technologies cannot be ranked using the first order stochastic dominance criterion ( Table 3 9 and Figure 3 5 ). In turn, t he second order stochast ic dominance criterion Further, ld most preferred investment option, is the second best choice among the three technologies considered Risk aversion of the decision maker is taken into consideration when we rank the investment alternatives with stochastic dominance with respect to a function (SDRF) analysis. The first pr eferred set based on SDRF at the lower risk aversion coefficient (RAC=0) shows the ranking for a risk neutral producer ( Table 3 10 ) The ranking for risk followed by technologies, which is consistent with the second degree stochastic dominance result. However, the investment preference among the alternative options changes for the extremely risk averse producer. The absolute risk aver sion coefficient is calculated by a ( w ) = ( r ( w ) / w ) = ( 4 / 100,000 ) = 0.00004 where w represents wealth and the relative risk aversion coefficients are PAGE 76 76 classified from zero to four representing, respectively, from the risk neutral to the extremely risk a verse person (Richardson and Outlaw 2008) Thus, extremely risk averse decision maker s prefer field grown tomato production over both greenhouse technolog ies The SDRF results also show when the decision maker is extremely risk averse ( Table 3 10 ). To explain this result, one can search for the cases where enhouse all other alternatives with s tochastic efficiency with respect to a function (SERF) SERF provides us a broad overview of the risky alternatives over a range of absolute risk aversion coefficients (ARAC). Figure 3 6 illustrates the certainty equivalent of the alternative technologies aversion levels (i.e., from risk neutral to extremely risk averse) technology for the risk neutral and normally risk averse producer. In turn, preferred risky alternative for moderately risk averse producer, and finally, preferred by an extremely risk averse producer Finally binomial decision tree for field grown tomato production is illustrated in figure 3 7. Field grown tomato production is taken as a base production technique for Florida, and the investment option for greenhouse tomato is investigated. T he procedure described by Copeland and Anti karov (2003 ) is followed for the multiplicative stochastic process to calculate ROA. T he u ncertainty in field grown production is estimated by generating 500 sets of net income based on the simulating cost and PAGE 77 77 revenue terms. We obtain the volatility from t he standard deviation of the simulated annual rate of return defined as where PV 1 and NI 1 represent the net income and present value of field grown production, respectively, for 2014 season and PV 0 is the fixed present va lue at $16,855.19 for 2013 season. The mean ( z ) and the standard deviation ( z ) of the annual rate of return are found as 0.16 and 0.92, respectively. The standard deviation indicates the high volatility for the field grown production; therefore, we exp ect high option value to keep the option alive which incentivize growers to postpone the new investment (Dixit and Pindyck, 1994). The pres ent value for 2014 season ( $14,405 ) is the forecasted present value for the field grown technology (see table 3 6 ), and NPV for 2014 is calculated by adding net income ( $992 ) to the present value of the same year, yielding $15,397. The upper and lower values for 2015 are calculated by using the annual volatility of the field grown production, 0.92; therefore, NPV for 20 15 would either be $35,954 ( ) or $5,771 ( ) where dt =1. Then, we could find PVs for the 2015 season by discounting the calculated NPVs with the ratio calculated as This procedure is followe d for the all the years until we calculate all branches in the decision tree. As described in the Copeland and Antikarov (2003 ) we analyze the optimal execution of real options starting at the end of the tree when the option expires. We analyze two differ ent investment options for the field grown producer: (1) investment in Florida greenhouse; (2) investment in high tech greenhouse. The final nodes of the option calculation are chosen as the maximum of the three values from the present value of the final y ear, present value of high tech greenhouse in 2023 minus discounted PAGE 78 78 initial equity for 2023, and present value of Florida greenhouse in 2023 minus discounted initial equity for 2023 as For instance, the top node of the end of three is the maximum value of comparing present value $36,799,192 from binomial tree, the value given from Florida greenhouse as $308,825 $35,000/(1+0.3) 10 and the value given from Florida greenhouse as $558,720 $35,000/(1+0.3) 10 After we fill the values at t he end of the tree, the remaining nodes are calculated by replicating portfolio approach. Following Iwai and Emerson (2008), one can derive the equation for holding option value ( C t ) at time t as where q is the risk neutral probabili ty ( ), risk free rate of return is taken as 3% calculated from ten year Treasury bills and, C u and C d denote the up and down state of the option values, respectively. Next, we compare the holding option value with the investment opti ons as and repeat the procedure for the all the remaining nodes ( Figure 3 8). Finally, we compute NPV with option value as $421,240 and option value is simply calculated by subtracting NPV value from the NPV with option value which i s $421,240 $15,397 = $405,843. This option value indicates how much a farmer loses when the investment option is exercised. Table 3 11 summarizes the NPV results for each tomato production technologies with the option value. The results suggest that a f armer in field grown production still has a high option value to invest in greenhouse technology given assumed production information. The results explain why we may not see greenhouse investment in Florida yet PAGE 79 79 Discussion Florida tomato growers have los t market share in the last decade to the increasing Mexican greenhouse tomato imports Although Florida producers achieve d an agreement with Mexican producers for a fixed floor price for Mexican tomatoes in 1996, domestic tomato sales continue to decline i n the winter season The renegotiated antidumping investigation suspension agreement came into force in the summer of 2013 This agreement c ould help Florida growers but the lower priced import ed field grown tomatoes will still be a threat for the market share of the domestic growers The regular NPV analysis results suggest that investment in tomato production with the high technology greenhouse is preferred over regular Florida greenhouse and field grown production (assuming per plant crop yield for each technology is at the break even point ) Moreover, the investment decision preferences changes with an increase in the risk aversion coefficient of the decision maker Stochastic efficiency ranking of the investment decision shows that the high technology greenhouse is preferred by risk neutral and normally risk averse decision maker s. However, moderately risk averse decision maker s may invest in a regular Florida greenhouse technology, while extremely risk averse growers will continue to produce field grow n tomatoes. These results are consistent with what has been witnessed in tomato production in Florida. The increase in greenhouse investment shows that some growers are beginning to take more risk because they find greenhouse investment as a way to compete better in the market. The strength of this study lays in the examination of all possible tomato production alternatives for Florida producers by incorporating risk in to the decision making analysis However, the analysis depends on the budget data prepare d by PAGE 80 80 experts and university researchers as a representative farm, rather than actual budget data. Although the budgets are prepared for representative farms, we updated the si mulation. PAGE 81 81 Table 3 1 Risk identification for greenhouse and field grown tomato productions Risk parameters Risk source Greenhouse Field g rown Market Risk Product Perception Yield Risk Weather Low High Price Risk Supply/ Demand relationship Relatively low High Cost Risk I nput Energy Labor expense variability High Relatively low Source: Prepared by author based on the expert opinions and literature. Table 3 2 Key assumption s used in greenhouse tomato financial model Variable Unit Value Ownership Per cent 100% Operating Loan Length Years 1 Operating Loan Interest Rate Per cent 5.0 Long Term Loan Length Years 7 Long Term Loan Interest Rate Per cent 8.0 Interest on equit y invested Per cent 10.0 Corporate tax rate Per cent 25.0 Inflation rate Per cent 2.0 Increase in Energy Prices Per cent 7.0 PAGE 82 82 Table 3 3. Tomato budget for three production technologies (in dollars per acre ) Field g rown Greenhouse FL Greenhouse HT Production Cost Share Initial Equity $ $ 35,000.00 $ 35,000.00 Start up Cash $ 13,150.00 $ 196,322.35 $ 389,055.81 Construction Cost & Durables $ $ 459,596.72 $ 945,236.68 Growin g Costs $ 7,218.09 $ 27,043.08 $ 170,147.20 41.20% 11.48% 33.41% Energy Costs $ $ 58,040.68 $ 93,297.17 0.00% 24.64% 18.32% Labor Costs $ 354.92 $ 74,653.13 $ 131,167.23 2.03% 31.69% 25.76% Sales Costs $ 5,815.80 $ 53,005.56 $ 80,520.31 33.19% 22.50% 15.81% Administrative $ 4,132.85 $ 22,852.22 $ 34,151.64 23.59% 9.70% 6.71% Total Production Cost $ 17,521.66 $ 235,594.67 $ 509,283.54 100.00% 100.00% 100.00% ( w/o initial investment) Source: Based on three budget sets (see Appendix B ). Table 3 4. Net income statement s for alternative tomato production technologies, 2014 ($/acre) Field g rown Greenhouse FL Greenhouse HT Expected Production Amount 40 ,500 lbs 244,950 lbs 473,499 lbs Expected Revenue $ 19,501.47 $ 338,458.85 $ 666,456.25 Energy Cost $ $ 58,040.68 $ 93,297.17 Other Costs $ 7,573.01 $ 101,696.21 $ 301,314.43 Gross Profit $ 11,928.46 $ 194,106.46 $ 289,382.97 Sales and Administrative Cost $ 9,948.65 $ 75,857.79 $ 114,671.94 Depreciation $ $ 61,121.85 $ 79,9 53.60 Interest Payment $ 657.06 $ 40,015.95 $ 83,412.91 EBT $ 1,322.75 $ 1,726.38 $ (6,193.80) Tax on EBT (%25) $ 330.69 $ 431.60 $ Net Inc ome $ 992.06 $ 1,294.79 $ (6,193.80) PAGE 83 83 Table 3 5. Stochastic variables used in financial model of tomato production investment decision Variable Unit Value Tomato Yield (Field Grown) cwt/acre Mean Yield k [1 + MVE (S i F(S i ), CUSD 1 )] Sale Prices $/cwt Mean Price k [1 + MVE (S i F(S i ), CUSD 2 )] Electricity Price $/KW Mean Price k [1 + MVE (S j F(S j ), CUSD 1 )] Gas/Liquid Petroleum Gas Price $/Gallon Mean Price k [1 + MVE (S j F(S j ), CUSD 2 )] Table 3 6. Forecasted present values and net incomes for field grown and greenhouse tomato productions ($/acre) Years Field grown Greenhouse FL Greenhouse HT PV Net Incomes PV Net Incomes PV Net Incomes 2014 $ 14,404.89 $ 992.06 $226,838.19 $ 2, 478.53 $394,471.53 ($ 6,193.80) 2015 $ 15,654.05 $ 981.08 $257,196.79 $ 5,290.71 $400,997.94 $ 1,002.08 2016 $ 16,892.13 $ 964.64 $287,299.40 $ 8,245.50 $406,864.84 $ 6,923.71 2017 $ 18,113.69 $ 942.65 $261,829.38 $1 0,299.70 $402,877.48 $12,977.68 2018 $ 19,313.16 $ 914.97 $277,034.58 $13,328.65 $406,776.82 $19,539.92 2019 $ 20,484.85 $ 881.52 $252,064.54 $15,890.36 $409,288.96 $26,473.89 2020 $ 21,622.99 $ 842.15 $151,496.24 $18,725.4 2 $255,378.75 $33,679.74 2021 $ 22,721.66 $ 796.77 $199,911.79 $21,934.31 $303,641.17 $40,144.11 2022 $ 23,774.85 $ 745.24 $277,684.01 $21,639.57 $436,434.02 $39,720.92 2023 $ 24,776.40 $ 687.45 $308,825.43 $20,603.35 $558 ,720.30 $38,998.94 Table 3 7. Net present values per acre field grown and greenhouse tomato production s Present Value Initial Equity NPV Field g rown $3,705.19 $3,705.19 Greenhouse FL $74,130.33 $35,000.00 $39,130.33 Greenhouse HT $105,289.52 $35,000.00 $70,289.52 PAGE 84 84 Table 3 8. Summary statistics of Monte Carlo simulation for alternative technologies Greenhouse HT Greenhouse FL Field grown Mean 57,494.36 30,204.39 320.34 Standard Deviation 60,035.25 37,676.04 4,130.99 Coefficient of Variation 104.42 124.74 1,289.58 Minimum (122,421.19) (85,587.57) (14,079.44) Maximum 222,902.09 126,208.66 10,434.16 Table 3 9. First and second order stoc hastic dominance results for alternative technologies Greenhouse HT Greenhouse FL Field grown Approximate Area First Degree Dominance Greenhouse HT FDD: Greenhouse FL FDD: Field grown FDD: Second Degree Dominance Greenhous e HT SDD: Dominates Dominates 167,059.7 Greenhouse FL SDD: Dominates 194,511.2 Field grown SDD: 224,362.5 PAGE 85 85 Table 3 10. Stochastic dominance with respect to a function results Ranking Name Level of Preference Lower Risk Aversion Coefficie nt: 0 (Risk neutral) 1 Greenhouse HT Most Preferred 2 Greenhouse FL 2nd Most Preferred 3 Field grown 3rd Most Preferred Upper