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1 THREE ESSAYS ON THE ECONOMICS OF DISEASE MANAGEMENT IN PERENNIAL CROPS: A FRAMEWORK FOR DETERMIN IN G THE PERIOD WHEN AN ORCHARD (PLANTATION) IS NO LONGER PROFITABLE AFTER AN OUTBREAK By MAURICIO MOSQUERA MONTOYA 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
2 2013 Mauricio Mosquera Montoya
3 To my wife Diana and my children, Manolo and Fede
4 ACKNOWLEDGMENTS I would like to thank my Committee Chair, Dr. Edward Evans for his guidance and encouragement over the last few years. He introduced me to the way research is done in the United States. Together, we worked on papers that were accepted for academic meetings held in Saint Vincent and the Grenadines (Caribbean Agricultural Economics Association Meetings 2011) and in Al abama (Southeastern Agricultural Economics Association Meetings 2012). He trusted my work and helped me improve its quality. In addition, he helped me define my dissertation topic. I also would like to thank my Committee Co Chair, Dr. Thomas Spreen. He gav e me guidance when I needed it most, and reassured me when I was struggling with academic life in the United States. Dr. Spreen played a crucial role as my counselor by helping me to choose the right classes and to sharpen my research question. He may be u n aware, but I learned a lot from our long and enjoyable conversations at his office. I also thank Dr. Kelly Grogan, member of my Committee, who worked very close ly with me on my dissertation topics, especially on the empirical application of the model prop osed here to Pudricin del Cogollo in oil palm plantations. An earlier version of this work was accepted for presentation in Seattle (Agricultural and Applied Economi c s Association Meetings 2012). She cleared the main technical obstacles when I was feeling that I was facing a dead end. I will always appreciate how prompt she was in providing feedback to my work and that she taught a class on Disease Economics, just for me. I thank Dr. Pilar Useche, member of my Committee, because she taught me a class on de mand estimation, and from that class, I learned that the information requirements to carry out a state of the art demand analysis were not available for the
5 goods in which I was interested. I will always appreciate that she was there to act as a counselor and helped me to choose appropriately my dissertation topic. I thank Dr. Richard Weldon whose comments on my work opened an interesting field to which otherwise I would not have paid much attention. I am referring to the relevance of choosing a discount ra te. I also thank Dr. Ploetz whose input as Plant Pathologist certainly improved the quality of this work. He provided me with academic work that helped me clarify concepts from areas of knowledge far from my understanding such as disease control strategies taxonomic concepts and tropical diseases in perennials. I thank Cenipalma, the Fulbright Commission, Colciencias LASPAU, and Colfuturo because they awarded me with scholarships that allowed me to come to the United States and cover ed my living and tui tion expenses I will be always grateful to Dr. Jose Sanz and M Sc. Jorge Alonso Beltran from Cenipalma for their support. I thank my parents Dolly and Ricardo for giving me the education they did, for teaching me to work hard to accomplish my goals, fo r their financial support and for listening to me when I needed it the most. I am also grateful to my parents in law Martha and Gilberto, because of their moral and financial support. Finally, I thank my wife, Diana, and my children on the challenge of living in a different culture with me. I am proud of them succeeding in the USA, where we are out of our T hey were always supportive, gave me a reas on to do my best every day, and helped me put my mind somewhere other than academics. We, as a family, certainly have had very good times and have loads of good memories.
6 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 8 LIST OF FIGURES ................................ ................................ ................................ ........ 10 ABSTRACT ................................ ................................ ................................ ................... 11 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 13 2 FIRST ESSAY: THEORETICAL APPROACH TO DISEASE MANAGEMENT IN PERENNIAL CROPS ................................ ................................ .............................. 17 The Problem Faced ................................ ................................ ................................ 17 Pest Management Theoretical Approaches ................................ ............................ 18 Economic Threshold Models ................................ ................................ ............ 19 Decision Theory Models ................................ ................................ ................... 19 Behavi oral Decision Models ................................ ................................ ............. 20 Optimization Models ................................ ................................ ......................... 20 Models evaluating the productivity of pest control strategies ..................... 21 Reduced form of damage function ................................ ............................. 23 Structural damage function ................................ ................................ ........ 23 Invasive species ................................ ................................ ......................... 24 Main Findings from the Theoretical Approaches to Pest Management in Economics ................................ ................................ ................................ ..... 26 Proposed Theoretical Approach ................................ ................................ ............. 28 Model without Disease ................................ ................................ ..................... 29 Model with Disease ................................ ................................ .......................... 31 Concluding Remarks to the Proposed Theoretical Approach ................................ 35 3 SECOND ESSAY: EMPIRICAL APPLICATION OF THE PROPOSED MODEL TO CONTROL OF PUDRICION DEL COGOLLO IN COLOMBIAN OIL PALM PLANTATIONS ................................ ................................ ................................ ....... 37 Motivation ................................ ................................ ................................ ............... 37 The Colombian Oil Palm Industry ................................ ................................ ........... 37 Pudricin del Cogollo (PC) ................................ ................................ ...................... 38 Empirical Models ................................ ................................ ................................ .... 40 Scenario without PC ................................ ................................ ......................... 40 Scenario with PC ................................ ................................ .............................. 41 Data ................................ ................................ ................................ ........................ 45 Results and Discussion of the Empirical Application of the model to PC ................ 48
7 Results without PC (Optimal Replanting Period) ................................ .............. 48 Results with PC ................................ ................................ ................................ 49 PC disease s teady state ................................ ................................ ............ 49 Tree removal period ( ): model with PC ................................ ............ 51 Comparison among results from both models ................................ .................. 53 Concluding Remarks to the Empirical Application of the Proposed Model to Pudricin del Cogollo Threatening Colombian Oil Palm Plantations ................... 54 4 THIRD ESSAY: EMPIRICAL APPLICATION OF THE PROPOSED MODEL TO CONTROL OF LAUREL WILT IN THE FLORIDA AVOCADO INDUSTRY ............. 73 Motivation ................................ ................................ ................................ ............... 73 Overview of the Florida Avocado Industry ................................ .............................. 74 Laurel Wilt (LW) ................................ ................................ ................................ ...... 75 LW Management ................................ ................................ .............................. 77 Potential Economic Impact of LW on Commercial Avocado ............................. 79 Empirical Models ................................ ................................ ................................ .... 80 LW Free: Optimal Replanting Time ................................ ................................ .. 81 Model with LW ................................ ................................ ................................ .. 82 Period in which costs exceed revenue and NPV calculations .................... 82 Considered scenarios for the model with LW ................................ ............. 84 Data, Parameter Values and Model Calibration ................................ ...................... 85 Economic Data and Parameters ................................ ................................ ....... 85 Biological Data and Parameters ................................ ................................ ....... 86 Results and Discussi ons ................................ ................................ ......................... 87 Base Case Scenario: LW Disease Free ................................ ........................... 87 Do Nothing ................................ ................................ ................................ ....... 87 Fully Effective ................................ ................................ ................................ ... 88 Intermediate Effectiveness ................................ ................................ ............... 89 Low Effectiveness ................................ ................................ ............................ 90 Concluding Remarks to the Empirical Application of the Proposed Model to Laurel Wilt Threatening South Florida Avocado Orchards ................................ ... 91 5 CONCLUSIONS ................................ ................................ ................................ ... 111 APPENDIX A MODELS USED TO PARAMETERIZE THE MODELS ON PUDRICI"N DEL COGOLLO ................................ ................................ ................................ ............ 117 B MODEL USED TO PARAMETERIZE THE MODEL ON LAUREL WILT (NO DISEASE SCENARIO) ................................ ................................ ......................... 121 LIST OF REFERENCES ................................ ................................ ............................. 124 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 129
8 LIST OF TABLES Table page 3 1 Parameters used for estimation (PC models) ................................ ..................... 56 3 2 Optimal replanting period (PC free) ................................ ................................ .... 57 3 3 Optimal T for selected values of a ccording to different combinations of net price and discount rate ................................ ................................ ....................... 58 3 4 Oil palm standings lifespan ) for selected values of according to d ifferent combinations of net price and discount rate ................................ ......... 59 3 5 Comparison among optimal ( ) from the model with PC, and optimal replanting from the model without PC at discount rate equal to 0.4% per month ................................ ................................ ................................ ................. 60 3 6 Comparison among optimal ( ) from the model with PC, and optimal replanting from the model without PC at discount rate equal to 0.8% per month ................................ ................................ ................................ ................. 61 3 7 Comparison among o ptimal ( ) from the model with PC, and optimal replanting from the model without PC at discount rate equal to 1.25% per month ................................ ................................ ................................ ................. 62 3 8 Comparison among optimal ( ) from the model with PC, and optimal replanting from the model without PC at net price equal to $56 ......................... 63 3 9 Comparison among optimal ( ) from the model with PC, and optimal replanting from the model without PC at net price equal to $108 ....................... 64 3 10 Comparison among optimal ( ) from the model with PC, and optimal replanting from the model without PC at net price equal to $160 ....................... 65 4 1 Potential direct impact from a Laurel Wilt outbreak on the Florida avocado industry ................................ ................................ ................................ ............... 94 4 2 ........... 95 4 3 Scenarios cons idered with respect to LW control strategy ................................ 96 4 4 Period at which net returns become negative according to age at LW initial infec tion, assuming 5% cost increase, and =1% ................................ ............. 97 4 5 Period at which net returns become negative according to age at LW initial infection, assuming 10% cost increase, and =1% ................................ ........... 98
9 4 6 Period at which net returns become negative according to age at LW initial infection, assuming 5% cost increase, and =10% ................................ ........... 99 4 7 Period at which net returns become negative according to age at LW initial infection, assuming 10% cost increase, and =10% ................................ ....... 100 4 8 NPV according to age of initial infection and control strategy scenarios, assuming control strategy increases costs 5%, and =1% ............................. 101 4 9 NPV according to age of initial infection and control strategy scenarios, assuming control strategy increases costs 10%, and =1% ........................... 102 4 10 NPV according to age of initial infection and control strategy scenarios, assuming control strategy increases costs 5%, and =10% ........................... 103 4 11 NPV according to age of initial infection and control strategy scenarios, assuming control strategy increases costs 10%, and =10% ......................... 104 4 12 Decision rules for the model with LW. Period at which net return becomes negative, and NPV calculations (considered simultaneously) ........................... 105 A 1 OLS estimates of the effect of age and age squared on yield .......................... 117 A 2 OLS estimates of the effect of number of diseased trees and number of diseased trees squared on potential yield ................................ ........................ 118 A 3 OLS estimates of the effect of number of treated trees on PC control costs .... 119 A 4 OLS estimates of the effect of cumulative PC cases on new PC cases ........... 120 B 1 OLS estimates of the effect of age and age squared on yield .......................... 121 B 2 Parameters used for the model ................................ ................................ ........ 122 B 3 Costs per acre of producing avocado in South Florida ................................ ..... 123
10 LIST OF FIGURES Figure page 3 1 Solution for according to yield (which in turn is a function of age) ................ 66 3 2 Sensitivity analysis for varying discount and ceteris paribus for a high yield oil palm standing ................................ ................................ ................. 67 3 3 Sensitivity analysis for varying discount rate and PC disease spreading rate at = (yield at = 3640 kg/hectare) ................................ 68 3 4 Sensitivity an alysis for varying discount rate and net price at = (yield at = 3064 kg/hectare) ................................ ................................ .. 69 3 5 Optimal solution for scenario with PC. ................................ ................................ 70 3 6 Optimal ( ) from the With PC model according to discount rate, holding constant the net price at $108 per kilogram of oil palm fruit ................................ 71 3 7 Optimal ( ) from the With PC model according to price, holding constant the discount rate at 0.8% per month ................................ ................................ ... 72 4 1 Disease incidence along time according to the considered laurel wilt possible spread rates (Gompertz) ................................ ................................ .................. 106 4 2 Period at which net returns become negative according to age at LW initial infection, assuming 5% cost increase, and =1% ................................ ........... 107 4 3 Period at which net returns become negative according to age at LW initial infection, assuming 10% cost increase, and =1% ................................ ......... 108 4 4 Period at which net returns become negative according to age at LW initial infection, assuming 5% cost increase, and =10% ................................ ......... 109 4 5 Period at which net returns become negative according to age at LW initial infection, assuming 10% cost increase, and =10% ................................ ....... 110
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 THREE ESSAYS ON THE ECONOMICS OF DISEASE MANAGEMENT IN PERENNIAL CROPS: A FRAMEWORK FOR DETERMINING THE PERIOD WHEN AN ORCHARD (PLANTATION) IS NO LONGER PROFITABLE AFTER AN OUTBREAK By Mauricio Mosquera Montoya May 2013 Chair: Edward A. Evans Cochair: Thomas H. Spreen Major: Food and Resource Economics A decision making framework was developed for disease management of perennial crops that addressed significant production aspects. Key factors that distinguish perennial crop systems from those for annual crops include the need for long term disease control measures the greater potential for development of pesticide resistance by pathogens and the management of disease predisposing factors such as water excess or nutritional stress that may occur over multi year rotations Complicating matters further is the fact that diseased trees may still bear fruit Thus, growers must decide whether to destroy individual tree s, replant the entire orchard or try to maintain productivity of the trees at a profitable level while run ning the risk of further spread of disease and damage by the pest. T heoretical approaches from the economics discipline on plant disease control are explored. They emphasiz e the suitability of each approach with respec t to analyzing the economics of pest control on perennial crops. It is assumed that the grower had a plan in terms of when to replant under disease free circumstances, so a theoretical
12 model is developed to determine the optimal replanting period. The latt er constitutes the theoretical approach is developed for finding the optimal age to remove an orchard after a di sease attack that Empirical applications of these models are presented for two cases. The first relates to p udricin del c ogollo which threatens oil palm plantations in Colombia. The second relates to laurel wil t, which threatens avocado orchards in South Florida.