Risk Aversion Coefficient: 0.00004 ( Extremely Risk a verse) 1 Field grown Most Preferred 2 Greenhouse FL 2nd Most Preferred 3 Greenhouse HT 3rd Most Preferred Table 3 11 Net present values with option value for field grown and greenhouse tomato production ($/acre) Present Value Initial Equity NPV Option Value Field g rown $3,705.19 $3,705.19 Greenhouse FL $74,130.33 $35,000.00 $39,130.33 $405 842 66 Greenhouse HT $105,289.52 $35,000.00 $70,289.52 $ 405 842 66 PAGE 86 86 Figure 3 1. T omato imports from M exico by t echnology Figure 3 2. Fresh tomato s upply in the U.S. m arket PAGE 87 87 Figure 3 3. Do mestic f resh t omato m arket in the U.S. Source: Adapted from Copeland and Antikarov (2003) Figure 3 4. Risk modeling in the n et p resent v alue a nalysis PAGE 88 88 Figure 3 5. CDFs of simulated NPVs for alternative technologies Figure 3 6. Stochastic e ffi ciency with r espect to a function u nder a n egative e xponential u tility f unction PAGE 89 89 Figure 3 7. Present value binomial tree for field grown tomato production PAGE 90 90 Figure 3 8. Real option calculation for greenhouse tomato investment PAGE 91 91 CHAPTER 4 RISKS AND F TO DEVELOP FERTILIZER BEST MANAGEMENT PRACTICE Introductory Remarks Nutrient management is a key decision for an agricultural producer. The amount of nitrogen fertilizer and its placement, type, and ti ming can have a direct impact on the crop yield and hence, profitability of a farm. Nutrient management also has important implication s for water quality in local streams and rivers helping to reduce fertilizer runoff from agricultural fields The decisio n about the optimal fertilizer rate is based on comparison of the marginal fertilizer cost and revenue, which are influenced by imperfectly known future yields. To evaluate the relationship between their fertilizer use and future yields, agricultural produ cers rely on observations collected through many years of their production experiences. Fertilizer use recommendations developed by the State Cooperative Extension Service referre d to as Best Management Practices (BMPs), are also used by producers Moreov er, given the extent of nutrient water pollution issues nationwide, there have been calls for making the use of fertilizer BMPs mandatory for agricultural producers. In Florida, BMPs are already mandatory for agricultural producers operating in the watersh eds with impaired water bodies where watershed management plans (referred to as Total Maximum Daily Load, TMDL, plans) were established. Such mandatory requirem ent for BMP implementation requires a precise BMP definition, acceptable to all stakeholder grou ps, and providing for economically viable agricultural production and water quality protection. Historically, agricultural producers often deviate d from fertilizer BMP t PAGE 92 92 yield variability (Feinerman et al. 1990; Huang 2002); (2) systematic biases in Extension production experiments used to develop recommendations; or (3) the la ck of considerations of socio economic factors in the development of the Extension recommendations, which leads to overly restrictive recommendations. In this study, we focus on the third potential reason The overall objective of the study is to provide r ecommendations for BMP definition and development process to better account for the economic factors influencing the Existing studies identified a variety of economic and non economic factors affecting fertilizer use. Antle ( 2010 ), Isik ( 2002 ) and Pope and Kramer ( 1979 ) focus on p roduction risk (defined as the variance of yield) and price risks (defined as the variance of input and output prices ) Since the fertilizer use influences yield variability and hence, product risk aversion. Specifically, if the increase in fertilizer use leads to higher yield variability, then farmers who dislike the risks (i.e. more risk averse) apply less fertili zer, in comparison with those farmers who enjoy risky enterprises (i.e. less risk averse or risk loving). Given that nitrogen and phosphorus are found by many studies to increase the variability of yield, more risk averse farmers should apply less fertiliz er. For example, in a study of corn production experiments in Canada, Rajsic et al. (2009) found that it is economically optimal for a risk neutral farmer to apply 14% more nitrogen than the current Canadian BMP recommendations, while for a very risk avers e farmer it is optimal to apply 37% less nitrogen than the BMP recommendations. Existing studies states variability can differ from the effects observed by researchers. For example, in his stu dy PAGE 93 93 of twelve Texas grain sorghum producers, SriRamaratnam et al. (1987) found that some of the growers believed that fertilizer reduces yield variability (contrary to conclusions of many production experiment studies) For the producers who believe in redu ction in yield variability due to greater fertilizer use, higher risk aversion would increase the fertilizer use. Published studies have also examined the uncertainty of future input and output prices. For example, Feinerman et al. (1990) showed that the output price uncertainty lowers the levels of fertilizer use, while the expected increase in future fertilizer prices lead to higher fertilizer application rates. Several studies have also considered the effects of uncertainty of weather and soil fertility on the substitution between nitrogen and land (Babcock and Blackmer 1994), as well as the link between fertilizer use and crop choices (Babcock and Pautsch 1998). Overall, fertilizer BMP implementation rate depend s on the BMP implementation to asset ratio) (Paudel et al. 2008 Prokopy et al. 2008). F BMP development and implementation, severity of water quality problems, and the effectiveness of BMPs in reducing potential environmental impacts can also change the likelihood of BMP implementation (FDACS 2011a Prokopy et al. 2008). Finally, BMP impleme ntation rate can depend on organizations (Feather and Amacher 1994). In this study, the economic factors important for fertilizer BMP definition are explored by considering (a) variability in yield driven by uncertainty in weather and PAGE 94 94 fertilizer input use ; (b) alternative levels of input and output prices ; (c) various decision criteria that can be used by producers (i.e. maximizing profits or expected utility); and ( d ) various levels of produce aversion. Florida potato industry around Lower St Johns River Basin is used as a case in this study Contested fertilizer BMP requirement for the potato production, sandy soil s that facilitate fertilizer leaching and potato farms located in close proximity to waterways make this region attractive for this study. The study show s that the fertilizer BMP level depend s on the assumption s about the decision criteria, risk aversion, and the market prices. Since the decision criteria and risk aversion varies among producers, and the prices vary from year to year, developing a unique optimal fertilizer rate BMP applicable for all producers and all production and market conditions is impossible. Instead, it should be explicitly recognized that re stricting fertilizer rate to a BMP level can result in reductions in profits for some producers and some market conditions. The acceptable tradeoffs between water quality protection and reductions in agricultural profits should be explicitly discussed as a part of BMP development process, and possible funding mechanism to compensate farmers for reductions in profits should be developed (such as water quality credit trading ). This research makes several contributions to the existing literature. First, this study examines an advanced yield response function quadratic stochastic plateau production function that has not yet been used in published studies. Second ly unlike other existing BMP studies that rely on short term field trials to model yields, this research examines the yield variability using a long term historic time series to capture a range of weather and market conditions. Thirdly, the combination of production PAGE 95 95 function estimation and Monte Carlo simulations applied to financial statement allows for a more rigorous modeling of profits and risks than what is found in other agronomic and agribusiness studies. Existing agronomic studies primarily model annual yields using non stochastic production functions, and rarely analyze profits. In turn, exis ting agribusiness studies use financial statement to simulate profits, but they do not utilize yield response functions. The combination of stochastic yield response function and financial statement simulation allows for a more comprehensive and rigorous m odelling of agricultural profits and risks. And finally, this research is the only study found that utilizes economic methodology to examine the costs associated with the alternative nutrient management BMP definitions. The BMP definition is especially imp ortant given the unique water quality polic y that balances water quality improvement goal with the goal of economic growth associated with population increase and protection of the economically important agricultural industry. BMP implementation is mandatory in many watersheds in Florida in contrast to the voluntary approach used in other states. This mandatory policy requirement has resulted in the heated stakeholder discussions about what should constitute a BMP and how BMP development process s hould be structured. In many respect, Florida is in the forefront of water quality policy development, serving as testing ground for the policies that are to be adopted to address similar issues in other states. Water Quality Policies to Address Agricultur al Water Pollution Issues Agricultural BMPs are the cornerstone of water quality policy to address agricultural water quality issues nationwide (USDA Nonpoint Source Water Quality Policy, 1986) Given that the 1972 Clean Water Act does not give the federa l government the authority to regulate runoff from nonpoint sources (including most of the PAGE 96 96 agriculture), federal and state agencies rely on cost share programs to encourage voluntary BMP implementation (USDA 2006) Agricultural BMPs are developed to impro ve the efficiency and environmental sustainability of agricultural production. Florida provides an interesting study area for BMP research because of its unique regulatory environment. Florida is at the forefront of the water quality policy development to address the challenge of accommodating raising population, supporting agricultural industry, and protecting natural resources. As the population in Southern US continues to grow (US Census, 2013), other states will likely revise their agricultural water q uality policies, possibly following example and adopting similar innovative programs. In Florida, the implementation of BMP is mandatory for agricultural producers operating in the watersheds with impaired water bodies, for which Total Maximum Da ily Load (TMDL) plans and their implementation components (referred to as Basin Management Action Plans, or BMAPs) are developed and adopted. To formally participate in the BMP program, agricultural producers should use the Florida Department of Agricultur e and Consumer Services (FDACS) adopted BMP manual(s) appropriate to their operations and geographical regions, identify the applicable BMPs on a notice of intent (NOI) to implement the BMPs, and submit the NOI to FDACS. Agricultural producers also must ma intain records, such as fertilizer use, and allow FDACS staff to inspect the BMPs (Migliaccio and Boman 2008). Farmers who submit an NOI and implement and maintain FDACS adopted BMPs have a presumption of If farmers choose not to file NOIs, then t hey are required to monitor their pollution runoff to pro ve that they are not causing PAGE 97 97 water quality impairments. Given that the BMPs are mandatory for implementation and that they guarantee the presumption of compl iance with water quality standards BMP development and implementation process attracts increased attention of agricultural producers and environmental groups S tate agencies and the Cooperative Extension service work to address concerns and facilitate the dialogue among various stakeholder groups related to BMP development and implementation Similar to the definitions used in federal regulations and the definition adopted by other states, ed to benefit water quality and water conservation while maintaining or even enhancing BMP definition, BMP development largely rely on agronomic research and stakeholder di scussions, while a comprehensive economic analysis is rarely conducted. As a res ult, there is a room for debate among producers, researchers, and the state agencies about whether specific BMP recommendation s are p Moreover, BMP manuals are adopted by rule by FDACS, and are largely based on recommendations established by the Florida Cooperative Extension. Extension faculty face the challenge of conducting production experiments to serve the informational needs of the agricultural producers, while at the same time providing technical support to the state agencies developing water quality programs. While improving the efficiency of agricultural operation s can often lead to the dual benefits of increased envi ronmental sustainability and economic viability, situations can arise when there are tradeoffs between the profitability and environmental sustainability objectives. PAGE 98 98 As a result, the dual role of cooperative extension as benefactor of both agricultural pro ducers and the state agencies can result in distrust in BMP recommendations of one or both stakeholder groups. This research develops an economic model that can be used in fertilizer BMP development process. Costs associated with alternative fertilizer B MP definition s are explicitly examined. The economic model is developed and applied for a particular study area Tri County Agricultural Area where BMP development process has been especially widely discussed and disagreed about (Borisova et al., 2010) Study Area and 26 BMAPs have already been developed (FDEP, 2013). The BMAP for the Lower St Johns River Basin was the third BMAP developed in Florida, and it has been one o f the most detailed and still one of the most contested BMAPs developed in Florida ( US EPA, 2009). The importance of the region and the increased attention to the region of the stakeholders in the state make it an interesting case study. The main stem of the Lower St. Johns River is classified as impaired with respect to the narrative biologic water quality standard 1 and the numeric DO standard (FDEP, 201 3 ). The main causes of impairment are the discharges from wastewater treatment facilities, and nonp oint source pollution from septic tanks, marinas, silviculture, dairies, storm water from urban development and tributaries, and row crop agriculture (FDEP, 2013 ). The effect of agricultural runoff is especially significant in the up stream, southern porti on of the Basin, which is largely rural. TMDL and BMAP were adopted for 1 Although FL will be using numeric as opposed to narrative standards to identify nutrient impairment, existing TMDLs will be used as Site Specific Alternative Criteria under the new rule. PAGE 99 99 the main stem of the Lower St. Johns River Basin in October of 2008, and implementation of BMPs is currently mandatory for agricultural producers in the Basin Florida is the leading s upplier of potato es in the nation during the spring harvesting season (National Potato Council 2012), and most of the p otatoes are grown in the Northe ast portion of the state, in TCAA most of which is located in the Lower S t. Johns River Basin (TCAA, Fig ure 4 1) Agriculture is an important economic sector for TCAA, and along with potato farmers grow sod, cabbage, and other vegetables. The total value of agricultural production in the region was $126.1 M in 2007 (US DA, 2007 ). The rate of agricultural BMP implementation, as well as signing the Notices of s regions and agricultural crop types. For example, only 37% of agricultural producers in Suwannee River Water Management District signed NOIs (Katz, 2 013). For a long time, the rates of signing NOIs and implementing fertilizer BMP were also relatively low in TCAA This study uses the situation in TCAA as a case study to explore the BMP development and implementation process. Specifically, potato produce rs in TCAA argue d that fertilizer BMP proposed in 2010 2012 did not account for the economics of t heir production, and hence, was not economically feasible and could not therefore be called a BMP. Indeed, large discrepancies between BMP recommendations a nd actual fertilizer use were observed, with the BMPs being 200 lb/acre, while growers were using up to 300 lb N/acre. Recently, FDACS set a BMP for potato growers in this area that allows growers to use up to 250 lb of N /acre (FDACS 2011b). This new rul e gives growers some flexibility to respond to the changing market and weather conditions ; however, it is set without conducting an economic analysis of costs and benefits associated with this or PAGE 100 100 other possible BMP levels Such a discrepancy between past a nd current BMP and the and the multiple stakeholder conflicts surrounding TMDL and BMAP development in the Basin make TCAA an interesting case study for this research. 2 Below, the data related to the potato production in TCAA a re presented. The discussion of the data is followed by the methodology used to examine the fertilizer use decisions and the costs associated with alternative fertilizer BMP definition. Data The land area, per acre yield and prices specifically for Hasting s potato production in each of TCAA counties were obtained from potato stati sti cs published by USDA NASS for 1949 to 2006. Data for additional years (2007 2010) were obtained Center was used to collect temperature and precipitation data for the study region. Information for Hastings area climatic station (COOP: 081978) was available only for the period of 1952 to 2010. Thus, this analysis focuses on this time period ( Table 4 1) County level fertilizer sale data for the three counties in TCAA were obtained from US Geological Survey (USGS, 2012), National Oceanic and Atmospheric Administration (NOAA, 2012), and Florida Department of Agriculture and Consumer Services (FDACS, 2012) Specifically, NOAA data cover the period from 1945 to 1991, USGS data span the period from 1987 to 2001, and FDACS reports the data for 1997 2010. Since the three sources are used for the fertilizer sales, the overlapping years are 2 Note that similar issues related to the definition of fertilizer BMP are being widely discussed in other regions (see, for example, discussions of fertilizer rate for tomato production in southwest Florida in Hendriks and Shukla, 2011). PAGE 101 101 used to adjust time series data after the unit conversation was made. T ime series data for the change s in acreage of different agricultural operations was not available, and hence, the total fertilizer use could not be adjusted to account for the use in specific crops. Potat o production was considered to be the primary agricultural land use type in TCAA that requires fertilizer use, and hence, all county level agricultural fertilizer sales were attributed to potato production. It is important to acknowledge that this assumpti on is an over simplification. For example, the most recent Agricultural Census showed that in 2007, 24 026 acres were devoted to vegetable production in TCAA, and potato was grown on 67.5% of this area (i.e., 16 224 acres ; USDA, 2007 ). 3 The percentage of agricultural area devoted to potato production varies over time, and it would be important to account for this variation in estimating fertilizer use. However, as stated above, the time series data on the proportion of potato production in the total vegeta ble production area was not available. Moreover, the average fertilizer use estimated in this study ranges from approximately 50 to 250 lb N / acre, which is close to the levels historically observed in potato production in the area. The analysis of desc riptive statistics shows that fertilizer sales increase over time, corresponding to the rise in potato yield in TCAA. The biggest rate of increase in estimated fertilizer sales and yield are seen in the late 70 s and the early 80 s and this increase coinc ides with the green revolution period associated with a series of research and technological improvements in 1970s that increased agriculture production in US and around the globe (Figure 4 2) It is also important to mention that planted potato land does not fluctuate much in th e study period (Figure 4 3) and hence the increase in 3 In addition to vegetable production, othe r types of agriculture included woodland, pasture, and other uses, along with a relatively small percentage of sod and floriculture crops (USDA, 2007). PAGE 102 102 total potato production is primarily attributed to increase s in yield, especially after 1980. This increase in yield can be linked, for example, to the introduction of more prod uctive potato varieties. The p recipitation data indicates the distribution of the number of rains over 1 inch during production season of TCAA (this precipitation level is based on the definition of the fertilizer BMP d efinition). 4 Methodology To examine the effect of economic factors on fertilizer use decisions, t his study develops a comprehensive model that integrates various production and risk analysis methods First, potato production function is estimated. Producti on function (also referred to as a yield response function) represents the relationship between nitrogen fertilizer use, weather conditions, and per acre potato yield. In this study, l inear and quadratic stochastic plateau production function s are derived, and then estimated using data for the study area and m aximum likelihood technique. Next, financial analysis model is developed to assess profits for a typical potato farm in the study area. The financial model and the estimated potato production function are then combined to simulate ten year net present value of profits using Monte Carlo technique The simulations are conducted given alternative weather conditions, nitrogen fertilizer and potato sale prices, and nitrogen fertilizer application rates. The nitrogen fertilizer rates are evaluated using two criteria of ranking risky alternatives : (1) expected profit maximization; and (2) stochastic dominance. The results are used to rank alternative 4 Note that temperature records for TCAA was also examined, but the correlation between temperature and potato yield was relatively small, and hence, temperature was excluded from further analysis. PAGE 103 103 fertilizer rates and to calculat e costs associated with alte rnative nitrogen fertilizer rates, as well as to develop recommendations for BMP development process Production Functions Most agronomic fertilizer BMP studies focus on estimating a production function to find the optimum level of fertilizer that maximiz es yield. Only a few studies also estimate the optimum level that maximizes the profit (Hochmuth et al 2011). Note that in both cases, production and price risks are ignored The d eterministic quadratic plateau production function is commonly used in agronomic BMP research and some economic studies (Anderson, 1973; Cerrato and Blackmer, 1982; Bullock and Bullock, 1994). The assumption is that increase in nutrient level after a certain level does not influence the yield (i.e., the plateau level). The pl ateau level in such function is selected as the maximum point of the quadratic function ( estimated with the production experiment data ) disregarding the potential stochastic nature of the plateau, as well as the quadratic or linear components of the funct ion. To account for the stochastic variations in yield, switching regression methodology was introduced by Maddala and Nelson (1974). In addition to agricultural production research, the methodology is commonly used in labor economics, the modeling of hous ing demand, and the modeling of markets in disequilibrium to evaluate endogenous switching between two or more regions (Lokshin and Sajaia 2004). The methodology allows estimation of data from regions or time periods even though these regions / periods can be characterized by different functional forms for the dependent variable. Tembo et al. (2008) developed an alternative methodology referred to as response model with a stochastic plateau. This methodology gives better results when PAGE 104 104 applied to complex fun ctional forms with error terms as compared with the switching regression. Tembo et al. (2008) applied the methodology to the data from wheat production experiments, and the methodology allowed the researchers to account for year random effect in modeling p lateau level that is lin k ed to weather effect s Comparison of the stochastic plateau method with switching regression showed that stochastic plateau methodology better explained the variation in the production experiment data. Moreover, Brorsen (2013) pre sented an alternative to this estimation technique by introducing Bayesian estimation with random effects using Marco Chain Monte Carlo method. This technique is appropriate for small data samples (since it does not require asymptotic or plug in approaches for standard error to determine optimal levels of input use ). The other advantage is the evasion from convergence problem of nonlinear estimation methods used in prior methodologies. In this study we compare the production functions