13 CHAPTER 1 INTRODUCTION Agricultural activity can disrupt the delicate equilibrium of natural ecosystems by eliminating or providing feeding sources for some species that directly affect s their environmental carrying capacity. 1 This in turn can enable organisms that were not cons idered to be pests before the introduction of the crop to become pests as a result of them outnumbering their natural predators 2 or due to radial increases in the prevalence of a susceptible host. Additionally, a crop may host invasive species that increas ingly represent major threats for agriculture. Moreover the development of high yielding and/or pest resistan t varieties while being desirable from technical and cost effective point s of view, modifies natural landscape s by encouraging the cultivat ion of large areas with identical germplasm. Monoculture production increases risks considerably should the crop succumb to a particular pest or disease. Agricultural activity is not the only thing t hat upset s the natural equilibrium. Pest problems have intens ified in the last decades due to globalization and international trade. Increased international trade (and movement of people) has been associated with the introduction and spread of invasive alien species (foreign pests and diseases). Pests and diseases h ave the potential to destroy agricultural industries in a short time and to cause considerable environmental damages, thus turning what might have been a profitable operation into an unprofitable one. Evans (2003) identified six types of economic impacts a ssociated with a pest outbreak. These include: a) production (yield 1 The carrying capacity is the maximum population size of the species that the environment can sustain indefinitely. It considers available food, habitat and water requirements. 2 ( such as insect, bacteria, fungus, rod ent, bird, plant, etc.) likely to cause economic damage.
14 decline and costs increase); b) price and market effects (demand and supply); c) trade (policy responses of trading partners to pests outbreaks); d) food security and nutrition (local econ omy dependence upon the threatened crop in terms of income generation or as a source of staple food); e) human health and the environment (possible negative externalities from using pesticides or other pest control methods such as removing riparian vegetat ion); and f) financial cost impacts (assumed by the public sector). O ften growers are the ones who are left to bear the brunt of costs resulting from outbreaks and who must employ various tactics (range of management options) to control costs in an effici ent and cost effective manner. However deciding on a particular course of action can be extremely challenging especially when the crop in question is a perennial rather than an annual. There is a need to develop a specific framework for decision making on disease management for perennial crops. When compared to annual crops, p erennials require long term disease control measures ; have an increased risk of development of pesticide resistance ; and may be exposed to disease predisposing factors such as wate r excess or nutritional stress over multiple years (Ploetz 2007) Additionally, most research analyzing pests in perennial crops focus on assessing the disease economic impact, rath er than evaluatin g pest control strategies in perennials. Studies related to economic analysis of pest and disease infestation in perennial plants can be classified into two broad categories: farm level and market level. In market level studies, the impact of the disease on aggregate supply is model ed and then its impact on pri ces is estimated. Farm level studies may well be at the field level in
15 which a hypothetical planting of a particular crop is considered. In these studies, the market impacts of the disease are not considered ( i.e., crop prices are assumed to be fixed ) In t his study measures are evaluated that mitigate disease at the field level. The goal of this work is twofold. The first goal i s to develop a theoretical framework that provides growers with guidance as to when a grove is no longer profitable in the presen ce of disease, given that disease infestation affects crop yield and production costs. The second goal i s to demonstrate how the framework developed could be used in empirical applications. Th is work is organized as follows. Chapter 2 present s an essay th at propose s a theoretical approach to disease management in perennials by means of finding the optimal period to either replant a disease free orchard or discontinue production after a lethal and contagious disease attacks an orchard. Additionally, Chapter 2 highlight s the need for developing this theoretical framework as well as various theoretical approaches that have been proposed to evaluate the economics of managing pests on perennial crops S alient features of each approach are explored while emphasi z ing their suitability for analyzing the economics of pest management on perennial crops. Chapter 3 corresponds to an essay describ ing an empirical application of the proposed Theoretical Framework developed in Chapter 2. This empirical application assess es to which extent and under what conditions the pudricin del c ogollo (PC) control strategy proposed by Cenipalma is feasible and cost effective in Colombian oil palm plantations Chapter 3 refers to the economic and social importance of the Colombian oi l palm industry, and present the main features of pudrici n del c ogollo (PC) It also
16 present s the empirical model used, the data sources used for parameterizing the empirical model and the results obtained. Chapter 4 presents an essay c orrespond ing to an empirical application of the proposed Theoretical Framework to studying the case of laurel wilt (LW) threatening South Florida avocado orchards. This chapter illustrates that even lacking crucial information it is possible to provide guidance for scienti sts and growers by means of using the model proposed in Chapter 2 Regarding scientists interests the empirical model developed here helps in setting goals for a control strategy in terms of disease spread rate and maximum cost of treatment. Considering growers interests the model helps in understanding at which period of time after LW attacks their avocado orchards are no longer profitable and it would be better to abandon avocado growing. Additionally, Chapter 4 discusses the main features of the South Florida avocado industry, as well as the main LW aspects. Then the empirical approach is presented and the results are obtained. Chapter 5 presents the general conclusions to this research, the possible applicatio ns of the developed framework, and the future research agenda
17 CHAPTER 2 FIRST ESSAY: THEORETICAL APPROACH TO DISEASE MANAGEMENT IN PERENNIAL CROPS The Problem F aced Most pest studies in the literature that deal wit h perennials or tree crops assess resultant yield reductions and/or economic damages. L ittle research has been conducted on decision making framework s that would help growers choos e management strateg ies when a pest is present (Mumford and Norton 1984; Marsh, Huffaker and Long 2000; Spreen, Zansler and Muraro 2003; Cobourn et al. 2008) Disease management strategies in perennial crops may include avoidance, exclusion, eradication, protection and treatment of diseased plants ; these strategies are non exclusive (Ploetz 2007) Avoidance limit s the chances of introducing the pathogen or refrain s from providing the conditions that are needed for its development. In this category, we may find strategies such as selectin g planting site s managing predisp osing factors, us ing pathogen free soils in nurseries and us ing pathogen free host plants Exclusion keep s pathogens out of fields by scouting, early detection, avoiding contaminated germplasm, and disinfest ing machinery and tools. Eradication remove s and dest roys infested plants/ tissues from fields. Finally, protectin g the host from pathogens includes a wide range of biological, chemical and host resistance strategies (Ploetz 2007) The present research focused on developing a framework that would facili tate economic evaluation of disease management in perennial crops. It considered the above pathogen considerations, as well as economic factors that are peculiar to these crops. U nlike row or field crops perennial s involve long term investment s that require substantial initial outlay s of capital. They usually do not reach maturity /produce fruit for
18 several years, and once these operations are established they are costly to amend or re establish Complicating matters further is the fact that dis eased trees may still bear fruit albeit at lower yields and /or reduced market value/quality Thus, growers must decide whether to destroy individual tree s, to replant the entire orchard or to continue p roducti on while risking further damage by and spread of the pest I f sanitation is considered ( destroy many questions must be answered such as 1) H ow many trees can be removed for the operation to still remain profitable ? 2) At what stage of pest incidence is i t better to replant the entire orchard? 3) Are the benefits of control and eradication measures worth the cost of implementation? An appropriate approach to the economic evaluation of disease management in perennial crops must consider all of the above fa ctors. Pest Management Theoretical Approaches The economics discipline has developed a set of analytical capabilities that can facilitate rational and consistent decision making These analytical capabilities consider a range of pest threats and management interventions monetary valuations cost benefit analysis as a tool to evaluate public intervention strategies allocation of scarce resources and formal consideration of risk and uncertainty (Evans 2003) Mumford a nd Norton (1984) state d that modeling approaches to decision making on pest management may be synthesize d into four types: 1) Economic T hreshold Mode l, 2) Decision Theory 3) B ehavioral D ecision Models and 4) O ptimization Models T hese approaches are revi ewed briefly to assess their suitability for the problem at hand.
19 Economic Threshold Models T his approach was advanced by entomologists and plant pathologists and involves monitoring the pest population and using a pest control strategy, which usually en tails pesticide applications. For these models to be effective in terms of supporting decisions, it is necessary to establish criteria that indicat e the maximum pest population that can be tolerated. The approach is based on the idea that while all levels of pest infestation can cause injury not all levels of injury cause economic damage. Thus the benefits associated with treatment (damages averted) should be greater or at least The main drawbacks of using an econo mic T hreshold M odel for decision making is the vast amount of information that is usually required in order to determine the threshold level. Accurate data and full knowledge about the effectiveness of the control strategy (treatment) are needed. At the sa me time such determination is made more difficult as the use of pesticides may encourage the pest to develop resistance which in turn affects the efficacy of the treatment and the threshold level. Additionally, the Threshold Model is often used for pest s that damage output but do n o t kill the tree ; at some point the value of lost output exceeds the cost of control. Since perennials produce for multiple seasons current damage potentially has a large effect when considering the entire productive life of t he tree. Since d etermining a threshold is more complicated for perennials than it is for short term crops the Threshold Model is often not well suited to analyzing diseases of perennial crops Decision Theory Models Carlson (1970) introduced uncertainty into the pest management literature. He did so by assuming that different pest population levels are states of the world and
20 a ssigned an occurrence probability. Assigning such probabilities in an objective manner relies on past realizations. When s can be substituted to give subjective probabilities. In this type of model, the assumed to be monetary income) by considering all payoffs and choosing the best payoff. Carlson (1970) indicated that risk averse growers may not maximize expected utility but rather minimize varianc e (mean variance criterion). The main drawback of e probabilities for each state of the world, a p oint conceded by Carlson (1970 ) in explaining why little empirical work follows this approach. Behavioral Decision Models T hese models originated from a need to understand why pesticide use displays a great deal of variation among farmer s growing the same crop (Mumford and Norton 1984) The premise of these models is that gro wers tend to make their pest control decisions based solely on their own previous experience and their attitude towards risk. This explains why growers decisions tend to remain constant across time (i.e. are standardized) which reduces the ir effort i n de cision making. This theoretical approach is not very appealing for dealing with control strategies for diseases in perennials because it ignores key aspects such as the effectiveness of control strateg ies disease incidence levels, cost efficiency, and the dynamic nature of diseases in perennials. Optimization Models Optimization Model s result from the joint work of scholars from diverse disciplines such as agricultural economi c s, agronom y plant patholog y plant physiolog y
21 mathematics, and ecolog y each attempts to develop an optimal pest control strategy. F our types of Optimization Model address the following : 1) evaluation of the productivity of pest control strategies, 2) reduced form damage, 3) structural form damage, and 4) examination of elements of th e se models with respect to Pudricin del Cogollo (PC) and l aurel w ilt. Models evaluating the productivity of p est c ontrol s trategies Lichtenberg and Zilberman (1986) studied the economics of pest management and indicated that potential output and abatement were of crucial importance during model development Potential output is defined as the maximum output that is obtainable in absence of pest attacks. Pest damage reduces output relative to the ma ximum possible output and d amage control inputs mitigate the se reduction s. Abatement is defined as the efficacy of specific control strategies in ameliorating pest damage. When modeling pest management, it is important to take into account the developmen t of tolerance or resistance to some pesticides in target species When this occurs these compromised inputs become increasingly ineffective. The abatement concept addresses a paradoxical phenomenon : g rowers often increas e the amount of pesticide that they use when its effectiveness declines If a model ignores pesticide abatement capacity and only considers the amount of the input, it will have a reduced ability to account for this behavior. If pesticides are treated as an input that directly cont ributes to productivity ( e.g. fertilizer) a compromised (ineffective) marginal impact on productivity will be overestimat ed with the possibility for corresponding flawed decisions For instance, one may recommend intensive pesticide
22 applicati on, even in cases of pesticide overutilization (Lichtenberg and Zilberman 1986) It should be noted that the abatement function concept is very useful when considering diseases in perennials, since the cost eff e c tiveness of pest control strategies often re lies on timely detection. This approach has been used by Brown Lynch and Zilberman (2002) to analyze two pest control strategies for Pierces d isease (PD) in vineyards in California. The first strategy consist ed of removing from riparian areas plants tha t host the causal bacteri um ( Xylela f astidiosa ) and its sharpshooter leafhopper vector s Since e arlier research had shown that the probability of an infectious in sect transmitting the bacterium is quite high (about 90% ), activities that reduced their potential contact with host plants were clearly desirable The second strategy consist ed of placing a barrier between the vineyards and the riparian area whose effectiveness is assumed to depend on its width Brown Lynch and Zilberman (2002) built on th e spatial model of optimal water conveyance (Chakravorty, Hochman and Zilberman 1995) Their main contribution to the literature was the introduction of an insect migration function, which in turn is a function of distance and the (i.e. its abatement capacity). They also estimated the difference in outcomes when consider ing the grower welfare (maximizing profit ) versus the social welfare (maximizing profit considering externalities) where the former only maximiz es profit and the latter maximiz es profit while consider ing positive attributes associated with riparian vegetation. These models assess the effectiveness of a given control strategy, whereas the present research assess es the point in time when profit will be maximized as suming that effective control/treatment options exist