estimated with altern ative methods using the time series data. This approach is drastically different from the approach used in the previous studies that relied on the field experiments and panel data. Panel data refer to the data that span several years (i.e., time series com ponent ) and include observation for several plots (i.e., cross section component ). Inclusion of both time series and cross section reduces omitted data variable bias (heterogeneity) and allows researchers to include dynamic relationship (Hausman and Wise 1979). However, panel data are also extremely costly to collect. Due to the complexity and the costs of field experiments, they are usually conducted for a few years only. In contrast, the time series data aggregated to a county level are collected by USD A and state PAGE 105 105 agencies on an annual basis, and historic data are available for more than 50 years that span the periods with vastly different weather and market conditions. The data are also widely available for the researchers. Finally, time series data can perform well for the regions where soils are fairly homogeneous, and spatial differences are not significant. In this study, we examine the feasibility of using time series data to substitute for the field experiments results in the analysis of fertilizer use decisions in TCAA. To summarize, the study makes the following contributions to the literature. First, it rel ies on time series data (as opposed to the panel data). Second, in contrast to traditional BMP research that relies on deterministic productio n functions, the study explicitly incorporate s weather effects into the stochastic production function. Third, in contrast to existing economic studies that use linear stochastic plateau, the study estimate s and test s quadratic stochastic plateau productio n function (which is more complex than the linear stochastic plateau function and hence, it does not allow for the explicit analytical solution for optimum nitrogen level). Fourth, numerical optimization routine is used to account for price variability and risks. The following two sub sections describe the two stochastic production functions analyzed in this study linear and quadratic stochastic plateau functions. Linear stochastic plateau production function Dillon (1961) stated that the majority of pro duction functions have a plateau where yield does not increase in response to additional input use. Following Tembo et al. (2008), assuming single input model, the plateau response function in general form is expressed as follows (4 1) PAGE 106 106 where y is the yield, N is the level of nitrogen, g ( N ) is the production function and y p is the plateau level and is the random error term. This function comes from a mathematical model called the plateau principle in which input contribution t o the yield eliminated by time (Spillman 1933). Tembo et al. (2008) described a univariate linear response function and the optimum level of nitrogen as follows: (4 2) where N refers to nitrogen use at the time t is a plat eau level, and v are random variables. The random shift of the plateau is represented by weather variance for which The stochastic variable for weather and random error term for the whole function are assumed to be independent and the production function and t are not linearly dependent ( Figure 4 4) As stated above, a ssuming a risk neutral producer that faces only the weather risk, the producer aims at maximizing the expected profit: (4 3) w here p is the output price and the w N is the input price. If we use non stochastic plateau model, the optimum input level is obtained from the first order condition as (4 4) where N p represents the nitrogen level at the plateau. We add distribution function to this solution to determine input level for stochastic plateau. The censored normal distribution theorem developed for Tobit models can be used to find the optimum input level for stochastic plateau model (Greene 2000). The optimum level can be on the plateau or to the left of the plateau, then the expected yield becomes PAGE 107 107 (4 5) where a represents the function and represents the probability of being on the function while (1 ) give s the probability of being on the plateau. Therefore, the terms ( ) and standard normal density function ( ) Substituting equation (4 5) into (4 3) yields (4 6) The first order condition of the profit function is (4 7) Note that (McDonald and Moffitt 1980). Application of the chain rule results in the following equat ion PAGE 108 108 The cancellation of the terms allow us to reduce the equation (4 7) into (4 8) Since rearranging the terms to find the optimum level of nitrogen value yields (4 9) w here shows the inverse standard normal cumulative distribution function. Quadratic stochastic platea u production function Tembo et al. (2008) described the estimation procedure for linear stochastic plateau production function and the expected profit function. In this study, this methodology is extended for the case of quadratic stochastic plateau functi on. Assuming a univariate quadratic function of the form the following stochastic plateau function can be developed: PAGE 109 109 (4 10) where t subscript is the years and i for i=0,1,2 are the parameters estimated. Yield at plateau level and further is showed as and is the minimum level of the nitrogen input needed to reach the plateau with the same assumptions applied for stochastic variables. A risk neutral producer fa cing only weather risk aims to maximize the expected profit : (4 11) w here p is the output price and the w N is the input price. If one uses non stochastic plateau model, the optimum input level is obtained from the first order c ondition as (4 12) The censored normal distribution theorem developed for Tobit models can be used to find the optimum input level for stochastic plateau model (Greene 2000). The optimum level can be on the plateau or to the lef t of the plateau. The expected yield becomes (4 13) where and The first order condition of the profit function when we substitute equation (4 13 ) into (4 11 ) yields (4 14) PAGE 110 110 The c hain rule allow s us to reduce the equation into (4 15) Since rearranging the terms to find the optimum level of nitrogen value yields ( 4 16 ) w here shows the inverse standard normal cumulative distribution function. Using quadratic function 5 solution, two possible solutions are obtained as (4 17 ) Since both sides of the equation have the nitro gen value, we find the optimum level of nitrogen numerically. Maximum likelihood estimation of linear and quadratic plateau production functions Let f (.) be the probability density function and A be the vector of estimated parameters for quadratic or linea r production function s where is equal to zero for linear function Then the joint conditional probability density function is obtained as (4 18) 5 Quadratic formula for is given as PAGE 111 111 The maximum likelihood function can be found by integrating the y t with respect to t and taking the product over time as follows : (4 19) where a and b are the limits of integration for the distribution of t Although maximum likelihood estimation (MLE) maximizes t he logarithmic transformation of this function, t prevents this function from having an open form solution. Therefore, numerical approximation is used for the estimation of the value of coefficients through nonlinear optimization. SAS NLMIXED procedure fa cilities this process. The procedure includes Gaussian quadrature methods, the common method used to approximat e complex integral similar to the integral in equation ( 19 ) (SAS Institute Inc 2004). Various combinations of starting values, optimization algor ithms, and integral approximation with quadrature method were applied to get the convergence of the equation and the global maximum. The same MLE technique is also applied to estimate the coefficients of the linear response stochastic plateau production fu nction (described in the previous section). Maximization of Expected Profit Assuming a risk neutral producer that faces only the weather risk, the producer aims at maximizing the expected profit: (4 20) w here p is the output pr ice w N is the input price y t is yield, and t is the year index The optimum level of nitrogen fertilizer, N t is obtained from the first order condition as : PAGE 112 112 (4 21) The specific level of nitrogen fertilizer use will depend o n the relationship between N and y which is described by the production function (see the section above). It is important to note that the assumption about the functional form of the production function will influence the optimal fertilizer use level, and hence, the assumption can have important implications for the fertilizer use decision and BMP recommendations. Financial Analysis Model The analysis described above employs expected profit maximization criterion to find the optimal fertilizer rate. While this analysis accounts for the production risks associated with variability in yield, it ignores the market risk, i.e., the risk associated with the variability in sale prices. Furthermore, this analysis is based on the assumption that the producer is risk neutral, and is primarily concerned with the expected profits as opposed to the profit variability. To account for the effects on fertilizer use decisions of both production and market risks, financial analysis model is developed, as described in the nex t sub section. The financial analysis model is then integrated with the estimated linear plateau production function, and Monte Carlo simulations are conducted to estimate the effects of production and sale price variability on ten year net present value o f a typical potato producer. A variety of producers risk preferences are then examined. Financial sheet model Financial sheet model consist of financial statement, cash flow statement and balance sheet. The model is based on the model by Barker ( 2013 ) th at has been used PAGE 113 113 in evaluation of market risks associate with alternative investment portfolios. The financial model is constructed in MS Excel The model allows calculating total costs, revenues, and the annual present values (PV) of a business enterprise (see Appendix E for more details). For this study, ten year net present value is computed as follows: (4 22) The NPV for a typical potato producer in TCAA is estimated base d on discussions with industry experts and the latest fi nancial and business literature (Richardson et al. 2007a; Richardson et al. 2007b; Palma et al. 2011). T he firm is chosen to be a 100% financed by the equity holder; in other words, it is totally owned by the producer. The start up equity value (beginning wealth) for potato production is approximately $325.00/ acre This amount is chosen as the minimum amount to insure that the farmer does not run out of cash over 10 year period Farmers use operating loan s which account for 90% of total variable cost at a 5% interest rate annually ; in addition, 80% of the fixed costs are financed at an 8% interest rate over a 7 year period. These levels of operating loans for variable and durable expenses the annual interest rates and the loan periods are based on literat ure and discussions with experts Farmers are also assumed to receive 10% interest for their equity investment at the end of each year The interest on equity investment positive net income, and 10% level is assume d as the minimum level typically used in existing studies To reflect production and price risks faced by the potato producers in the region, yield level and sale prices used in N PV estimation for each year are assumed to be PAGE 114 114 stochastic. NPV levels are then estimated for a variety of fertilizer and sale prices, and fertilizer use levels, as described in the next sub section. Simulations The model uses a Monte Carlo simulation method and financial statements to analyze the returns for alternative nitrogen fer tilizer rates Monte Carlo simulation is a method that utilizes repeated random sampling to calculate probabilities of events and it is well suited to approximate probability distribution s of stochastic variables (Palma et al. 2011). This method is applie d to simulate stochastic components in the financial model A sample of values for all stochastic variables is selected simultaneously, and the process is repeated 500 times to estimate the probability density functions (PDF) and c umulative distribution fu nctions (CDF) for the stochastic outcomes The approach is used to obtain the distribution of yield, revenue, cost and net present value (NPV) for ten year period. The simulations are conducted using Simetar add in for MS Excel (Richardson, Schumann and F eldman, 2008). The following stochastic variables are used to model