23 Reduced form of damage function Literature on pest management tends to link biological and economic systems through damage functions (Jetter, Sumner and Civerolo 2000; Alamo et al. 2007) A commonly used approach for specifying a damage function assumes that yield loss is a function of pest population. In other words, there is a known parameter relating pest population and economic damage These models can be used to assess welfare effects due to a di sease outbreak and their consequent effects on prices, which in turn affect supply and demand, but they are less useful for assessing direct impacts of diseases on perennial production since they ignore the time dimension. Moreover, care must be exercised when using reduced damage function models to en sure that they are appropriate for the problem at hand. Structural damage function T o overcome the lack of dynamics in reduced damage function models, scholars developed structural damage function models that endogenized pest behavior. For example Cobourn et al. (2008) built a theoretical model for studying olive orchards threatened by the olive fruit fly. Their model specifie d fruit damage at a time and location as a function of climate variables, fruit char acteristics that attract the insect and management practices. By i ncluding space and time dimensions decision maker s could consider damage rates for a given site and when that damage occur red rather than obtaining a cumulative figure for the whole orcha rd. A more rational and cost effective use of pesticides was possible with their model, in that they found that pesticide applications in May and June were not required ( Cobourn et al. 2008). This possibility is very attractive for managing diseases of perennials but is demanding as far as the
24 necessary information (at tree level) and knowledge of the pest (what factors attract the pest under study). A similar study was carried out by Marsh, Huffaker and Long (2000). Th eir model considered relationshi ps among the vector, pathogen and host plant T o validate their theoretical model, the y used P otato leafroll virus (PLRV), its aphid vectors, and potato production data for the s tate of Washington. Although there was an effective control strategy for p ota to leafroll there were three major drawbacks: 1) the vectors developed resistance to the insecticides that were used ; 2) natural predators of the vector were killed with the insecticides; and 3) there were increasing consumer concerns over the high toxic i ty of the insecticides. In the discrete dynamic model of Marsh, Huffaker and Long (2000) net profit wa s maximized by choosing numbers of insecticide applications subject to three constraints: 1) aphid dynamics 2) predator dynamics and 3) quality constr aint s Their results showed that an aphid control strategy that includes both biological and chemical control Natural predators help control aphid re infestations which reduces middle and late season applications of aphicide s Even though this model does not deal with a perennial crop, it is appealing for the present study since it considers time, net revenue and disease vector host dynamics (equation of motion). Invasive s pecies Sharov and Liebhold (1998) studied the gypsy moth in commercial forests in the northeastern U nited States Strategies for this invasive insect have include d combinations of quarantine, detection and eradication of isolated colonies, total a nd include d dynamics, spatial information and net present value for determining the
25 cost benefit value of alternatives. It consisted of a single equation, present value of total net benefits in which t he cost term is a function of control costs, targeted spreading rates, length of population front, distance from introduction point and time and the n et benefits were affected by non colonized area, length of the population front, distance from the introduction point, and time (Sharov and Liebhold 1998) A similar study, in S outhwest Florida citrus orchards examined c itrus c anker ( caused by Xanthomonas citri subsp citri ) a bacterial disease targeted in a federal eradication program ( Spreen, Zansler and Muraro 2003). Citrus c anker is spread by contaminat ed equipment reduces yields (5 30%) and makes symptomatic fruit unacceptable for fresh market. Spreen, Zansler and Muraro (2003) quantified economic loss for grower s with affected trees defin ed as the difference between net present value of destroy ed trees and net present value of replacement trees They considered scenarios in which the eradication program was : 1) effective or 2) in effective (eradication is discontinued and citrus canker is considered endemic) They assumed historical prices and highe r prices that would result from a reduced supply of citrus and focused on processed oranges and fresh and processed grapefruit. Their results highlight ed the importance of future prices on the results. When historical prices were used the loss wa s higher i f eradication w ere successful However, if the authors used a higher optimistic future price higher losses were calculated for the endemic scenario (Spreen, Zansler and Muraro 2003) T his paper also indicated what grower s should be compensated in case o f mandatory eradication.
26 Main Findings from the Theoretical Approaches to Pest Management in Economics E conomic analys e s of pest s and disease s o n perennial plants can be classified into two broad categories: farm level and market level. In t his study measures that mitigate disease at the field level were evaluated Four types of models were identified in the literature for making economic decisions on pest management: Threshold Model s, Decision Theory Model s, B ehavioral M odels and Optimization Model s Threshold Model s are decision rules that consist of using a specific pest control strategy, mainly pesticides, once the pest population reaches certain level. It is assumed that removing the pest from the field is not possible if the crop is to remain cos t efficient, and that intervention is justified only if the marginal cost of the control strategy is less than the economic damage caused by a marginal increase in the pest population. When Threshold Model s we re used to optim ize decision making in perennia ls, they were found to lack dynamics inherent to pest infestation and treat the pest population as exogenous Additionally these models do not recognize that diseased individuals serve as inoculum reservoir s from which neighboring trees can be attacked S ince p erennials have a long lifespan, current damage can have a large effect on the productive life of the tree. Determining a threshold is more complicated for trees than it is for short term crops. Th us, Threshold Model s are ill suited for evaluating dis ease management in perennials. Decision Theory Model s consider possible pest scenarios and control strateg ies, and assign to each a respective probability of occurrence based on either past s In this family of models the a lternative control strategies tend to be variations on the amount of control strategy that is applied (i.e.
27 doses of pesticide). It is assumed that for each combination of control strategy and pest population, there is a known utility valuation ( often net profit). These models yield recommend ed control strateg ies though bringing uncertainty into a model is quite appealing from a theoretical standpoint, determining the utility function for growers and as signing probabilities to possible states are features of these models that have hindered their empirical application. Their adaptation for evaluating disease control strategies in perennials w ill require a stochastic setting that would be complicated by th e numbers of possible paths that would arise over time. T he main goal of b ehavioral models is to determine why grower pest control strategies remain constant through time and their primary finding s are often rule s for control strateg ies that relate to gro wer experience ( i.e., they assume that growers avoid the costs of pest control decision making by relying on past experience ) B ehavioral m odels lack many features that influence disease control in perennials including control strategy effectiveness ; dise ase incidence and severity levels ; cost efficiency ; and the dynamic nature of diseases in perennials. Finally Optimization Model s were considered that included models evaluating the productivity of pest control strategies, reduced form damage function s s tructural form damage functions, and Invasive Species Models Productivity of pest control strategies models include two concepts that are of crucial importance when modeling pest management potential output and abatement. D amage functions link biological and economic systems and can consider a reduced form damage function approach or the structural damage function approach. R educed form damage function s assume that
28 yield loss is a function of exogenous pest population s, and are useful for assessing welfa re effects due to a disease outbreak and their consequent effects on prices, which in turn affect supply and demand. However, they are less accurate for evaluating control strategies at the field level because they ignore pest dynamics In contrast, struct ural damage functions address pest dynamics by endogeni zing pest populations with equations of motion ( information on spread rates ) and environmental and host characteristics that promot e pest attack. Invasive Species Models incorporate temporal and spatia l dimensions of the pest under study to assess the best strategies to reduce the impact of invasive species Of special interest to the present study, t he se models include biological (pest dynamics ) and economic ( net present value ) considerations Proposed Theoretical Approach The developed model seeks to maximize n et p resent v alue (NPV) by determining the optimal time period to replant disease free orchards or destroy plantings in which a lethal and contagious disease is present In the first case, it is a ssume d that replant ing will occur with the same crop and same producti on features whereas i n the second, growers are allowed to change to another economic activity which may be done with a scrap value function The disease and includes the optimal replanting period in the absence of disease. In the disease scenario a disease control strategy must be in place The range of disease control strategies includes th option Since disease affects yield and may increase costs, it is very likely that NPV will be affected. It is of crucial importance that the latter model consider s when in the expected life of a planting that a disease
29 develops/begins to im pact the crop, as this will influence greatly the economics of a given situation. Since the disease free and disease models have the same yield functions, time period s and area units, results from each are comparable. T heoretical features of the models a re presented below Model w ithout Disease Typically perennial crop s require an establishment phase during which yield increases until it enters the production phase during which yield will remain at or near maximum levels Although some perennials can be productive for many years replanting orchards is considered after the ir economic li ves have passed Th us, perennial yield functions are often well represented by concave functions of yearly production over time T he approach of Faustmann (Mitra and Wan 19 86) in a forestry type model is used to address the rotation problem. The present model differs from it in that aggregate income from periodic sales of fruits is considered as opposed to selling all output (wood in the forestry models) in the final period (Clark 2005) For one rotation, the NPV for one rotation is given by: ( 2 1) where is the net price which is defined as the unit price less unit cost of production (for simplicity it is fixed) ; is the production per land unit at period may be interpreted as tree age ) ; represents the time at which the perennial crop needs to be replanted ; is the discount rate ; and represents the repl anting costs. Since one of the concerns is to de termine the optimal age of replanting, specification future income from
30 future projects (rotations ) is include d in the model. This is accommodated here by using perpetual rotations : ( 2 2) ( 2 3 ) If the second term in the above expression can be written as ( 2 4) According to the geometric series formula it was obtained as follows: ( 2 5) ( 2 6) T hen the problem is ( 2 7) The First Order Conditi on (FOC) corresponding to ( 2 7) is ( 2 8) Taking the common denominator of the first two terms it was obtained as follows: ( 2 9) The left hand side (LHS) of E quation 2 9 illustrates the marginal benefit of waiting an extra period in order to replant, while the right hand side represents the marginal cost of doing so. An alternative interpretation comes from rearra nging Equation 2 8 to yield ( 2 10) The LHS of Equation 2 10 represents the marginal benefit of waiting one more period to replant which is the benefit from selling the harvested fruit in that period
31 instead of removing the trees. The RHS of Equation 2 10 represents the marginal cost of waiting an additional year to replant. The first term in the RHS represents the interest on the whole stream of profits (which would be delayed for an ex tra year) and the second term in the RHS or the value at which the bare ground could be sold under perfect land market conditions. At the optimal replanting time, the grower is indifferent between replanting and waiting one mor e period. Model with Disease As mentioned earlier, decreasing yields due to disease and increasing costs resulting from adoption of control strategies impact NPV Thus the optimal period to remove the current standing differs from the optimal replanting p eriod from a non disease situation and determining the time at which this should be done is a key objective of the Model with disease When an orchard is affected by a lethal, contagious disease, the grower must decide when to destroy the orchard or trea t the trees The disease model assumes that a treatment exists that impedes or stops disease progress and may (or may not) allow diseased trees to fully recover. Since treatment has associated costs the grower must find an optimal level of control strate gy (control variable) to keep the number of diseased trees such that NPV is maximized from one rotation to another N et profit will be affected which in turn changes the optimal time for removing the en tire orchard. The model with disease considers a scrap value ( ) unlike the model without disease where perpetual rotations are considered. U nder the scenario with disease, some growers may stop producing the affected crop at the end of the current
32 rotation while others may replant with new ly developed breeds (if available) or the current breed if the control strategy is cost effective The scrap value, determined by land market values, measure s the value of the land conside ring its highest valued use which may or may not include additional rotations (Deininger, Jin and Nagarajan 2008) ( 2 11) Subject to ( 2 12) ( 2 13) ( 2 14) ( 2 15) w here is the net price defined as above is the production per unit of area of a perennial crop at age with disease incidence and age at first disease detection is T his model differs from the disease free model where the age of the trees at its start is 0. A ge and time are measured in the same time units represents control costs as a function of treated diseased tree s is the monthly discount rate and represents the scrap value function N ote that the scrap value function is associated with values at time which correspond to the orchard removal period (Leonard and van Long 1992) Equation ( 2 12) describes PC disease incidence dynam ics and it relates disease control to ; it demonstrates how the control strategy (control variable) influences the number of disease cases (state variable). Equation 2 13 indicates that the number of trees treated ranks from 0 to the total number of diseased
33 trees present in period t Finally, E quations 2 14 and 2 15 are transversality conditions (TC) which indicate that the grower choose s the optimal orchard removal per iod and disease incidence at that point in time rather than set ting predetermined values. In order to solve the opt imization problem expressed in Equation s 2 11 t hrough 2 15 an optimal control problem strategy is used The Hamiltonian 1 for this op timization problem is given by ( 2 16) The optimal solution must satisfy the necessary conditions given by E quation s 2 17 t hrough 2 23 (Leonard and van Long 1992) : ( 2 17) FOC1 equates the marginal cost of disease control to the marginal benefit of reducing the number of diseased trees in every period. ( 2 18) Equati on 2 18 implies that a Current Value Hamiltonian is used as opposed to a Present Value Hamiltonian, in order to facilitate the process of finding the optimal solution. Equation 2 18 indicates that a change in the marginal incr ease in disease cases must be compensated by a change in the costate variable Note that is the value of the costate variable at the optimal solution ( T ) and represents the imputed value (shadow price) of a diseased tree in the field. ( 2 19) 1 The Hamiltonian is a mathematical function used to define the state of the system. For the problem at hand, the Hamiltonian incorporates the objective function at time t (net revenue) and the equa tion of motion (disease along time as a function of control strategy and its abatement on disease incidence.
34 Equation 2 solution. It is important to recall that the equation of motion provides information on the dynamic relationship between disease cases a nd the control strategy. ( 2 20) Equation 2 20 indicates that a decrease in the scrap value due to a marginal increase i n the number of diseased trees equals the negative effect of an additional diseased tree on NPV So a t o ptimal T, the grower is indifferent between making additional disease control effort s for an extra period and the loss of scrap value that would result from a n additional disease d tree ( 2 21) Equation 2 than the marginal effect on scrap value of waiting an extra period to destroy or replant an orchard there is still profit to be made by using the control strate gy and continuing production This means that at optimal T the grower must be indifferent between getting the scrap value and staying in business for an additional period, which is equivalent to ( 2 22) Note that the moment at which disease affects the orchard is of crucial importance and at the optimal solution: ( 2 23) As in the without disease model a necessary condition to optimiz e in the disease case is for to be a concave function, a realistic assum p tion for perennial crops. With this assumption, two important results are obtained: 1) the number of diseased trees to
35 be treated in all periods in order to keep the disease at a level that ensures the NPV maximization goal, also known as the state variab and 2) the period at which it makes economic sense to remove the orchard for each possible initial infection period Concluding R emarks to the Proposed Theoretical Approach Two Dynamic Optimization Models are pr esented using a theoretical framework within which to determine the optimal level of disease control required and when orchards should be destroyed after a lethal and contagious disease a ffect s an orchard. The first model determine s the optimal replanting period for an orchard without disease which is founded on the Faustmann model. The second model determine s when to replant the same orchard if it is attacked by a In the latter case, an effective strategy exists to control the disease. The proposed framework makes several novel contributions. Apart from determinin g when orchards should be replant ed it 1) assess es the conditions under which management str ategies are cost effective; 2) determin es a threshold level of disease incidence and by extension the number of trees that can be removed before full scale replanting of the orchard is warranted ; and 3) evaluat es various control strategies. N o simila r theoretical framework has been developed to simultaneously address the optimal orchard removal age and the optimal disease control when disease is present in perennial crop s The developed models are deterministic in that they assume time invariant biological relationships between disease and yield Information is presumed for disease
36 spread rates and treatment effectiveness as well as prices, costs and other parameters that would facilitate decision making by growers
37 CHAPTER 3 SECOND ESSAY: EMP I RICAL APPLICATION OF THE PROPOSED MODEL TO CONTROL OF PUDRICION DEL COGOLLO IN COLOMBIAN OIL PALM PLANTATIONS Motivation Pudricin del cogollo (PC) affect s the Colombian oil palm industry. PC requires special considerations due to the perennial nature of the oil palm crop. T he theoretical framework described in the first essay was used in order to compare two scenarios: a benchmark consisting of an oil palm field with out PC and an identical oil palm field with PC. For the field with PC, the optimal management plan and length of rotation are determined In the first section of this e ssay background information is presented on the Colombian oil palm industry and the main aspects of PC, including its causal agent, symptoms, suggested management, and economic impact. In a second section data sources and empirical functions are described. R esults and concluding remarks are presented in the third and final sections of the e ssay The Colombian Oil Palm In dustry In Colombia, oil palm cultivation has increased at a yearly growth rate of 7.2% between 1980 and 2010 In 2011, the total area in Colombia planted with oil palm reached 850,000 acres (Fedepalma 2012) More than 90% of th at area has replaced activiti es such as the production of cotton, banana and rice or cattle ranch ing (Gmez, Mosquera and C astilla 2005 ) Continued increases in oil palm production are expected, due to increased global demands for fat s and oils, as well as biofuels (Carter et al. 2 007)
38 The Colombian oil palm industry account ed for 4% of the contribution of all Colombian crops to gross domestic product in 2010 (Fedepalma 2012) This figure only accounts for the value of crude palm oil and as such does not capture the full economic i mpact of the industry given the interdependency of several other sectors and the oil palm industry. For example the industry supplies many Colombian industries that would otherwise need to import palm oil substitutes (Gmez, Mosquera and Castilla 2005) Additionally, the versatility of palm oil and related products makes oil palm popular among growers since it protects them from international price fluctuations. At the Colombian government level, oil palm is a highly appreciated crop I t is labor inten sive ; represents a source of stable year round income for rural communities ; and provides a higher average income for workers relative to other economic activities in the same areas (Mosquera and Garc a 2005) W here oil palm is the most important activity welfare indexes tend to be among the highest for rural Colombian municipalities (Oliveira et al. 2011) In synthesis, oil palm lend s itself to sustainable rural development in Colombia despite the challenge of pests. Pudricin d el Cogollo (PC) The most i mportant pest affecting the Colombian oil palm cultivars is p udricin del c ogollo (PC) (Martinez et al. 2009) PC is caused by Phytophthora palmivora Butler a microorganism that is abundant in C olombian soils (Martinez et al. 2009) In the municipality of Tumaco and surrounding areas, more than 70,000 acres of oil palm were destroyed by PC. This destruction caused loss es in the vicinity of $2,300 per acre which is a significant fraction of the expected $14,500 per acre of average net profits a producer wo uld expect over the 25 year lifespan of an oil palm project (Mosquera 2007) This estimate is very conservative since it represents only direct costs to
39 producers and does not reflect the secondary (spill over) costs resulting from the multiplier effects. PC affects immature tissues of the emerging leaves of oil palms and interferes with the ir production and maturation. As the disease develops other opportunistic organisms attack the tree (insects, fungi, bacteria) and the meristem decompos es eventually causing the plant to die (Martinez et al. 2009) The symptoms of PC depend on the severity of the disease. Cenipalma (Colombian Oil Palm Research Center) developed a scale that quantifies damage o n the youngest leaf surface and is used to categorize disea se severity. If the youngest leaf is not damage d the oil palm is rated as Degree 0 (healthy palm) whereas Degree s 1 through 5 indicate relative increasing amounts of damage (b rown spots ) on this leaf When the youngest leaf is necrotic and collapsed, the stage. Eventually, t he most efficient way of controlling PC may be the use of varieties that are resistant to the disease which are presently under development. In their absence, regular scouting for and recording of P C incidence and severity is n ecessary (Martinez et al. 2009) When a diseased palm is detected, its infected tissues are removed and the wound is covered with pesticides (insecticide s fungicide s and bactericide s ). A white plastic roof is placed above the wound to protect it from sunlight and rain (which washes away the chemicals). Additionally, the young tissues of eight surrounding palms are sprayed with pesticide until the diseased palm recovers ( after 4.5 months) (Torres, Sarria and Martinez 2010) Al though t his strategy can be successful, its effectiveness depends on early detection as only D egrees 1 and 2 are treatable.
40 Since t rees are not likely to recover from more advanced degrees grower s should consider remov ing such palm s Our model assumes that growers are constantly scouting for the disease and when a PC case is found it is treated before it passes Degree 2. Empirical Models Scenario without PC T he optimal rotation length for a field that has not been affected by PC is considered; it is t 1 Y ield is estimated as a function of time and obtained by a quadratic equation (Appendix A): ( 3 1) For one rotation the NPV would be given by : ( 3 2) w here is the net price ; is the production of oil palm fruit per hectare at period measured in months ; T is the replanting period ; r is the discount rate ; and represents the replanting costs. Parameter values are summarized in Table 3 1 Following the calculations presented in the first essay the problem for perpetual oil palm rotations can be expressed as ( 3 3) The FOC corresponding to Equation 3 3 is ( 3 4 ) The former expression could be rearranged to obtain 1 We consider a field with high yields because complete data are available for such a field. As will be demonstrated, the qualitative results will remain unchanged when considering a field with average or low yields.
41 ( 3 5 ) Scenario with PC In the disease scenario, disease incidence, is the number of diseased trees in a hectare whose planting density is 143 trees/hectare the number of diseased trees to be treat ed is and the optimal rotation time to maximize net present value (NPV) is T It is assumed that the treatment proposed by Cenipalma is used and fully effective. S ince at the end of the rotation some growers may abandon their fields due to P C (Martinez 2010) and others may replant with newly bred varieties that have some PC resistance a scrap value function is used 2 The scrap value, determined by land market values, measure s land value in its highest valued use which may or may not include additional oil palm rotations (Deininger, Jin and Nagarajan 2008) ( 3 6 ) Subject to ( 3 7) ( 3 8 ) ( 3 9 ) ( 3 10 ) w here is the number of treated trees per hectare ; is the number of diseased trees in a hectare ; is the age of the plant ing ; is the net price defined earlier ; is 2 As mentioned previously, no varieties are entirely resistant to PC disease and data are lacking for these newer quasi resistant varieties.
42 the production per hectare of an oil palm field, featuring high yield, at age with disease incidence ; is the control costs as a function of diseased palms treated ; r is the monthly discount rate ; repre sents the scrap value function (Leonard and van Long 1992) ; and is the tree age at first disease detection This differs from the previous model where the age of the trees at the start of the model time horizon is 0. Both age and time are measured in months. Functions in the optimization problem are given by Equation s 3 6 through 3 10 (Table 3 1). In Equation 3 6 assum ing no PC disease, yield is a quadratic function of tree age. Th e proportion of yield that is lost due to the disease, also known as a damage function is quadratic and based on disease incidence (Appendix A): ( 3 11 ) Estimation of PC control costs yielded a fixed cost, F as well as a per unit cost, (Appendix A): ( 3 12) This implies constant returns to scale for treatment. Except in the case of a large treatment effort, the data support this assumption. Finally, the scrap value is defined as ( 3 13 ) w here L corresponds to the average l and value in Colombia estimated at 9.8 million Colomb ian pesos per hectare (Duarte and Gutterman 2007). L and value is reduced by disease incidence in the final period, which in turn depends on (per unit impact on land value due to removal of diseased palm s ). T he effect of disease incidence in the final period on land price is small (empirical data indicates ) in part due to imperfections in the Colombian land market (Valderrama and Mondragon 1998) An
43 entirely diseased field would sell for abou t 85% of its non diseased value where t he missing 15% corresponds to costs the buyer may incur when removing dead/diseased palms In Equation 3 7 the equation of motion inoculum pressure from the environment and diseased oil palms are represented by the previously discussed and The control strategy is represented by (treated trees) which is effective when imposed before Degree 3 Equations 3 9 and 3 10 are transversality conditions. To solve the optimization problem expressed in Equation s 3 6 through 3 10 an o ptimal control problem strategy is used with a control variable, and a state variable, Special attention must be devoted to the control variable because it enters the problem linearly. This implies a bang bang optimal c ontrol problem (Chiang 2000) 3 The Hamiltonian is given by ( 3 14) w hich yields the following first order conditions: ( 3 15) ( 3 16) ( 3 17) 3 A bang bang problem assumes that the contro l is either in place or it is not. It is not possible to have intermediate scenarios of control. A good example is a ban on fishing: the policy maker either allows fishing or forbids fishing.