production and price risks: yield (simulated using linear stochastic production functions described in the section above ), output price (assumed to be correlated with historical yield), an d fertilizer price. Potato y ield is simulated by using estimated linear stochastic plateau production function coefficients and the stochastic terms ( and ) shown in the Table 4 4. Stochastic terms are assumed t o be normally distributed in the estimation process and predicted yields are used as a mean yield for the simulation purposes. Sale prices are simulated jointly with the yields, since historical price and yield data show negative correlation. A multivariat e empirical (MVE) probability distribution is PAGE 115 115 used for the joint simulation of stochastic output prices and yields (Richardson, Klose and Gray 2000). First, the non random components are found for historic prices and yields as a function of linear time tre nd. (4 23 ) where X represents the historical data for each component i (where i =1 refers to yield, and i =2 refers to price), while t indexes the year. Then the random components are calculated as the difference between actu al and predicted values of historic prices and yields ( ) : (4 2 4 ) Relative variability of the observations is then measured as a fraction of random components to the predicted values: (4 25 ) The relative variability, D it is calculated for each observation X it and then relative variability values are sorted from small to large to find their distributions. The c orrelation matrix is calculated using the fract ion values calculated in equation (4 25). Given the historic values ( Table 4 1 ), the correlation matrix for potato price and yield variables is as follows: (4 26 ) Following Richardson, Klose and Gray (2000), one can calculate independent standard normal deviates ( R ik ) taking square root of the correlation matrix One can also calculate correlated standard normal deviates ( CSND ik ) by multiplying R ik by PAGE 116 116 Simetar ). CSND ik is generated for a ten year simulation time span (the simulated years indexed by k ). Multivariate Empirical distribution (MVE) for the price and yield variable s can be calculated using correlated uniform deviates ( CUD ) that are generated from correlated st andard normal deviates CSND ik and the distribution of the fraction values D it For a large sample, the c orrelated uniform deviates CUD approach the correlated fractional deviates ( CFD ) that incorporate fractional relationship among the simulated variables C orrelated fractional deviates are called MVE distribution : (4 27 ) At last, stochastic simulation ( ) is found by the multipl ying the predicted values calculated from trend function at equation (4 23) and MVE distribution, i.e., (4 28 ) where X is the yield inserted from the production function and the future values of prices, obtained from historical distribution ( i =1 refers to yield from production function and i =2 refers to forecasted price s ), while k indexes the simulated year s. Unlike yield and sale prices, historic data for nitrogen are not easily accessible. Farmers in TCAA are using a variety of fertilizer types with various nitrogen content, which complicates the sel ection of the historic price data to accurately represent the time series of nitrogen fertilizer prices. In agribusiness studies, t he variables that lack historical data are frequently simulated as a GRKS distribution (named after Gray, Richardson, Klose a nd Schuman; Richardson et al. 2007a). Following this approach, nitrogen input price is simulated with the GRKS distribution. This distribution uses mean, maximum and minimum value information to generate a distribution that can also PAGE 117 117 account for rare events outside the minimum and maximum values. Specifically, the GRKS distribution provides an advantage of accounting for the unforeseen risk which represents approximately 2.5% of quantiles from both ends the probability of the unforeseen event (Richardson et al. 2007a). Such unpredicted upside and downside risk y events are referred in the literature as Black Swans. The stochastic variables and the financial assumptions are provided in Table 4 2 while the detailed potato production budget for one acre of land is given in A ppendix C The potato yield is simulated using the stochastic production function and various levels of fertilizer use (as described in Simulation Scenarios section ) Output price is the other stochastic variable which is assumed to be fluctua ting around the mean of $14/cwt. At last, the nitrogen prices is simulated by using GRKS distribution having mean, maximum and minimum levels at 0.60, 0.65 and 0.55, respectively. The assumptions for the financial terms are explained in the previous sectio n and production cost values (variable, marketing and durable costs) are found at the potato budget by Smith and VanSickle ( 2009 ). Simulation scena rios Two set of simulation scenarios are developed in this study to evaluate the sensitivity of potato produc tion returns to changes in nitrogen application rate and potato sale prices. In the first set of scenarios (scenarios 1 3, Table 4 3 ), the distribution of potato sale prices is assumed to shift from the distribution with the mean of $12/cwt, to the one w ith the mean of $14/cwt, and then the mean of $16/cwt. Note that the fertilizer rate is fixed on the level which is estimated to be optimal from the PAGE 118 118 expected profit maximization (as described in the section above). 6 These scenarios allow one to explore the profit loss associated with different price expectation for determining optimum nitrogen level. In the second set of scenarios (scenarios 4 6, Table 4 3 ), the fertilizer application rate is assumed to vary between 150 lb N/acre to 207 lb N/acre, and the n to 250 lb N/acre. For these scenarios, potato sale prices are assume to be fluctuating around $14 /cwt Note that for all scenarios NPV is calculated on per acre basis. These scenarios help to evaluate preferred level of fertilizer application depends on the risk aversion level of the producer. Decision criteria used in scenario ranking The key outputs of the scenarios 1 3 and 4 6 are ranked using the mean variance method, first and second degree stochastic dominance, and stochastic dominance with res pect to a function (SDRF) to incorporate risk aversion. These tools help one to determine which risky alternative (i.e., fertilizer rate) is more feasible and how the fertilizer use decision changes with different risk behavior. All these risk r anking tools are available in the Simetar add in. Mean variance method simply looks for the le ast variance and the high est mean to rank the risky alternatives. In turn, the f irst degree stochastic dominance compares CDFs of the outcomes for the risky alte rnatives. If we represent the CDFs of two alternatives with F(x) and G(x) and F(x) dominates G(x) then it should be true that for all x The f irst degree stochastic dominance also implies that the CDFs of the two alternatives shoul d not cross (Richardson and Outlaw 2008). If they 6 As described below, this level is 207 lb N/acre, see table 5. The optimum i s based on the assumption of $14/cwt potato sale price and $0.6/lb N input price PAGE 119 119 cross, the f irst degree stochastic dominance criteria are not applicable, and the second degree stochastic dominance should be used to rank the risky alternatives. If F(x) dominates G(x) when one obtain s for all x At last, SDRF is used to incorporate risk aversion into ranking of the risky alternatives. SDRF can be defined as follows : (4 29 ) where F(x) is preferred to G(x) under given risk aversion coeffic ient ( r i ( x )) of the decision mak er (Richardson and Outlaw 2008), where i refers to the upper and lower limits of risk aversion coefficients, respectively, represented as ( r U ( x )) and ( r L ( x )). The negative exponent ial utility function is used since it allows increasing relative risk aversion proportional to wealth increase. Results This section starts with the estimation results for the linear and quadratic stochastic plateau production functions. For such production function specification, random factors eit her influence the maximum yield (reflecting plateau effects, such as heavy rains that influence the additional yield potential from nitrogen application), or they are captured in the residual error term. In comparison with the existing agronomic studies (e .g. Hochmuth et al. 2011), this approach allows for a more accurate representation of changing relationship between yield and fertilizer use given various weather conditions. The optimal fertilizer use is then defined as the level maximizing profit, which comparison to yield maximization used in agronomic studies (Anderson, 1973; Cerrato and Blackmer, 1982; Bullock and Bullock, 1994). PAGE 120 120 Next, multivariate empirical probability distrib utions (Richardson et al. 2000) are used to simulate output prices based on the historic correlation between yields and prices. Lastly, the distribution of ten year net present values (NPV) is estimated given stochastic yield, output prices, and fertilizer prices, and the negative exponential utility function is used to interpret the input decision of risk averse producer. Production Functions The estimation results for linear response stochastic plateau and quadratic response stochastic plateau, as well as quadratic response non stochastic plateau functions (for comparison purposes), are reported in the Table 4 4. All parameter and estimated variance components are significant at the 1% level. Standard error s for the coefficient s are given under the coeffic ient values in the parenthesis. Figure 4 5 demonstrates that estimated yield is reasonably close to the actual yields based on historic weather and nitrogen use levels. Y ield is higher for the drier seasons (with smaller number of rain events) and it is l ower for the rainy seasons. The results of the analysis are summarized below: The hypotheses that the production function as quadratic response stochastic plateau or non stochastic plateau functions are rejected at the 5% level (by log likelihood ratio tes t) by taking linear response stochastic plateau function as a base function. Standard errors of the optimum nitrogen level for non stochastic functions are not computed because the convergence is not satisfied for these estimations. The expected plateau e stimated in linear response stochastic function is higher than the estimated plateau level in the quadratic and non stochastic plateau functions. The estimated linear terms in the alternative specifications of the production function show that the estimat ed marginal productivity of nitrogen ( 1 ) is higher in quadratic response stochastic plateau function. PAGE 121 121 The optimum level of nitrogen is found as 207.26 l b N/acre in the linear model and 201.42 l b N/acre in quadratic stochastic plateau functions when pota to price is assumed to be $14/cwt and the price of nitrogen is $0.6/ lb Sensitivity Analysis Optimum fertilizer level given stochastic response functions is calculated by using the equation (4 7) and equation (4 15), respectively, for linear and quadratic response stochastic plateau functions. These equations are derived from the profit maximization function for specific nitrogen input price and output price. Therefore, we include sensitivity analysis to determine the different optimum nitrogen levels given both production functions. Table 4 5 indicates that optimum fertilizer level in the linear function increases when the output price increases and the nitrogen price decreases. The optimal ranges from 203.71 lb N / acre to 210.46 lb N / acre. Table 4 6 ill ustrates the sensitivity analysis of optimum nitrogen level for the quadratic function. Similar to the results above, the optimum fertilizer level increases when the output price increases and the nitrogen price decreases. The optimal ranges from 193.97 lb N / acre to 207.13 lb N / acre. As shown in the sensitivity analysis above, high output price results in high optimal fertilizer levels for a profit maximizing producer. Therefore, different price expectation of growers leads to various fertilizer rates a mong the growers. Similarly, a policy maker can have low price expectations, and in this case, BMP fertilizer level recommended by the regulators will be lower than the optimal. Financial Analysis Results The estimated coefficients of the stochastic plate au functions can be used to simulate (or forecast) yields and use the simulated values in the financial analysis. Stochastic terms allow fluctuation to be included in the forecasted yield values. Figure PAGE 122 122 4 6 illustrates the forecasted yield for quadratic an d linear stochastic plateau production