44 From (Equation 3 15) and (Equation 3 16), the singular path of disease incidence th at is, the number of diseased palms per hectare of oil palm that guarantees a stable condition that does not change over time, is solved : ( 3 18) Given the estimated parameter values in our empirical model (Table 3 1), the denominator of the first term of the right hand side (RHS) of Equation 3 18 is positive, G iven the parameter va lues for all possible tree ages (Figure 3 1). Since the number of PC cases cannot be negative it is conclude d that This means that it is optimal for growers to keep PC cases at zero throughout the life of the grove so once detected a diseased tissue should be immediately eradicated from the orchard In turn, t his implies that the steady state value for PC cases (disease incidence) is zero and the steady state level of control equals the environmental disease pressure ( see Data sec tion below) T he transversality conditions are used to determine the optimal (Leonard and van Long 1992) free implies that ( 3 19) However, as shown in Equation 3 15, the value of ex an te is un known To determine backwards induction is used. In the final period, the derivative of the scrap value function with respect to PC incidence at T represents the marginal value of control which is more than the marginal cost of control. Consequently, in the final period all disease will be removed yielding =0. Note at T, =0 and it must remain
45 on the singular path for the entire rotation ; th at is, any PC case in the field must be detected opportunely and treated immediately T free implies that ( 3 20) ( 3 21) Knowing that implies that s ubstitut ion into ( 3 21) yield s ( 3 22) From Equation 3 22 an optimal solution for T is obtained knowing that Equation 3 22 displays the marginal benefit ( LHS ), or the additional inc ome from waiting an extra period which equals the marginal cost of waiting an additional period (right hand side). Terms o n the right hand side of Equation 3 22 correspond, respectively to 1) monthly fixed cost f o r PC control, 2) control costs per treated palm times palms infected due to environmental pressure, and 3) interest from land value that is not received due to postpon ed removal of trees Data While many bioeconomic models lack empirical parameter values, there is a rich dataset with which the present model can be parameterize d Below, the information sources that are use d in the model are discussed (Table 3 1). Appendix A contains results from the empirical estimation of parameter values. The spatial scal e of the model is a hectare, the time scale is one month, and monetary values are given in Colombian pesos. P Research Station, Campo Experimental el Palmar de La Vizcaina (CEPLV) are used to calculate net prices and the pe r kilogram production costs for fresh fruit bunches (FFB)
46 of oil palm. M onthly information for January 2000 to December 2010, obtained from the Colombian Federation of Oil Palm Growers ( Fedepalma ), was used to estimate market prices net of production costs for a kilogram of oil palm fruit (Fedepalma 2008 2012) Due to price fluctuations three different price levels are set (mean price, mean price plus and minus one standard deviation) (Table 3 1). A 30 year monthly yield trend f or Colombia was calculated based on information from the Fedepalma yearly costs survey (Duarte and Gutterman 2007) A concave yield function was observed, wherein the oil palm goes through a develop mental stage yield is maximized after maturity, and then yi eld declines in older palms (Table 3 1 ; Appendix A ) Old palms bear fewer bunches from a great height determination of ripeness is difficult and have a decreased proportion of fruit weight to bunch weight. Th e yield function describes potential yield in the absence of disease (Lichtenberg and Zilberman 1986) For the disease model data for the effect of PC on yield was available for 2007 from more than 730 plots (about 15,000 acres) in the Tumaco area (Southwestern Colombia). The control strategy propos ed by Cenipalma was tested under actual PC pressure and displayed good efficacy Records on every activity, required input, and were studied at CEPLV with time and motion studies that provide d labor costs associated with PC control. From this information the cost per hectare and per treated palm we re modeled. Monitoring is set as a fixed cost once PC is present. The cost of removing diseased tissue and the cost of treat ing surroun ding palms with preventative pesticides were calculated on a per diseased palm basis. It was obtained using a linear
47 function of costs relating the number of diseased palms to actual control expenses; its intercept represents PC control fixed costs (Appen dix A). Data and grower experience indicate th at P. palmivora spreads from two sources. First there are sources Even when all diseased tissue is removed, new cases still appear. D ata from CEPLV were used to estimate exogenous pressure. Second, if diseased palms are left untreated they become pathogen reservoir s for the disease T his value was estimated from data from a PC outbreak near Tumaco, from 2005 to 2007. 4 Data from CEPLV indicate that the spread o f PC can be controlled with the Cenipalma PC strategy. L and value was estimated from cost surveys (Duarte and Gutterman 2007) .The share of the total costs (per ton of oil pa lm fruit) corresponding to land was multiplied by the expected production per hect are (kilograms of oil palm fruit) for the oi l palm stand ing rotation length, resulting in a calculated value of 9.8 million pesos per hectare When considering the discount rate for the model the safest interest rate for investments in Colombia was consid ered which corresponds to deposits at a fixed term plus inflation totaling 10% Although 10% corresponds to the most likely scenario regarding the discount rate (equivalent to 0.8% monthly), 5% and 15% we re also considered 4 In this outbreak, no control was implemented, allowing us to determine how the disease spreads from infections within the field. At CEPLV, the strict control program only allows estimation of the exogenous pressure.
48 Results and Discussion of the Empirical Application of the model to PC Results w ithout PC (Optimal Replanting Period) T hree different price levels ($56, $108, and $160) with three discount rate scenarios (0.4%, 0.8% and 1.25% per month) were considered The opt imal replanting period for Colombian oil palm cultivars that are highly productive and not affected by PC ranges between 25.5 and 36.6 years, depending on price level and discount rate. O ptimal replanting period is negative ly relat ed to the net price per kilogram of oil palm fruit (Table 3 2). If the price of oil palm fruit were at the low $ 56 level oil palm plantings should last between 372 (if a 0.4% monthly discount rate is assumed) and 439 months (1.25% monthly discount rate). From Equation 3 4 it is apparent that net price enters both sides of the equation. A higher net price, ceteris paribus has a positive effect on the marginal benefit of waiting (LHS of the equation), which lengthens the rotation period. Additionally, a higher net price increases the value of the marginal cost of waiting (RHS) because it increases the NPV. The latter tends to shorten the rotation length. With the above parameters, the effect of increasing the marginal cost dominates the effect of the increase in the marginal benefi t which implies that there is an incentive for the grower to replant earlier. Note that a higher discount rate corresponds to a greater rotation length. Consider a grower who faces a net price corresponding to the mean price per kilogram of oil palm frui t during the past two decades. In that case, the results indicate that the rotation length should vary according to the discount rate from 350 (r=0.4% per month) to 402 (r=1.25% per month) months (Table 3 2). The discount rate enters into Equation 3 5 on the right hand side, the side of the marginal cost of waiting a month to replant in multiple places. First, it enters in the interest on the whole stream of profits that gets
49 delayed by one year and in the interest on the site rent. The effect of increasi ng the interest rate and holding the value of the site rent and stream of profits constant would be an increase in the marginal cost of waiting and hence a shortened rotation length. However, the interest rate also enters into the stream of profits and sit e rent. An increase in the discount rate decreases the NPV of the stream of profit s because later periods in the rotation, which have higher yields than earlier periods, are more heavily discounted. This effect is a decrease in the marginal cost of waiting With the empirical model for PC the latter effect dominates, and an increase in the interest rate lengthens the rotation period. In short, with a high interest rate, keeping current trees in the ground is optimal for a longer period of time because rota ti o n brings low yields in early periods and higher yields occur in later periods that are heavily discounted. Results with PC PC disease steady state The first r esult concerning the disease scenario comes from Equation 3 18 which indicates is negati ve at all times (Figure 3 1) I t confirms the need to follow on thorough scouting and immediate treatment of d iseased tissue. S ensit ivity analyses of the parameter values w e re conducted to determine the conditions under which would be greater than zero (Equation 3 18). V arious scenarios w e re considered : High, average and low yield production curves with a variable discount rate.
50 High yield plantatio ns 5 at different ages 6 with variable rates of discount and PC spread High yield plantation s at different ages, with variable price and discount rate. For the se scenarios it is possible to obtain under the parameter values described below. However, when the following pairs of parameters we re evaluated over sensitive ranges it was not possible to observe : PC spreading rate and price; damage function parameters and price; marginal cost of treatment and PC spreading rate. First, w ith variable discount rate s, three different yield curves we re considered: a hig h yield plantation corresponding to Table 3 1 parameters, an average yield plantation, and a low yield plantation (Duarte and Gutterman 2007) A ll other parameters were held at their baseline values. The results indicate that for to be greater than zero for any yield parameter values the monthly discount rate had to be greater than 20.1% (equivalent to 151% annual discount rate). This is clearly unrealistic (Figure 3 2). Second, the discount rate and the rate of spread of PC we re varied, ceteris paribus. PC spread rate w as varied because PC may spread at lower rates in regions with less rainfall than the Tumaco region. For the monthly discount rate must be greater than 1% and the disease spread rate must be less than 1% per month as oppo sed to the estimated 20% (Figure 3 3). 5 Specifically, data from CEPLV where the data used in our empirical model w ere recorded (regarding yield, PC cases and PC treatment). 6 =60,120,180,240,300,360
51 Third, price and the discount rate we re varied, and tree age and spread rate ceteris paribus T he greater the price, the greater the monthly discount rate that is needed for The value of the monthly discount rate for which was found to be positively related to yield depends on age. The higher the yield (ages between 180 and 240 months) the higher the monthly discount rate required for (minimum monthly discount rate was 26% and the maximum above 40%, equivalent to yearly discount rates of 262% and 1157% respectively) ( s ee Figure 3 4). In synthesis, a large discount rate is necessary for which indicates that future control costs must be heavily discounted if some diseased palms ar e allowed to remain in the field. Tree removal period ( ) : model with PC In addition to considering the optimal control in each period, it was found the optimal period ( ) at which time the grower m ust remove trees from current rotation because it ceases to be profitable. A vailable actions for the grower include replant with the current variety, replant with a toler ant variety, replant with a different crop, or sell the land. Table 3 3 contains the results for the optimal relative to t he PC detection period. It illustrates the effects of PC on optimal for different initial ages at first detection of PC infection. In Table 3 4 the optimal period for destruction of all trees from the current rotation ( ) is displayed Since these tables are quite dense they are disaggregate d in Table 3 5 through Table 3 10. Figure s 3 6 and 3 7 illustrate the obtained results for two specific cases specifically those in Table s 3 6 and 3 9 Figure 3 6 contains results for a given net price of $108 per kilogram of oil palm fruit, and considers the three values for the discount rate referred to in Table 3 1. Figure 3 7
52 displays results for the case in which the discount rate is equal to 0.8% per month and consider s the three values for the net price presented in Table 3 1. The results indicate that there is a negative relationship between ( ) and the age of the trees at first PC detection ( ) and that this relationship is concave (Table 3 4 ; Figure 3 5). In addition, net price wa s positively related to ( ) I n Equation 3 22 price positively influences the marginal benefit of waiting an extra period ( this is the LHS ) and ceteris paribus implies greater income. In other words, a greater price provides an incentive to lengthe n the rotation (Table 3 4) Note that this contradicts an earlier finding in the without PC model where a greater net price resulted in earlier replanting periods. Regarding the discount rate, Equation 3 22 indicates that it enters the marginal cost. This parameter multiplies the land value and at the same time enters in the discount factor. If one only considers the discount rate multiplying the land value, then a greater discount rate increases the marginal cost and encourages earlier replanting. If one focuses on the discount factor a greater discount rate implies smaller marginal cost which would lengthen the rotation. Interaction of these two effects, coupled with the age of initial infection, determine the outcome. If the planting is younger than 20 0 months at initial PC infection a greater discount rate implies a decrease in the marginal cost, which in turn results in longer rotations. For plantings that are older than 300 months when attacked by PC, a greater discount rate increases the marginal c ost, which shortens the rotation length. For those between 201 and 299 months there is not a clear trend and one must consider other parameters, such as price, to determine the relationship between the optimal period for palm removal and the discount rate. It is
53 important to note that for scenarios with PC, changes in net price have a larger magnitude of effect on optimal replanting time than changes in the discount rate. Comparison among results f rom b oth m odels Table s 3 5 through 3 10 compar e optimal replanting vs. optimal palm removal periods for the without and with PC models T hree of the se tables consider a given discount rate (Table 3 5 through Table 3 7), and the remaining three display results for a given net price level (Table 3 8 thro ugh Table 3 10). There are two factors that greatly influence the se comparisons net price and when PC attacks an oil palm planti ng expressed in months. The latter, as shown above, affects the relationship between discount rates and the optimal time for r emoval As indicated above, there is a negative relationship between net price and optimal replanting period in the w ithout d isease model whereas a positive relationship is found in the with disease model. These results are quite important because they play a major role in the optimal solutions f or both models. In addition, with fixed annual discount rate s of 5% (0.4% per month), 10% (0.8% per month) or 15% (1.25% per month) (Table s 3 5, 3 6, and 3 7), lower net price s are a ffect ed earlier ( ) from the with disease model, compared to optimal (optimal replanting ) in the w ithout disease model. This trend is more prominent at higher discount rates (high risk perception scenarios). C onsidering different net prices per kilogram of oil palm fruit (Tab le s 3 8, 3 9 and 3 10), removal would take place at the highest net price ($160) later in the with disease scenario than in the without PC scenario T his optimal replanting strategy (Table 3 10) is due in part, to the fact that the results of the disease free model are more responsive to changes in prices and their promoti o n of earlier replanting period s The opposite occurs if one considers the lowest net price of $56 (Table 3 10), since the disease free
54 model indicates a longer planting lifespan with lo w prices. T his responsiveness to net price in the disease free model is the major factor in determining differences between solu tions for both w ith PC a nd w ithout PC models. Concluding R emarks to the Empirical Application of the Proposed Model to Pudricin del Cogollo Threatening Colombian Oil Palm Plantations The area planted with oil palm in Colombia has grown considerable at an annual rate of 7.2% between 1980 and 2010 T his growth has been associated with attributes that make the oil palm agroindustry a sustainable and promising Colombian economic sector. However, th e industry is threatened by PC a disease that has a ffected production in Colombia since the 1960s and caused massive destruction in the South w estern Colombian oil palm cluster (2007 2010) and other countries, such as Guyana and Ecuador. Martinez et al. ( 2009 ) proposed a PC control strategy that is effective if two conditions are met: 1) early detection of affected tissue and 2) eliminati o n of all affected tissues in a field. Two models w ere considered in order to maximize the oil palm plantation NPV by choosing on the period in time at which the current oil palm standing is no longer profitable : a model with PC and a model without PC. The disease model has two important results. First, th e steady state level of diseased cases was always negative which implies that growers must emphasize early detection and immediate orchard removal Second, the optimal time to destroy Colombian oil palm plantations affected by PC ( ) is negatively re lated to age when first attack ed by PC (holding constant net price and discount rate). The disease model indicates that the optimal time for destruction ranges from 328 to 407 months (27.3 to 33.9 years),
55 depending on a combination of the and discount rate. It was also found that regardless of the value of there is a positive relationship between net price and optimal time for destruction The relationship between the optimal plantation lifesp an and the discount rate depends upon the yield function. If the yield function has not reached its maximum when PC enters the field the relationship between discount rate and the optimal lifespan ( ) is positive. On the contrary, if the yield function has already reached its maximum this relationship becomes negative. In other words, i f the grower expect s that most production will occur in the future and the discount rate is high there is going to be an incentive to defer removal of the curre nt standing However, if most of the production has already occurred and the d iscount rate is high, there is an incentive for earlier removal The positive relationship between net price and ( ) differs from that obtained with the disease free model. As discussed previously, this occurs because in the disease free scenario net price is in both marginal cost and marginal benefit and the net effect of varying net price favors the marginal cost side. Meanwhile, the disease model displays net price only in the marginal benefit.
56 Table 3 1 Parameters used f or e stimation (PC models) Parameter Symbol Value Monthly d iscount rate r 0.4%, 0.8%, 1.25% Net price p 56, 108, 160 Quadratic y ield parameters 320.4161 27.2652 0.0668 Replanting costs 10,000,000 Effect of disease on yield 0.00322 0.00002 PC control fixed costs 50,900 PC control variable costs 6,332 External PC spread rate 0.4500 Internal PC spread rate 0.2000 Land Value 9,800,000 Decrease in land price from a diseased palm 0.001
57 Table 3 2 Optimal replanting period (PC free) Net price r=0.4% r=0.8% r=1.25% 56 372 413 439 108 350 387 402 160 342 377 386 r=monthly discount rate
58 Table 3 3 O ptimal T for selected values of a ccording to different combinations of net price and discount rate Discount rate p= 56 p= 108 p= 160 1 0.4 % 376 398 405 0. 8 % 379 399 406 1 25 % 381 400 406 50 0.4 % 325 348 355 0. 8 % 329 350 357 1 25 % 332 351 357 100 0.4 % 273 297 305 0. 8 % 277 299 306 1 25 % 280 301 307 150 0.4 % 221 246 254 0. 8 % 223 248 255 1 25 % 228 250 256 200 0.4 % 168 195 204 0. 8 % 167 196 204 1 25 % 172 198 205 250 0.4 % 114 144 153 0. 8 % 106 143 152 1 25 % 10 144 153 300 0.4 % 58 92 101 0. 8 % 28 87 99 1 25 % A.R. 86 99 350 0.4 % 1 39 50 0. 8 % A.R. 28 45 1 25 % A.R. 8 40 p is n et price r is discount rate, is the A.R. : Orchard a lready remov ed
59 Table 3 4 Oil palm standings lifespan for selected values of according to different combinations of net price and discount rate Discount rate p=56 p=108 p=160 1 0.4 % 377 399 406 0. 8 % 380 400 407 1 25 % 382 401 407 50 0.4 % 375 398 405 0. 8 % 379 400 407 1 25 % 382 401 407 100 0.4 % 373 397 405 0. 8 % 377 399 406 1 25 % 380 401 407 150 0.4 % 371 396 404 0. 8 % 373 398 405 1 25 % 378 400 406 200 0.4 % 368 395 404 0. 8 % 367 396 404 1 25 % 372 398 405 250 0.4 % 364 394 403 0. 8 % 356 393 402 1 25 % 260 394 403 300 0.4 % 358 392 401 0. 8 % 328 387 399 1 25 % A.R. 386 399 350 0.4 % 351 389 400 0. 8 % A.R. 378 395 1 25 % A.R. 358 390 p is n et price r is discount rate, is the A.R. : Orchard a lready remov ed
60 Table 3 5 Comparison among optimal ( ) from the model with PC, and o ptimal r eplanting from the model without PC at discount rate equal to 0.4% per month Model p=56 p=108 p=160 With PC 1 377 399 406 50 375 398 405 100 373 397 405 150 371 396 404 200 368 395 404 250 364 394 403 300 358 392 401 350 351 389 400 Without PC N/A 372 350 342 p is net price represents selected initial infection periods (t = 1, 50, 100, 150, 200, 250, 300, 350) N/A ; there is no infection period for the W ithout PC scenario
61 Table 3 6 Comparison among optimal ( ) from the model with PC, and o ptimal r eplanting from the model without PC at discount rate equal to 0.8% per month Model p=56 p=108 p=160 With PC 1 380 400 407 50 379 400 407 100 377 399 406 150 373 398 405 200 367 396 404 250 356 393 402 300 328 387 399 350 A.R. 378 395 Without PC N/A 413 387 377 p is net price represents selected initial infection periods (t = 1, 50, 100, 150, 200, 250, 300, 350) A.R. : Orchard a lready remov ed N/A ; there is no infection period for the W ithout PC scenario
62 Table 3 7 Comparison among optimal ( ) from the model with PC, and o ptimal r eplanting from the model without PC at discount rate equal to 1.25% per month Model p=56 p=108 p=160 With PC 1 382 401 407 50 382 401 407 100 380 401 407 150 378 400 406 200 372 398 405 250 260 394 403 300 A.R. 386 399 350 A.R. 358 390 Without PC N/A 439 402 386 p is net price represents selected initial infection periods (t = 1, 50, 100, 150, 200, 250, 300, 350) A.R. : Orchard a lready remov ed N/A ; there is no infection period for the W ithout PC scenario
63 Table 3 8 Comparison among optimal ( ) from the model with PC, and o ptimal r eplanting from the model without PC at net price equal to $56 Model r = 0. 4 % r = 0. 8% r =1 25% With PC 1 377 380 382 50 375 379 382 100 373 377 380 150 371 373 378 200 368 367 372 250 364 356 260 300 358 328 A.R. 350 351 A.R. A.R. Without PC N/A 372 413 439 r is the monthly discount rate represents selected initial infection periods (t = 1, 50, 100, 150, 200, 250, 300, 350) A.R. : Orchard a lready remov ed N/A ; there is no infection period for the Without PC scenario
64 Table 3 9 Comparison among optimal ( ) from the model with PC, and o ptimal r eplanting from the model without PC at net price equal to $108 Model r = 0. 4 % r = 0. 8% r =1 25% With PC 1 399 400 401 50 398 400 401 100 397 399 401 150 396 398 400 200 395 396 398 250 394 393 394 300 392 387 386 350 389 378 358 Without PC N/A 350 387 402 r is the monthly discount rate represents selected initial infection periods (t = 1, 50, 100, 150, 200, 250, 300, 350) N/A ; there is no infection period for the Without PC scenario
65 Table 3 10 Comparison among optimal ( ) from the model with PC, and o ptimal r eplanting from the model without PC at net price equal to $160 r = 0. 4 % r = 0. 8% r =1 25% With PC 1 406 407 407 50 405 407 407 100 405 406 407 150 404 405 406 200 404 404 405 250 403 402 403 300 401 399 399 350 400 395 390 Without PC Disease free 342 377 386 r is the monthly discount rate represents selected initial infection periods (t = 1, 50, 100, 150, 200, 250, 300, 350) A.R. : Orchard a lready remov ed N/A ; there is no infection period for the Without PC scenario
66 Figure 3 1 Solution for according to yield (which in turn is a function of age)
67 Figure 3 2 Sensitivity analysis for varying discount and ceteris paribus for a high yield oil palm standing
68 Figure 3 3 Sensitivity analysis for varying discount rate and PC disease spreading rate at = (yield at = 3640 kg/hectare)
69 Figure 3 4 Sensitivity analysis for varying discount rate and net price at = (yield at = 3064 kg/hectare)
70 A B Figure 3 5 Optimal solution for scenario with PC A) Mesh grid for T optimal solution. B) Contour plot T he thicker and solid line represents the optimal solutions for T w here the mesh grid function reaches the zero value. These results illustr ate the case of net price equal to 108 and discount rate equal to 0. 8% (month).
71 Figure 3 6 Optimal ( ) from the With PC model according to discount rate, holding constant the net price at $108 per kilogram of oil palm fruit
72 Figure 3 7 Optimal ( ) from the With PC model according to price, holding constant the discount rate at 0. 8 % per month
73 CHAPTER 4 THIRD ESSAY: EMPIRICAL APPLICATION OF THE PROPOSED MODEL TO CONTROL OF LAUREL WILT IN THE FLORIDA AVOCADO INDUSTRY Motivation Laurel w ilt (LW) has recently emerged as a threat to plants in the Lauraceae family, including important native trees and the significant commercial crop avocado. It is a lethal vascular disease caused by the fungus Raffaelea lauricola which has an invasi ve ambrosia beetle vector, Xyleborus glabratus Laurel wilt has moved rapidly in Florida since it was first detected in Duval County in 2005. In February 2011, it was confirmed for the first time in Miami Dade County, 6 km from the northern boundary of Flo detected in an avocado tree with in the CAPA. While the loss of native members of the Lauraceae family is of ecological significance, laurel wilt could have a considerable economic impact on avocado production. The re are 7,000 acres under production in Florida, more than 99% of which are located in southern Miami Dade County. Avocados are a $15 million industry in the state Since t he disease could cause a perma nent reduction in the long term profitability of the Florida avocado industry growers, policy makers and other stakeholders are concerned about the impact laurel wilt will have on the industry and how limited resources should be allocated to mitigate its threat and to ensure the long term survival of the industry. It is within this context that this research has been undertaken. Its goals are to develop a framework to assess the potential economic impact of laurel wilt and provide growers with a decision tool to maximize returns in the presence of the disease.
74 The approach of Salifu et al. ( 2012) was used to address h ow laurel wilt impacts profitability, considering different spread rates, disease incidence in and the age of the grove when first affected and treatment costs. In general, simulation techniques were used to determine when a grove affected by LW would cease to be profitable with and without the use of control strategies. The without disease model described in the first essay was used to det ermine when a grower should replant a laurel wilt free grove. That question had not been considered previously, and constitutes the benchmark scenario in the present study. Two contributions are made in this article. First, although other studies ( Evans and Crane 2009 ; Evans et al. 2010) have estimated the potential impact of laurel wilt, none ha s provided guidance on when production is no longer profitable. This is especially important since sanitation, which involves early detection and removal of affec ted trees, has emerged as a preferred control strategy. Second, a framework was developed to provide quantitative guidance to evaluate LW management strategies. This essay begins with background information on the South Florida avocado industry ; outlines the caus e symptoms, and economic impact of LW; and present s data sources and empirical models The essay finishes with a results section and concluding remarks Overview of the Florida Avocado Industry Avocado is planted on about 7,400 acres in Florida, a nd represents around 60% of the total area planted with tropical fruits in th e state. Most avocado orchards are located in Miami Dade County and 93% of the plantings are less than 15 acres each (Evans et al. 2010)
75 F arm gate values for Florida avocado s range from US$12 to US$1 5 million dollars a year with a wholesale market value of US$30 million T he Florida avocado industry has an overall economic impact of US$54 million and generates about 550 full time jobs earnings and US$1.8 million in tax revenue (Evans and Nalampang 2010) Significantly, t he property on which mature avocado trees are grown in Florida is valued at US$326 million (Evans et al. 2010) There are three botanical races of a vocado : the West Ind ian or Antillean ( Persea a mericana var. americana ), the Guatemalan ( Persea a mericana var. guatemalensis ) and the Mexican ( Persea americana var. drymifolia ) Commercial production occurs in Florida of 23 major and 20 minor cultivars of the West Indian and Guatemalan race s and hybrids of each (Crane, Balerdi, and Maguire 2010) Laurel Wilt (LW) LW is a vascular disease caused by a recently described fungus Raffaelea lauricola (RL) (Fraedrich et al. 2008; Harrington, Fraedrich, and Aghayeva 2008) RL has a symbiotic relationship with X glabaratus ( Coleoptera: Scolytinae: Xyleborini) which cultivates the fungus in its natal galleries and consumes it rather than wood RAB carries RL in its mycangia 1 (Harrington, Fraedrich, and Aghayeva 2008) and when borin g galleries into woody plants, the plant is inoculated with RL. The fungus moves systemically through the xylem vessels of the host and causes LW (Harrington, Fraedrich, and Aghayeva 2008; Mayfield III, Crane, and Smith 2011) LW disrupts nut rient and wate r transport in host trees ultimately causing host death (Ploetz et al. 2011; Inch and Ploetz 2012) 1 Mycangia is defined as a morphological structure, common in ambrosia beetles, where their fungal symbionts are carried.