functions for 2010 2020. Lower and upper confidence intervals for forecasted yield levels at the 95% are illustrated in the figure for each production function. The upper and lower limits include the error term of t he estimation and variance of error which represents the weather effect on the plateau function. Therefore, yield is close to the upper limit for the drier seasons (with smaller number of rain events) and it is close to the lower limit for the rainy season s. In contrast to the expected profit maximization described in the previous section, explicitly considering the output and input price variability in the financial analysis. Spe cifically, instead of finding the optimal fertilizer level for each pair of output and input prices, the simulations allows one to compare the distribution of NPV given a range of input and output prices, and then consider the changes in NPV distributions for different fertilizer levels. Moreover, risk aversion behavior of the farmers is accounted for in the model, making the analysis even more comprehensive. Scenario Analysis: Alternative Fertilizer Application Rates First, NPVs are compared for three dif ferent fertilizer levels: 150, 207, and 250 lb N/acre ( Table 4 7). Recall that 207 lb N/acre was found to be the optimal fertilizer use level given the expected profit maximization criterion (see the previous section and fixed output and nitrogen prices). Note that this level is approximately equal to the fertilizer BMP level used in 2008 2012. The high nitrogen use scenario is selected to represent the current BMP level that allows producers to add extra fertilizer if required (FDACS, 2011b). The low nit rogen use scenario is selected hypothetically to represent exceptionally low fertilizer use requirement. The summary statistics for the three PAGE 123 123 fertilizer use scenarios is summarized in Table 4 7. The mean variance technique does not reveal the clear dominan ce of one fertilizer level, since the levels with higher mean NPV (i.e. 250 lb N / acre) is also associated with higher variability of the NPV (with the standard deviation equal to 1,054.13). As a second step in ranking scenarios, PDFs and CDFs of the 10 y ear NPV are drawn for alternative fertilizer use levels ( Figure 4 7). The figure indicates that fertilizer application at 207 and 250 lb N/acre level robustly dominates fertilizer application at 150 lb N/acre level given the first degree stochastic dominan ce criterion. However, the comparison of NPV distributions for 207 lb N /acre and 250 lb N / acre is not so each other, and the first degree stochastic dominance does not allow selecting the preferred fertilizer use level. Nevertheless, an alternative criterion the second degree stochastic dominance since the result shows that higher NPV is expec ted when more fertilizer applied ( Table 4 8). Note the difference between the preferred levels of fertilizer use given the two decision models considered expected profit maximization given fixed prices, and the second degree stochastic dominance given st ochastic prices. For the expected profit maximization, the optimal fertilizer level ranged from 203.71 lb N / acre to 210.46 lb N / acre (see the sensitivity analysis above). For the second degree stochastic dominance, it is shown that fertilizer level of 250 lb N / acre dominates the lower levels of the fertilizer use. This difference in the results can be explained by the effect of price variability that is not accounted for in profit maximization. PAGE 124 124 risk aversion on the fertilizer use decision is examined. SDRF is applied to incorporate various degrees of risk aversion into the ranking of alternative fertilizer use rates. The absolute risk aversion coefficients ranged from 0 to 0.00131 in the analysi s. The absolute risk aversion coefficients, a are based on the relative risk aversion, r and are calculated as a ( w )= r ( w )/ w where w is the level of wealth, which is taken as the mean NPV value in this analysis. The relative risk aversion coefficients con sidered in this study are 0.0, and 2.0, which, respectively, indicating risk neutral and moderately risk averse producers (Richardson and Outlaw 2008). For example, for a moderately risk averse producer, a ( w ) = 2.0/1,524=0.00131 where $1,524 is the expecte d worth (i.e. 10 year NPV). Table 4 9 presents the results of the SDRF ranking. The results show that the preferred level of fertilizer application depends on the risk a version level of the producer. Specifically, Risk neutral producers would prefer the s cenario with fertilizer moderately risk averse prefer s caused by the high fertilizer expense and low yields. Scenario An alysis: Shifts in the Output Price Distributions As shown in the sensitivity analysis above, high output price results in high optimal fertilizer level for profit maximizing producer when the fertilizer price is constant. Therefore, different price expecta tion leads to various optimal fertilizer rates selected by the growers. In the second set of scenarios, different output price expectations are compared ( Table 4 10) Note that the prices are kept stochastic, and hence, the difference in the price expectat ions is captured in the shifts in the pri ce distributions. PAGE 125 125 The reduction in NPV profits is then estimated for the case when the recommended fertilizer BMP level is set below the optimal level for a given output and fertilizer prices Specifically, a policy maker can have low price expectations, and in this case, BMP fertilizer level recommended by the regulators will be lower than the optimal. Figure 4 8 shows the PDF approximations of simulated NPVs of optimum nitrogen levels at various output prices. The graphs illustrate the mean values and the distribution around the mean. As illustrated in the figure, the mean value increases when the output prices are high; however, high output prices decreases the risk For instance, ghest mean and the lowest risk. Table 4 1 1 shows NPV for two levels of N application, give n different mean sale prices. The first N application level is fixed at 204.94 lb N/acre (i.e. the optimal N rate if the sale price is $12/cwt input price is $0.60/l b and the producer is maximizing expected profits ). The second level is fixed at 209.22 lb N/acre (i.e. the optimal level for the output price of $16/cwt and the fertilizer price of $0.60/lb ). Note that for both fertilizer levels, NPV is simulated given s ale prices of $16/cwt and fertilizer prices of $0.60/lb There is a slight difference between NPV simulation when the fertilizer level Table 4 5), while the actual ou tput price is $12/cwt. However the loss to producers at the mean is $16.56/acre and the loss could increase up to $137.54/acre when weather and production conditions are favorable for a grower (the difference of the NPV values at the Table 4 11 ). Summary a nd Discussion This study aims at exploring the socio economic factors that should be considered in the development of the fertilizer best management practices (BMPs). PAGE 126 126 Specifically, the study examined various decision criteria used by producers, alternative specifications of crop production function, alternative levels of input and output prices aversion. The analysis focuses on TCAA region in northeast Florida. It is shown that the selection of the production function specification plays an important role in predicting the growers input use decision. The optimum level of nitrogen is found as 207.26 1b N/acre in linear, and 201.42 1b N/acre in quadratic stochastic plateau functions (given potato price of $14/cwt and nitr ogen prices of $0.6/lb). For a 400 acre farm (which is typical for the TCAA), the difference translates into 2,336 lb N This result also implies that the fertilizer BMP definition will depend on the assumption about the production function. And it is pos sible that the assumptions about the yield response relationship captured in the production function may differ for the farmers, policy makers, and researchers. The study also shows that the optimum nitrogen rate varies significantly depending on input an d output prices. Specifically, the optimal rate varied from 193.97 lb N / acre (for quadratic stochastic plateau production function, low potato sale prices, and high nitrogen fertilizer prices) to 210.46 lb N / acre (for linear stochastic plateau product ion function, high potato sale prices, and low nitrogen fertilizer prices). Again, for a 400 acre farm, the difference is 6596 lb N. This result shows that the fertilizer BMP recommendation should account for the range of input and output prices. The s tudy also examined the effect of risk preferences of the farmers on the choice of preferred fertilizer rate. Given the stochastic input and output prices, as well as stochastic yields, fertilizer rate of 250 lb/acre is more preferred for a risk neutral PAGE 127 127 pro ducer, but the rate of 207 lb/acre is more preferred by a risk averse producer. This result is consistent with other existing studies that shows that risk averse growers prefer to apply less fertilizer than risk neutral growers. Finally, the profit loss is estimated for a producer when the fertilizer BMP is selected for one level of output prices, but the growers expect to receive a higher level of prices. Given a BMP developed for only four dollar lower expectation of output prices (i.e., $12/cwt instead o f $ 16 /cwt ) t he average cost of the fertilizer BMP is $16.56/acre (or $6,624 for a 400 acre farm). However, the costs can reach $137.54/acre (or $ 55,016 for a 400 acre farm) at the favorable weather conditions. The latest BMP regulation developed for TCA A allows farmers to adjust fertilizer application if necessary; therefore, it gives the farmers the flexibility to avoid reductions in profits associated with too restrictive BMP recommendations. Overall, this is consistent with the conclusion derived from this study that no single fertilizer BMP can be recommended for all growers and all market conditions. This study shows that as a part of the BMP development process, state agencies and extension agents should he relationship between crop yield and fertilizer rates. Specifically, when high fertilizer use can be critical for high profits should be examined. Production function estimation results that a re used in BMP development should also be discussed with producers, along with profit variability analysis. Based on the assessed costs and associated water quality improvements, cost effectiveness of alternative fertilizer recommendation should be evaluat ed, and the most cost effective recommendation should be identified as the BMP. The effect on optimal fertilizer use decisions of the PAGE 128 128 In addition to fertilizer BMP, cost eff ectiveness should be examined for alternative pollution reduction strategies (such as improved irrigation technologies, or regional storm water treatment facilities). The effect of potato varieties on optimal fertilizer use should also be examined. Next, w ater quality policies should be developed to encourage the implementation of the most cost effective pollution reduction strategies. In addition to traditional cost share payments, such policies can include an insurance to compensate for yield losses attri buted to fertilizer BMP use. Labeling of sustainably produced agricultural products (e.g., Czarnezki 2011), performance based payments (Shortle et al. 1998; Winsten 2009), and payments for environmental services (PEPA 2011) are the strategies that can i ncrease the rate of BMP implementation without affecting agricultural profits. Overall, Sheriff (2005) stated that there is no one policy appropriate for all crops and locations, and a policy mechanism should be designed based on specific characteristics o f a particular region. PAGE 129 129 Table 4 1. Descriptive statistics summary for TCAA potato production, 1952 2010 Variables Average Standard Deviation Minimum Maximum Potato Yield (cwt/acre) 209.9 55.1 110.0 330.0 Planted Potato Area (acre) 22.9 4.1 15.5 30.5 Fertilizer Sale (lb N /acre) 117.0 57.0 34.4 235.1 Precipitation (Number of rain events over 1 inch per potato production season ) 5.3 2.6 1.0 12.0 Total Potato Production (1000 cwt) 4 605.8 1 223.6 2 376.0 6 930.0 Potato Price ($/cwt) 6.9 4.1 1.9 18.0 Table 4 2. Stochastic variables and financial model assumptions Variable Unit Value Potato Yield cwt/acre Output Prices $/cwt Mean Price k (~$14) [1 + MVE (S i F(S i ), 1)] The Nitrogen Input Prices $/ lb GRKS(0.55,0.60,0.65) P roduction financed % 100% equity Start up equity $/acre 325.00 Operating Loan Length Years 1 Operating Loan Interest Rate % 5.0 Durables Loan Length Years 7 Durables Loan Interest Rate % 8.0 Interest on equity invested % 10.0 Total Variable Cost (ex cl. Nitrogen fertilizer expense and