76 As LW develops, subsequent generations of RAB develop and eventually disperse to new trees RAB females serve as the primary vectors of RL (males are flightless) (Harrington and Fraedrich 2010) and seasonal component s ha ve been identified for their activities. For example, in South Carolina RAB catches (in flight populations) were highe st between April and September (Hanula et al. 20 08) Two distinctive features are highlighted in the LW literature. The first is that RAB is attracted to healthy trees, wh ereas most ambrosia beetles are attracted to dead or stressed trees (Batra 1967) RAB is unusual among ambrosia beetles in that it is not attracted to ethanol (tissues in a fermentation process due to organic decomposition) but rather to host plant volatiles (Harrington and Fraedrich 2010 ; Kendra et al. 2012 ) Second, RL has been found to be a very aggressive pathogen capable of colo nizing an entire tree from a single introduction 2 RL often causes host death while most fung i that are associated with ambrosia beetles are saprobes (Harrington and Fraedrich 2010) RAB is native to Asia where it has been found in Asian spicebush ( Lind era latifolia ) yellow litsea ( Litsea elongata ), and other host trees (Rabaglia et al. 2006) However, despite the presence of numerous species in the Lauraceae in Asia, LW has not been reported in the region (Ploetz et al. 2013). Most literature on LW states that RAB was introduced into the United States in infested wooden packing materials in Port Wentworth, Georgia in 2002 (Harrington, Fraedrich, and Aghayeva 2008; Koch and Smith 2008) A year later, RAB was associated with diseased redbay ( Persea b orbonia ) trees in Georgia and South Carolina. By 2005, LW Duval County and since then, has spread southward In 2010, it was detected in 2 This result was obtained specifically for red bay.
77 Miami Dade County. A bundan t, susceptible hosts and the mobile vector have facilita ted the spread of LW throughout the southeastern United States ( Ploetz et al. 2013 ) However, anthropogenic activities are probably also important (Mayfield et al. 2009). While Koch and Smith ( 2008) estimated the rate of LW spread at 54.8 km per year it h as spread faster than that in the southeastern United States (Hanula et al. 2008 ; Mayfield et al. 2009 ) Susceptibility to LW varies among avocado cultivars (Ploetz et al. 2012). Simmonds ( = 35% of trees in commercial production ) and other West Indian cultivars that are important in Florida are the most susceptible (Ploetz et al. 201 2 ) There is a positive correlation between the LW (Ploetz et al. 201 2 ) LW symptoms recognized to date include t he following: Small strings of compacted sawdust ejected from holes bored in to evident because sawdust structures disintegrate easily, and beetle activity is initially incon spicuous Additionally, it does not necessarily indicate RAB presence since other ambrosia beetles also bore into trunks and produce s (Mayfield III, Crane, and Smith 2011) When bark is removed one may find holes of about 2mm in diameter around which dark coloration caused by RL can be observed (Mayfield et al. 2009; Ploetz et al. 2011 ) External LW symptom s include wilted leaves that become greyish or bluish before turning brown (desiccated) when the lea f tissue die s O nce leaves in the canopy desiccate, they remain attached to the stems for two to three weeks ( Ploetz et al. 201 2 ) Trees die within weeks of the development of the first external symptoms of LW Internally affected trees display dark brown patches of sapwood that contrast with he althy tissue (Ploetz et al. 201 2 ) LW Management Unfortunately, controlling the vector (RAB) is difficult since it is not exposed to insecticide once it has bored a gallery into the host tree (Mayfield et al. 2009 )
78 Propiconazole macroinfusion (injection) has prevented LW in redbay trees in field trials (Mayfield et al. 2008 ) This practice is also effective in a vocado (Ploetz, et al. unpublished) However, due to its labor intensity and the probable need for annual applications, it is not cost effective f or trees in commercial production (Ploetz et al. 2011). I n vitro tests against RL with products in 10 fungicide groups and greenhouse tests against LW with the most active compounds indicated that demethylation inhibitors (DMIs) quinine outside inhibitors (azoxystrobin, pyraclostrobin and fluoxastrobin), and quinine inside inhibitor (fluazinam) affected growth of the pathogen, but o nly DMIs and t hiabendazole were effective against the disease (Ploetz et al. 2011) The c ost effectiveness of macroinfusion was evaluated for two different products (Alamo 3 and Tilt 4 ) with two macroinfusion methods mechanized and manual over a 3 year period (Ploetz et al. 2011) Mayfield et al. (2008) also used Alamo in their redbay experiments and after 34 months some treated redbay trees still survived Thus Ploetz et al. (2011) proposed three different scenario based treatment efficac ies for 1, 2 or 3 years. For cost calculations, they considered a representative avocado o rchard in S outh Florida. Cost efficiency was assessed using a partial budgeting approach 5 Results indicated positive net returns only if treatment was effective for 3 years ($2 per tree for both mechanical and manual applications). They concluded that un der the current circumstances the macroinfusion technique is not cost effective. Research 4 Naturally, it is used at a comparable rate. However, whether or not Tilt is suitable and effective for macroinfusion is still being tested 5 Partial budgeting allows researcher s to compare different profitability outcomes by examining changes in income and expenses of the different alternatives. Additional costs include labor, equipment and inputs required for macroinfusion. Meanwhile, net income value is the additional avocado production sold after discounting marketing and harvesting costs. The authors compared paired additional costs and net additional production value for each treatment under consideration.
79 continues t o find cheaper alternative chemicals and to decrease the cost of application. Research is also being carried out on insect repellents and insecticides for controlling RAB ( Pea et al. 2011) Potential Ec onomic Impact o f LW o n Commercial Avocado Evans and Crane (2009) conducted a study to estimate replacement costs for commercial avocado trees in South Florida. They used the Tree Value Analysis internet too l (University of Florida 2006) to estimate the value of a mature tree, which was found to be US$330 6 Th is approach considers the avocado tree to be an asset and utilizes the income method in its valuation. While accounting for forgone income from the sale of fruits, it considers the present value of the net costs of replacing lost trees and growing replacemen t trees to the same developmental stage at which the lost trees were when removed. Net costs include 1) tree removal, land preparation, tree cost and planting; 2) maintenance costs incurred during the 7 year replacement period (fertilizer, pruning, weedin g, and pest control) ; and; 3) lost revenue from nonbearing trees. T o assess the economic impact of LW, Evans et al. (2010) consider ed potential direct and indirect losses from a hypothetical LW outbreak o n Florida avocado. Direct losses we re due to lost in come, lower property values and increased management costs ( e.g. monitoring, plant protection products, dead tree disposal and replanting costs). Indirect losses referred to the secondary or spillover effects due to inter industry linkages and include d avocado related industries, such as input selling industries (nurseries, fertilizers, fungicide s packaging materials etc. ) and those for which avocado is an input (packing houses, transportation services, retailers, etc.). They used 6 Parameters used in 2006 were the $150 per tree stump removal costs an d 5% discount rate.
80 an input output model (I O) known as Impact Analysis for Planning (IMPLAN) to quantify indirect losses (Evans et al. 2010) Evans et al. (2011) established three likely scenarios gi ven the uncertain impact of th is disease on avocado plantation s : 1) total loss, 2) 75% loss and 3) 50% loss. In order to determine the decline in property value, the value of mature avocado tree s (US$500) was obtained by using the Tree Value Analysis internet tool (University of Florida 2012) 7 Regarding increases in manag ement costs, they use d current recommendations for permethrin applications, which costs US$333 per acre in a year (labor and insecticide ). Results of direct cost estimation under the se assumptions are synthesized in Table 1. Considering the indirect impact of LW on the S outh Fl orida avocado industry, Evans et al. (2011) built the 100%, 75% and 50% loss scenarios ( Table 2 ) If the whole industry disappeared due to LW, industry sales would decline (US$30 million), and its estimated output impact (US$54.3 million) would not contri but e terms of employment, 546 jobs would be lost in a 100% loss scenario. This represent s worker earnings of US$19.7 million and tax revenue of US$1.9 million that would not circulat e A 100% loss scenario would re sult in an indirect loss of about US$77 million a year. Similar analyses were done for the 75% and 50% scenarios. Empirical Models The research undertaken sought to address the following research questions: What is the optimal period for replanting the gro ve in the absence of the disease? When 7 This tool is very sensitive to changes in the parameters entered. For this study, the authors used US$0.45 per pound (which was the average price received by growers in 2012; cost of removal US$150 )
81 does the grove cease to be profitable in the presence of LW ? The model developed in t he first essay was used to investigate the first question. Due to the unavailability of scientific data to parameterize the model, a slightly different approach was taken in addressing the second research question. In particular, the approach followed that of Spreen et al. (2003) which is based on determining the value of an asset, in this case the avocado orchard, through application of the income method. Both models are elaborated below. LW Free : Optimal Replanting Time The model starts by assuming that avocado production (pounds of fruit per tree) can be represented by a concave function of the age of the tree (time in years). The n et p resent v alue (NPV) function for one avocado rotation is given by ( 4 1 ) w here is the net price (price less cost of pr oduction in terms of unit, assumed fixed) rep resents the time period at which replanting should take place is the discount rate and represents the replanting cost (Appendix B, Table B 1) Following the calculations presented in t he first essay the optimization problem corresponding to perpetual rotations can be estimated : ( 4 2 ) So the FOC is given by ( 4 3 ) The solution for the South Florida avocado optimal rot ation problem is obtained by solving for T in Equation 4 4:
82 ( 4 4) Equation 4 4 may be rearranged to obtain ( 4 5) Interpretation s of Equation s 4 4 and 4 5 are identical to those in t he second essay That is, at the optimal solution the costs associated with wait ing for an extra period to replant are equal to the benefit s associated with waiting. In both equations the left hand side (LHS) represents the marginal benefit. Model w ith LW Period in which costs exceed revenue and NPV calculations The model w ith LW assumes an avocado orchard is an asset and estimat es the economic impact of LW by applying the income method (Spreen et al. 2003) 8 T hat is, future costs and revenues are estimated in order to obtain net revenue per annum. Net revenue from future peri ods is discounted so the NPV is obtained by using the f ormula: ( 4 6) w here indexes the corresponding time period ; is the price paid per pound of avocado after packing and marketing ; is the marketable yield per acre of avocado in time period ; represents the variable costs per acre (harvesting, packing and marketing) at time period ; represents cultivation (sanitary, irrigation, weed control 8 Considering the avocado orchard as an asset implies that it has a useful life and can provide a stream of future net benefits.
83 and nutrition expenses) and fixed costs (land, supervision and overhead) per acre ; and is the discount rate. It should be noted that LW affect s the net revenue at each period of an infected avocado orchard in two ways: by decreasing avocado production and by increasing management costs The anticipated increase in management cost can therefore be accommodated in the model through an adjustment of the net price received by the growers. In this application the n et price was adjusted by assuming 5% and 10% increase s in total costs due to LW management. The effect of LW on avocado production was obtained as in Salifu et al. (2012) by taking into consideration three variables namely: the spread rate ( the age of the grove at first detection and the disease incid ence at first detection ( ). All of t hese measures will have an impact on the aggressiveness of LW. A unique solution (the decision of when to destroy all trees in the orchard or replant the grove ) can be determined depending on the values of chosen for each of these variables. The profit maximizing objective implies that the grower will stay in the avocado business until the moment at which costs become greater than returns At suc h a time the grower will either exi t the business (destroy any remaining trees) or replant the orchard depend ing on whether resistant varieties are available. However, it was necessary to evaluate whether avocado project s in the presence of LW were viable provided the lifespan of an avocado project. The lifespan of an avocado project was defined as the number o f years from planting to the period in which the grower destroys all trees in the orchard (due to negative net revenue ) This evaluation was carried out by means of calculating the NPV of each avocado project. A s
84 usual, a positive NPV implies the operation is profitable while a negative NPV implies it is not at the chosen interest rate. Considered scenarios for the model with LW Four scenarios were considered based on the management strategy adopted and the assumed effe ctiveness of the treatment The first scenario ( D o N othing ) assumes that the grower takes no action to limit the spread of the disease. In this case a 100% LW spread rate is assumed. The second scenario ( ) assumes that the grower, having detected the disease take s action to limit the spread of the disease and that the control treatment is fully effective Under this scenario the LW spread rate decreases from 100% to 0%. Scenarios three and four are considered intermediate scenarios for c ontrol effectiveness Scenario three ( ) assumes that the control strategy is only partially effective in slowing the spread rate from 100% to 50%, while scenario four ( ) is similar to scenario three but assumes that the treatment is more effective In this case it is assume d that LW spread rate is reduced from 100% to 25%. For each of the above scenarios two levels of disease incidence were assumed at first detection ( : 1% and 10%. The former implies that at first detection 1% of the grove or 1 tree (assuming 87 trees per acre) was infected with the LW. The use of a control strategy implies the grower incur s extra costs. Based on discussion s with scientists working on treatment s, we assumed both a 5% and 10% cost increase ; t his translate s into net price s of US$0.13 per pound and US$0.12 respectively. The magnitudes of the costs increases (5% and 10%) are proposed by consideration of the narrow margins shown by previous South Florida avocado profitability analysis (Evans and Nalampang 2010).