marketing) $/acre 2,409.36 Marketing Cost $/acre $1/cwt Yield Nitrogen Fertilizer Expense $/acre GRKS(0.55,0.60,0.65) Durable Cost $/acre 185.00 Note: Cost items are inserted from Smith and VanSickle (2009) and the others are constructed by author. PAGE 130 130 Table 4 3. Sets of scenarios Scenario Name Set Key Stochastic Variables 1 Mean Output price $14 1 Mean Pricek (~$14) [1 + MVE (Si, F(Si), 1)] 2 Mean Output price $12 1 Mean Pricek (~$12) [1 + MVE (Si, F(Si), 1)] 3 Mean Output price $16 1 Mean Pricek (~$16) [1 + MVE (Si, F(Si), 1)] 4 Fertilizer Applied Opt 2 where N=207 5 Fertilizer Applied 150 2 where N=150 6 Fertilizer Applied 250 2 where N=250 Table 4 4. Production f unctions and the o ptimum n itrogen l evels Estimated Parameters Linear Response Stochastic Plateau Linear Response Non Stochastic Plateau Quadratic Response Stochastic Plateau Quadratic Response Non St ochastic Plateau Intercept 103.79 (10.96) 113.38 (10.55) 46.77 (3.63) 63.02 (3.95) Linear term 1.03 (0.09) 0.88 (0.07) 2.71 (0.29) 2.03 (0.19) Quadratic term N/A N/A 0.0074 (0.0015) 0.0057 (0.0008) Plateau level 260.54 (7.69) 257.80 227.67 (7.83) 239.25 (0.82) Variance of year random 1061 (34) N/A 2342 (669) N/A Variance of error term 1034 (214) 1240 (218) 653 (2 04) 1382 (238) N Optimum Nitrogen Level 207.26 (2.79) 163.36 201.42 (4.96) 206.39 2 Log Likelihood 588.50 590.70 599.60 597.80 Note: The expected price of nitrogen is $0.6/lb, the price of potato is $14 / cwt. PAGE 131 131 Table 4 5. Sensitivity analysis of opt imum nitrogen level for linear function (in pounds of nitrogen per acre) Sale Prices $/cwt Nitrogen Prices $ / lb $ 0.55 $ 0.60 $ 0.65 $ 12 206.26 204.94 203.71 $ 14 208.54 207.26 206.07 $ 16 210.46 209.22 208.05 Note: Nitrogen levels are provide d in lb N/acre. Table 4 6. Sensitivity analysis of optimum nitrogen level for quadratic function (in pounds of nitrogen per acre) Sale Prices $/cwt Nitrogen Prices $ / lb $ 0.55 $ 0.60 $ 0.65 $ 12 202.07 199.64 193.97 $ 14 205.55 201.42 197.27 $ 16 207.13 204.69 199.13 Note: Nitrogen levels are provided in lb N/acre. Table 4 7. Summary statistics for 10 year NPV s imulations for v arious f ertilizer r ates Linear Stochastic production Function, Output price = $14, various N fertilizer rates Fert ilizer Applied 207 Fertilizer Applied 150 Fertilizer Applied 250 Mean 1,524.00 706.62 1,608.32 Standard Deviation 997.96 968.25 1,054.13 Coefficient Var. 65.48 137.03 65.54 Minimum (1,516.84) (2,083.70) (1,912.51) Maximum 5,128.98 3,708.96 4,325.47 PAGE 132 132 Table 4 8 First and second order stochastic dominance results for alternative fertilizer uses Fertilizer Applied 207 Fertilizer Applied 150 Fertilizer Applied 250 Approximate Area First De gree Dominance Fertilizer Applied 207 FDD Dominates Fertilizer Applied 150 FDD Fertilizer Applied 250 FDD Dominates Second Degree Dominance Fertilizer Applied 207 SDD Dominates 3641.46 Fertilizer Applied 150 SDD 4459.33 Fertilizer Applied 250 SDD Dominates Dominates 3557.23 Table 4 9 Analysis of Stochastic Dominance with Respect to a Function (SDRF) Rank Name Level of Preference Lower Risk Aversion Coefficient : 0 (Risk neutral) 1 Fertilizer Applied 250 Most Pref erred 2 Fertilizer Applied 207 2nd Most Preferred 3 Fertilizer Applied 150 3rd Most Preferred Upper Risk Aversion Coefficient : 0.00131 ( Moderately Risk averse) 1 Fertilizer Applied 207 Most Preferred 2 Fertilizer Applied 250 2nd Most Preferred 3 Fert ilizer Applied 150 3rd Most Preferred Table 4 10 Summary statistics for 10 year NPV s imulations for v arious o utput p rices Linear Stochastic production Function, optimum N fertilizer rates, various output prices Mean Output Price $14 Mean Output Pric e $12 Mean Output Price $16 Mean 1,508.97 (345.67) 2,893.31 Standard Deviation 1,004.01 1,079.03 996.38 Coefficient Var. 66.54 (312.16) 34.44 Minimum (1,516.84) (3,596.91) (361.44) Maximum 5,128.98 2,505.62 5,991.60 PAGE 133 133 Table 4 11 Simulated NPV of a strict fertilizer level determined at the $12/cwt sale price Linear Stochastic production Function, optimum N fertilizer rates, various output prices Fertilizer Level=204.94 lb N / acre Mean Output price $16 Mean 2,868.02 2,884.58 Standard Devia tion 976.77 969.67 Coefficient Var. 34.06 33.62 Minimum (199.51) (192.27) Maximum 6,111.92 6,249.46 PAGE 134 134 Figure 4 1. The counties of Tri County Agricultural Area and agricultural areas PAGE 135 135 Figure 4 2. Potato y ield and n itrogen u se d ata (per acre) for Tri County Agricultural Area Figure 4 3. Potato a creage and t otal p roduction in Tri County Agricultural Area PAGE 136 136 Notes: Based on Tembo et al. (2008). Figure 4 4. Plateau shift for the stochas tic function due to weather effect Figure 4 5. Predicted and a ctual y ields given historic weather conditions and fertilizer use Fertilizer Level Optimal Fertilizer Level Yield No Leaching Rain Heavy Leaching Rains PAGE 137 137 Figure 4 6. Predicted, actual and forecasted yields Figure 4 7. CDFs of s imulated n et p resent v alues for v arious f ertilizer u se d ecisions PAGE 138 138 Figure 4 8. PDF approximations of simulated net present values of optimum nitrogen levels at various output prices PAGE 139 139 CHAPTER 5 CONCLUSION The three essays in this dissertation explore a few of the many issues related to the mana gement of risk and uncertainty in agricultural production The particular emphasis is on global competition, trade negotiations and environmental policies. In the first essay, the trade conflict between the U.S. and Mexico tomato producer s in the winter t omato market is examined. The renegotiated suspension agreement for the antidumping investigation raises the reference prices of Mexican tomatoes by 50% 300% as compared with the previous agreement depending on tomato category (US DC, 2013). This agreeme nt distinctively covers four different tomato categories including open area (i.e., field grown) controlled environment (i.e., greenhouse production) specialty loose and specialty packed tomatoes Although this study confirms the importance of catego riz ing tomatoes, it also emphasizes the significant substitution and complementary effects between these categories. For instance, an increase in total consumer expenditure for field grown tomatoes would increase the demand for U.S. tomatoes more than the dem and for imported tomatoes (see the result of the aggregate analysis, Chapter 2) However, the disaggregated analysis shows that the demand for Mexican greenhouse tomatoes responds similarly to the expenditure change that of U.S. field grown tomatoes. There fore, a policy that increases tomato expenditure would increase the demand for both U.S. field grown tomatoes and Mexican greenhouse tomatoes. Since the beginning of the 21st century, we have witnessed a large increase in the production and mark eting of greenhouse tomatoes, taking market share away from field grown tomato producers. Mexican greenhouse tomatoes are competing with and taking market share from U.S. field grown tomatoes PAGE 140 140 but have led to a growth in production of U.S. greenhouse tomato es. When a sector is in a boom phase of growth (as has been the greenhouse tomato market), it appears that competitive produc ts are complimentary in the market as we see a synergistic relationship between imported and domestically grown greenhouse tomatoes in this analysis. This phase will continue until the market matures and it moves into the bust side of the boom bust business cycle in sector analysis (Schmitz 1995). When the market matures, we hypothesize that U.S. and imported greenhouse tomatoes will shift from being complementary products to being substitutes in the market. Until then, the investment in greenhouse tomato production will continue to grow in the U.S. while the demand for field grown tomatoes continues to shrink. In the second essay, th e investment in Florida greenhouse tomato production is examined This production technology is considered as a strategy to mitigate the impact of the increasing Mexican greenhouse tomato imports producers The NPV anal ysis results suggest that investment in the high technology greenhouse is preferred over regular greenhouse and field grown production (if the crop yield for each technology is fixed at the break even point ) However the investment decision preferences ch anges with an increase in risk aversion coefficient. Stochastic efficiency ranking of the investment decision shows that the high technology greenhouse is preferred by risk neutral and normally risk averse decision makers. However, moderately risk averse decision makers would prefer to invest in a regular Florida greenhouse technology, while extremely risk averse growers would continue to produce field grown tomatoes. These results are consistent with what has been witnessed in tomato productio n in Florida. The increase in greenhouse investment PAGE 141 141 shows that some growers are beginning to take more risk because they find greenhouse investment as a way to compete better in the market. However, at this point in time, the producers continue to choose t o have option open instead of committing to investment in greenhouse technology because of high option values in Florida This explains why there are few g reenhouse operations in Florida. T he risk of the new tomato production technology is related to the p rice, production and financial risks. T herefore, policies or market conditions that decrease these risks ( credit availability, interest rates, insurance, energy prices, high tomato prices, technological advance in greenhouse production etc.) would decrease the option value. In the third essay, an economic model is developed to assist in the development of the fertilizer best management practices. Specifically, the model allows to account for various decision criteria used by producers, alternative specific ations of crop production function, alternative levels of input and output prices risk aversion. The model is applied to examine fertilizer use decisions in potato producing Tri County Agricultural Area (TCAA) in Florida. Overall, the conclusion is that no single fertilizer BMP can be recommended for all growers and all market conditions. The latest BMP regulation developed for TCAA allows farmers to adjust fertilizer application if necessary; therefore, it gives the farmer s the flexibility to avoid reductions in profits associated with restrictive BMP recommendations. This regulation is consistent with the conclusion derived from this study. It is show n that as a part of the BMP development process, state agencies and exten sion agents should attempt to elicit PAGE 142 142 fertilizer use can be critical for high profits s hould be examined. Production function estimation results that are used in BMP development should also be discussed with producers, along with profit variability analysis. Based on the assessed costs and associated water quality improvements, cost effectiv eness of alternative fertilizer recommendation should be evaluated, and the most cost effective recommendation should be identified as the BMP. Overall, the three essays contribute to the economic literature on agricultural risk management, and generate in formation to assist agricultural producers and policy makers. PAGE 143 143 APPENDIX A DERIVATION OF CONSUMPTION MODEL Consumption theory starts with maximization of utility in general form Utility function is assumed to be twice differentiable so that (A 1) There is generalized diminishing marginal utility, so the Hessian matrix of the utility function is negative definite and it is also symmetric. (A 2) We can derive demand equatio n by maximizing the utility function subject to the (A 3) where p i is the price of tomato, q i is exported quantity and M is the total budget: and ( A 4) Next differentiating proportionality (resulting from differentiating q and with respect to p j and M yields: wher e is kronecker delta and ( A 5). PAGE 144 144 (A 6) Solving the matrix, gives the following result: (A 7) Where That yields the following differential demand equation. (A 8) Note that the budget component, is the contribution of good i to the Divisia volume index and also the d ependent variable in the equation. The general system in simple parameterization gives us Rotterdam model and can be written as (A 9) The following conditions are satisfied for the Equation 11; Adding up Homogeneity Slutsky Symmetry i ) and the slutsky price ij ) are calculated by using Barten (1993), in addition, cournot price elasticity (c ij ) is also shown below; (A 10) PAGE 145 145 (A 11) (A 12) Replacing gives us CBS equation; (A 13) The income share elasticity of CBS changes as; (A 14) AIDS model is obtain ed by substituting by ; (A 15) by satisfying the conditions ; Adding up Homogeneity Slutsky Symmetry Elast icities are found as the following formulas; (A 16) (A 17) (A 18) PAGE 146 146 At last, we could get the NBR model by replacing in AIDS model. (A 19) One can write following equation from budget share components (A 20 ) which gives us a relationship between and When we insert equation (A 15) into equat ion (A 20), yields (A 21 ) Thus, t hose four models could be mentioned in a general model (A 22 ) The parameters could be used by restricting and as shown below and even test the demand to find out which model suits well to the given data; Rotterdam and CBS and AIDS and NBR and PAGE 147 147 APPENDIX B BUDGET TABLES FOR ALTERNATIVE TOMATO PRODUCTION TECHNOLOGIES Table B 1. High technology greenhouse production expenses Cost of Goods Sold Unit Quantity Total Cost Materials Plant Material (January / August) Acre 1.00 38,400.00 Substrate Acre 1.00 15,680.00 Fertilization Acre 1.00 99,000.00 Plantprotection chemical Acre 1.00 2,946.53 Plantprotection bio logical Acre 1.00 1,180.67 Small/other materials Acre 1.00 4,800.00 Work by third parties Acre 1.00 800.00 Transport/waste plants Acre 1.00 700.00 Plant i nsurance Acre 1.00 6,000.00 Other cultivation costs Acre 1.00 640.00 Total Materials $ 170,147.20 Energy Gas Boiler Acre 1.00 36,666.67 Electricity Acre 1.00 49,666.67 CO2 Acre 1.00 6,963.84 Total Energy $ 93,297.17 Labor Corporate Labor Acre 1.00 30,113.89 Maintenance and Other Acre 1.00 2,021.07 Harvesting Team Acre 1.00 33,347.60 Cultivating Team Acre 1.00 57,600.40 Packing Team Acre 1.00 8,084.27 Total Labor $ 131,167.23 Sales, General & Administrative General & Administrative Maintenan ce company Acre 1.00 16,576.00 Other costs Acre 1.00 10,000.00 Growing advice Acre 1.00 919.80 Insurance Acre 1.00 2,242.98 General costs Acre 1.00 3,204.32 Real Property Tax (Est.) Acre 1.00 384.53 Unforeseen Expenses (Contingency) Acre 1.00 824.00 Total G&A $ 34,151.64 Sales & Marketing Packing/cask Acre 1.00 19,685.72 Transport (Est.) Acre 1.00 Sales costs Acre 1.00 60,000.00 Sales Commissions Acre 1.00 834.58 $ 80,520.31 Total Annual Production Costs $ 509,283.54 PAGE 148 148 Table B 2. Regular Florida greenhouse production expenses Cost of Goods Sold Unit Quantity Price Total Cost Materials A mix 8 12 32 lbs 4,235.00 1.64 6,945.40 CaNO3 lbs 3,630.00 0.68 2,468.40 Sulfuric acid gal 60.50 24.00 1,452.00 Soap gal 6.05 36.88 223.12 Neem qt 12.10 95.50 1,155.55 DiPel lb 12.10 5.95 72.00 Liquid sulfur qt 12.10 7.95 96.20 Layflat bags each 3,549.29 2.29 8,127.88 Trust (seeds) each 10,648.00 0.44 4,685.12 Speedling flats 128 each 84.70 1.55 131.29 Fafard Germ Mix bag 12.10 15.60 188.76 Greenshield gal 24.20 49.95 1,208.79 Mousetraps pair 36.30 7.95 288.59 IPM box 24.20 Pollentation box 36.30 Total Materials $ 27,043.08 Energy Electricity kwh 158,510.00 0 .11 17,436.10 LP Gas gal 26,196.50 1.55 40,604.58 Total Energy $ 58,040.68 Labor Pre harvest hrs 5,662.80 7.79 44,113.21 Harvest hrs 3,484.80 7.79 27,146.59 Cleanout hrs 435.60 7.79 3,393.32 Total Labor $ 74,653.13 Sales, General & Administrative General & Administrative Analytical services& repairs units 12.10 150.00 1,815.00 Travel milage 2,940.00 0.56 1,646.40 Overhead % 131,011.97 10.00% 13,101.20 Taxes & Insurance % 459,096.72 1.37% 6,289.63 Total G&A $ 22,852.22 Sales & Marketing Delivery costs mi lage 6,000.00 0.56 3,360.00 Packing labor hrs 1,913.63 7.79 14,907.20 Boxes, foams & labels box 21,300.00 0.76 16,188.00 Marketing & miscellaneous box 21,300.00 0.80 17,040.00 $ 51,495.20 Total Annual Production Costs $ 234,084.31 The taxes and insurance are taken as the 1.37% of the total structure cost. PAGE 149 149 Table B 3. Field grown tomato production expenses Cost of Goods Sold Unit Qu antity Price Total Cost Materials Seeds/Transplants Acre 1.00 624.00 624.00 Fertilizer, mixed and Lime Acre 1.00 1,449.25 1,449.25 Fumigant Acre 1.00 736.00 736 .00 Tractors and Equipment Acre 1.00 1,882.29 1,882.29 Tractors and Machinery Acre 1.00 241.65 241.65 Herbicide Acre 1.00 21.40 21.40 Insecticide and Nematici de Acre 1.00 448.85 448.85 Fungicide Acre 1.00 392.21 392.21 Stakes + others Acre 1.00 771.17 771.17 Plastic String Acre 1.00 28.75 28.75 String and Stake Disposal Acre 1.00 123.42 123.42 Pull and Bundle Mulch Acre 1.00 181.50 181.50 Cross Ditch Acre 1.00 27.20 27.20 Tie Plants Acre 1.00 145.20 145.20 Trickle Tube Acre 1.00 145.20 145.20 Total Materials $ 7,218.09 Energy Total Energy $ Labor General Farm Labor Acre 1.00 140.63 140.63 Tractor Driver Labor Acre 1.00 214.29 214.29 Total Labor $ 354.92 Sales, General & Administrative General & Administrative Land Rent Acre 1.0 0 500.00 500.00 Overhead and Management Acre 1.00 3,632.85 3,632.85 Taxes & Insurance % 1.37% Total G&A $ 4,132.85 Sales & Marketing Pick, Pack and Haul Box 1,620.00 2.60 4,212.00 Sell Box 1,620.00 0.15 243.00 Containers Box 1,620.00 0.75 1,215.00 Organization Fees Box 1,620.00 0.09 145.80 $ 5,815.80 Total Annual Production Costs $ 17,521.66 PAGE 150 150 Table B 4. High technology greenhouse construction cost Cost Life Greenhouse Groundwork 40,937.33 20.0 Infrastructure Utility 30,382.79 20.0 Infrastructure Greenhouse European 275,260.57 15.0 Infrastructure Greenhouse US Purchased 83,719.71 15.0 Packing and Warehouse 71,759.40 10.0 Offi ce Area 5,833.33 7.0 Corporate IT and Other Set Up items 8,333.33 3.0 Canteen 1,800.00 20.0 HVAC Installation Heating & CO2 81,382.92 15.0 HVA C Installation Cooling 134,790.66 10.0 Screen Installation 28,695.68 7.0 Electrical Installation 55,542.67 12.0 Water Technical Installation 41,123.47 10 .0 Growing gutters 25,555.47 7.0 Logistics automation greenhouse 26,541.83 10.0 Logistics automation working area 6,673.33 7.0 Other Installations 5,6 00.00 7.0 Unforeseen Investments 21,304.17 12.0 Total Greenhouse Investment $ 945,236.68 PAGE 151 15 1 Table B 5. Regular Florida greenhouse construction cost Cost Life Greenhouse Ground cove r 6,776.00 7.0 Irrigation/fertigation system 20,570.00 7.0 Environmental control 11,047.30 7.0 Warehouse (10'x10') 15,125.00 10.0 Site preparati on + inflation kit 50,299.70 10.0 LP gas heating system 26,402.20 10.0 Plant support system 9,075.00 10.0 Backup generator + electrical 17,545.00 10.0 Labor (const. + equip. install.) 84,700.00 10.0 Greenhouse frame (30x120) 105,270.00 20.0 Total Construction Costs $ 346,810.20 Durables Shade system 30% 6,969.60 3.0 Cooling pads 9,105.25 3.0 Spray mask 798.60 3.0 Emitter & tubing 3,726.80 3.0 Convection tube 3,630.00 3.0 Blower fan 2,795.10 3.0 Thermometer 762.30 3.0 Timer 4,840.00 3.0 Clips 955.90 3.0 String 14,907.20 3.0 Scale 605.00 3.0 pH/EC meter 1,210.00 3.0 Tools 1,028.50 3.0 Poly cover 13,140.60 4.0 Cooling pump 2,148.36 5.0 Cooling fans 19,093.80 5.0 Sprayer 8,820.90 5.0 HAF fans 7,260.00 5.0 Speedling 128 flats 461.62 5.0 Tapener 907.50 5.0 Light meter 1,210.00 5.0 Harvest bins 5,082.00 5.0 Harvest aids 907.50 5.0 Pad curtain 2,420.00 5.0 Total Durables Costs $ 112,786.52 Total Greenhouse Investment + Durables $ 459,596.72 PAGE 152 152 APPENDIX C POTATO PRODUCTION EXPENSES FOR AN ACRE Table C 1. Potato production expenses in TCAA ($/acre) Cost of Goods Sold Unit Quantity Price Total Cost Materi als Seed/Transplants Units 26.00 11.87 308.62 Fertilizer, mixed and Lime Units 1.00 426.24 426.24 Nitrogen lb N/acre 207.26 GRKS(0.60) 124.67 Crop Insurance Units 1.00 35.00 35.00 Cover Crop Seed Units 1.00 20.00 20.00 Herbicide Units 1.00 22.48 22.48 Insecticide and Nematicide Units 1 .00 146.92 146.92 Fungicide Units 1.00 131.55 131.55 Tractors and Equipment Units 1.00 413.98 413.98 Farm Trucks (driver cost included in overhead expense) Units 88.67 0.51 45.22 Aerial Spray Units 1.00 19.50 19.50 Total Energy $ 1,694.48 Labor General Farm Labor Hrs 15.92 7.79 124.00 Tractor D river Labor Hrs 20.54 7.79 160.00 Total Labor $ 284.00 Sales, General & Administrative General & Administrative Analytical services& repairs Units 1.00 100.12 100.12 Land Rent Units 1.00 150.00 150.00 Overhead and Management Units 1.00 445.69 445.69 Taxes & Insurance % 185.00 1.37% 2.53 Total G&A $ 698.34 Sales & Ma rketing Dig and Haul Box 268.53 0.70 187.97 Grading Box 268.53 0.30 80.56 $ 268.53 Total Annual Production Costs $ 2,945.36 The taxes and insurance are taken as the 1.37% of the total durable cost. Source: E nterprise budget information for potato production is constructed by authors by using experimental plot data and Florida research center and UF/FRED published data (Smith and VanSickle 2009). PAGE 153 153 APPENDIX D SA S CODES FOR ESTIMATING PLATEAU FUNCTIONS *** Straight with a random component included; Data one; *Hastings,Fl Potato Production Data; input n yield rain ; proc nlmixed data=one noad hess qmax= 199 tech=trureg gconv=.00000000001; PARMS b0=30.8 b2=.5 plateau =30.43 s2u=21.2 s2e=1.2; **Rescaling; s2u_actual=s2u*100; s2e_actual=s2e*100; mean = min(b0 + b2*n, plateau + U); model yield ~normal(mean,s2e_actual); random U ~normal(0,s2u_actual) subject= rain ; /*optimal N equation */; estimate 'optimal N' (1/b2)*(Plate au b0+sqrt(s2u_actual)*probit(1 .6/(14*b2))); estimate 's2u_actual' s2u*100; estimate 's2e_actual' s2e*100; RUN; *** Quadratic with a random component included; Data one; *Hastings,Fl Potato Production Data; input n yield rain ; proc nlmixed data=one no ad hess qmax= 199 tech=trureg gconv=.00000000001; PARMS b0=40.8 b1= .01 b2= .001 plateau=60.5 s2u=20.25 s2e=.6; **Rescaling; s2u_actual=s2u*100; s2e_actual=s2e*100; mean = min(b0 + b1*n + b2*n*n plateau + U); model yield ~normal(mean,s2e_actual); random U ~normal(0,s2u_actual) subject= rain ; /*optimal N equation */; estimate 'optimal N' (1/(2*b2))*( b1 sqrt(b1*b1 4*b2*(b0 Plateau sqrt(s2u_actual)*probit(1 .6/(14*(b1+2*b2* 20 1)))))); estimate 's2u_actual' s2u*100; estimate 's2e_actual' s2e*100; RUN; PAGE 154 154 APPE NDIX E FINANCIAL SHEET FORMULATIONS Stochastic Variables Grower Price t = Mean Price t [1 + MVE ( S i F ( S i ), C 8 )] (E 1) Potato Yield t = (E 2) Input Price t = GRKS (minimum, middle, maximum) (E 3) Receipts Potato Product ion t = Potato Yield t Grower Price t (E 4) Expenses Fertilizer Cost t = Nitrogen Used t Fertilizer Price t (E 5) Marketing Cost t = Potato Yield t Marketing Expense t (E 6) Total Variable Cost t = Potato Production Cost t + Fertilizer Cost t + M arketing Cost t (E 7 ) Other Costs Debt Interest t = Principal Owed t Fixed Interest Rate t (E 8 ) Operating Interest t = Total Variable Cost t OP Interest Rate t Fraction of year (E 9 ) Carryover Loan Interest t = Cashflow Deficits t 1 OP Interest Rat e t (E 10 ) Total Interest Cost t = Debt Interest t + Operating Interest t + Carryover (E 1 1 ) Loan Interest Total Expenses t = Total Variable Cost t + Total Interest Cost t + Depreciation t (E 1 2 ) Net Returns t = Total Receipts t Total Expenses t (E 1 3 ) Net Cash Income t = Total Receipts t Total Variable Costs t Total Interest Cost t (E 1 4 ) Cashflow Cash Inflows t = Net Cash Income t + Positive Cash Reserves t 1 (E 1 5 ) Principal Payment t = Fixed Annual Payment Debt Interest t (E 16 ) Federal Inc ome Taxes t = Positive Net Returns t Income Tax Rate (E 17 ) Cash Outflows t = Principal Payment t + Repay Cashflow Deficit t 1 + Capital Replacement t + Federal Income Taxes t (E 18 ) Ending Cash t = Cash Inflows t Cash Outflows t (E 19 ) Balan ce Sheet Assets t = Land Value + Value Firm t + Positive Ending Cash t (E 20 ) Liabilities t = Debt Interest t 1 Principal Payments t + Negative Ending Cash t (E 21 ) Net Worth t = Assets t Liabilities t (E 22 ) Financial Ratios NPV = Beginning Net W orth Net Worth i ) / (1 + 0.10) ^(years) (E 23 ) PAGE 155 155 LIST OF REFERENCES Asymmetry, Partial Moments, and Production Risks American Journal of Agricultural Economics 92(2010 ): 1294 1309. 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Serhat's research focuses on three key areas: agricultural decision making under uncertainty, agricultural demand modeling, and land allocation dynamics. He has applied his analytical and quantitative skills to the projects about water quality policy for agricultural areas; stochastic production function modeling; investment under uncertainty; international trade; differential demand and production systems; and agricultural land allocation. For the las t three years, Serhat served as a teaching assistant for PhD level econometrics, price analysis and macroeconomics, leading laboratory sessions, holding stems from his work on multi disciplinary projects on alternative production methods for Florida vegetable production. Serhat also served as a president of the Graduate Student Organization, and a member of the Academic Committee. Serhat worked as a researcher in the multinat ional EU projects focused on traceability, logistics and food quality schemes having primary duties on public survey design, administration, and analysis, public outreach, project management, budget analysis, and development of funding proposals. 