85 A vocado production curve s were simulated with LW spread rates ( =0%, 25%, 50%, 100%) and LW incidence at infection period (1% and 10%). Since LW could attack an avocado orchard at any age, there is a curve for each assumed LW infection period. For each of these curves the year when the orchard would cease to yield positive net returns was determined T hen the NPV was calculated, from the planting year to the period found above (when net returns bec ome negative). A 10% discount rate was employed in the analysis. The choice of the discount rate was based on what the growers considered to be a reasonable return for their risky investment (Table 4 3) Data, Parameter Values and Model Calibration Econom ic Data and Parameters The data for this study are comprised of two types : economic and biological data. In order to parameterize the model without LW, a production function was created for avocado in South Florida L inear regression s of yearly avocado pro duction (University of Florida 2012) on age and age squared, where age is ex pressed in years were estimated P ersonal communications with South Florida avocado experts indicated that the economic life of an orchard is around 40 years. Based on the opinions of industry experts, it was assumed avocado production decreases after year 30 at an annual rate of 5% This obtained a statistically significant model capable of explaining up to 70% of avocado production variability (Appendix B, Table B 1) Mos t of the economic data were obtained from the University of Florida Agricultural Economics Extension Service, and reflect South Florida avocado cultivation costs such as plant nutrition, pest control, weed control and pruning. Altogether, cultivation acti vities represent 40% of the total cost of producing a pound of avocado. Regarding fixed costs land rent, supervision and overhead, which represent 30% of
86 total costs of production for South Florida avocado were taken into consideration Finally, activit ies from harvesting to marketing account for the remaining 30% of avocado total costs (Appendix B, Table B 3 ). Establishment/replanting costs of an avocado acre are US $ 2610 ( around US $ 30 per tree ) (University of Florida 2012). After considering per acre av ocado production in terms of pounds (University of Florida 2012) a US$0.35 cost per pound of avocado was obtained Calculation of the net price required information on the price recei ved by growers per pound of avocado Data from the United States Depart ment of Agriculture (USDA) were used for the series of avocado price s per ton received by Florida growers (USDA 2013) Values for the past ten years were averaged resulting in a price of US$0.32 per pound. To that value were added the picking, packing an d marketing costs (US$0.17/pound) for a total price of US$0.50 per pound of avocado. The net price per pound of avocado was found to be US$0.15. Biological Data a nd Parameters For the model with LW a Gompertz spread function was used that drives the disease incidence along time to 100% as in Salifu et al. (2012). Our disease spread model depicting disease incidence along time is represented as ( 4 7) Equation 4 7 contains two parameters of extreme importance wh en assessing disease impact as they relate to disease aggressiveness. The first is the disease spread rate and the second is the disease incidence at first det ection As mentioned earlier, r esults from this work are obtained based on four yearly values of 0%, 25%, 50%, and 100%. P reliminary data gathered in South Florida avocado orchards during
87 2012 indicates that the spread rate of LW may be close to 100% per year, so this value was used for depicting the 9 ( Figure 4 1 ; Table 4 3). Results and Discussions Base C ase S cenario: LW Disease F ree A discount rate of 10% per year and a net price of US$0.15 per pound of avocado were used to calculate the optimal replanting period for an acre of an average South Florida avocado orchard. The result suggests that avocado grower s whose orchard s are not threatened by LW should replant their orchard s in year 40. the first essa y This result is not comparable to those obtained by using simulation techniques because the assumptions and the structure of maximizing NPV assuming a yield continuous f unction simulations are obtained from maximizing NPV from a discrete framework. However, the result is very important because it provides a tool for growers to determine when to replant their avocado orchards in the absence of LW Do Nothing This scenario assumes there is no action from the grower in order to slow down LW spread rate so there are no additional production costs from controlling LW spread and the LW spread rate remains equal to 100%. Two cases regarding disease incidence at first detection ( ) were considered (1% and 10%). If LW attacks an avocado orchard (of any age) and = 1%, LW will spread so fast that all trees will be 9 It was found that in a South Florida avocado orchard there was a n LW case H owever no action was taken against LW and then, a year later 75 trees were diseased with LW
88 infected 2 years later ( Table s 4 4 and 4 5 ; Figure s 4 2 and 4 3 ) The same result holds when = 1 0 % is assumed (Table s 4 6 and 4 7 ; Figure s 4 4 and 4 5). NPV calculations considering the age of t he orchard at initial infection and disease incidence at first detection yield negative values for orchards 6 year s old and younger (Table s 4 8 4 9, 4 10, 4 11, and 4 12) Th e s e results suggest that avocado orchards 6 years old or younger that are attacke d by LW should be destroyed immediately (Table s 4 8 and 4 9). In synthesis if growers do not take any action towards slowing LW spread rates, they will need to destroy their entire orchard s after 2 years of detecting the disease in their fields, independe ntly from age of infection. Additionally, orchards 6 years old or younger attacked by LW are not viable, so the grower s will be better off by destroying all trees in their orchard s, or replanting if there is an avocado resistant variety available (Table 4 12). Fully Effective A fully effective control strategy implies that the LW spread rate slows from 100% to 0% per year. At first, it was assumed that the fully eff ective control strategy increases the total costs of production by 5% (in this case the net price = US$0.13/pound ). Again two cases with respect to are considered. If =1%, avocado orchards would take as long as 42 years to reach the period in whic h net revenue becomes negative (Table 4 4 ; Figure 4 2). The NPV criterion indicates that these are viable avocado projects so there is no need for immediate tree removal although increased costs affect negatively NPV (Table 4 8). If =10%, the period at which the avocado project reaches negative net revenue is year 41 (Table 4 6 ; Figure 4 4). Regarding NPV values for these scenarios it
89 was found they are positive but smaller in magnitude than NPV from an orchard without disease due to LW management cost s (Table 4 10). Alternatively, it was assumed that the control strategy increases costs by 10% ( net price = US$0.12/pound ). If =1% the period at which net returns become negative is year 41 (Table 4 5 ; Figure 4 3 ) NPV remains positive for any value of and NPV magnitudes are negatively affected by the greater increase in control costs ( Table 4 9 ) I f = 10% net revenues are expected by year 39 (Table 4 7 ; Figure 4 5 ). NPV is positive for any value of and NPV magnitudes are negatively affected by the greater costs of production (Table 4 11). Intermediate Effectiveness We define intermediate effectiveness of the LW control strategy as a reduction of the LW spread rate from 100% to 25% a year. First, it was assumed that using the control strategy increases costs of production (per pound of avocado) 5% (net price =US$0.13/pound). If =1%, this control strategy allows growers to stay in business, on average, for 8 years after LW attacks (Table 4 4 ; Figure 4 2). Additionally, it was found that any avocado orchard 3 years or younger attacked by LW should be removed immediately due to negative NPV (Table 4 8). If =10%, the period of destruction of all orchard trees due to negative net returns takes place on average 5 years a fter LW attacks ( Table 4 6 ; Figure 4 4 ). It was also found that grower s would be better off if t he y immediately remove avocado orchards 6 years and younger since NPV calculations yield negative values (Table 4 10) Alternatively, it was assumed that the con trol strategy increases costs by 10% (net price =US$0.12 /pound ) (Table 4 9). If = 1%, on average, the period at which
90 costs exceed returns will take place 7 years after LW attacks (Table 4 5 ; Figure 4 3 ). Additionally orchards 4 years or younger must be removed immediately once attacked by LW due to negative NPV values (Table 4 9). If =10%, t he period of destruction of all orchard trees due to negative net returns would take place 4 years after LW attacks (Table 4 7 ; Figure 4 5 ). Additionally, orchards 7 years or younger would need to be removed due to negative NPV (Table 4 11). Low Effectiveness Low effectiveness of the LW control strategy is defined as a strategy that is capable of slowing down the LW spread rate from 100% to 50% a year. First, it was assumed that using this control increases the production costs 5% (net price = US$0.13/pound ). If = 1%, t his control strategy allows growers to stay in business, on average, for 4 years after LW attacks ( Table 4 4 ; Figure 4 2 ). Additionally, orchards 8 years or younger should be removed immediately due to negative NPV (Table 4 8). If = 10%, the period at which the orchard reaches negative net returns takes place 3 years after LW attacks ( Table 4 6 ; Figure 4 4 ). A dditionally, avocado orchards 7 years and younger must be removed immediately (Table 4 10). Alternatively, it was assumed that the control strategy increases costs of production by 10% ( net price = US$0.12/pound ) (Table 4 9). If = 1%, negative net returns would be reached 4 years after LW attacks ( Table 4 5 ; Figure 4 3 ). Additionally, orchards 6 years or younger must be removed immediately once attacked by LW due to negative NPV values (Table 4 9). If = 10%, negative net returns would take place on average 2 years after the attack by LW ( Table 4 7 ; Figure 4 5 ). In addition, i t was found
91 that orchards 8 years or younger that are attacked by LW are not viable due to negative NPV (Table 4 11). Table 4 12 summarizes our results and the orchard remov al rules obtained for scenarios with LW ( Note : it does consider the two criteria used. ) First, the moment at which LW causes the net revenue to be negative (period of destruction of all orchard trees due to negative net returns). This is the moment in whi ch the grower s realize their avocado operation s must close. However, it is possible that the NPV calculated from year 1 to the period of destruction of all orchard trees due to negative net returns is not profitable, which is indicated by a negative NPV. W hen a negative NPV is calculated it is said that the orchard should be removed immediately. Concluding R emarks to the Empirical Application of the Proposed Model to Laurel Wilt Threatening South Florida Avocado Orchards LW is a recently discovered disease that threatens South Florida avocado orchards. Given its lethal nature and how fast it kills avocado trees, major concerns for the future of the Florida a vocado i ndustry have arisen. Unfortunately, many questions about LW are unresolved, and this has prevented scientists from devising a cost efficient means of controlling the disease T wo empirical models were developed each of them having as its goal to determine either the optimal replanting period (if LW does not attack the orchard) or the period of destruction of all orchard trees due to negative net returns (if LW attacks the orchard and control strateg ies are in place) The first model followed the model proposed in the first essay T he lack of informat ion on LW cost effective management, spread rate, treatment effectiveness, among others stand s as an obstacle for using the theoretical framework
92 W the first essay Thus, an asset valuation model was proposed tha t considers production information from the South Florida avocado industry and simulates LW attacks. These simulation s assume on the one scenario and on the other hand scenarios in which a control strateg y is in place. However, for the latter scenario several different levels of effectiveness from the use of a control strategy were assumed The s imulations presented here assume d that control strategy may increase costs either 5% or 10%, and also two values for disease incidence at period of infection. The goal was to find the time period at which costs become greater than gross avocado returns ; this is referred to as the period of destruction of all orchard trees due to negative net returns In a ddition, the NP V of these simulations ( from planting to period in which negative net returns are reached) was calculated to determine if avocado project s infested with LW are viab le. R esults suggest that for South Florida avocado production conditions, a control strateg y that lowers the spread rate to either 50% or 25% would have a moderate effect in controlling the damage caused by LW. Such a control strateg y would translate into a slightly delayed period at which negative net revenue is reached, and immediate destructi on of the orchard (because of negative NPV) would be suggested for a smaller number of ages compared with the do nothing scenario Encouraging results are found only for those scenarios in which it was assume d the control strategy is fully effective in controlling the spread of the disease Similarly, NPV values for all curves were found to be positive regard less of age of infection or the
93 cost increase. However, avocado profitability would decrease which is n ot good news for an economic activity in which the net margin is already low. In other words, for Florida avocado, a control strategy that is fully effective in control ling the spread of LW and that costs at a maximum 10% of the current production costs is required to keep avocado growers in business For our parameter values, this means a yearly investment of US$490 per acre per year, or US$5.6 0 per tree per year. Additionally, it was demonstrated that LW incidence at the first detection period is impo rtant because of the magnitude of its effect on the optimal period of destruction of all orchard trees due to negative net returns and that it is negatively related to NPV. It was also found a negative relationship between costs and period of destruction o f all orchard trees due to negative net returns This happens because when costs increase due to the control strategy costs become greater than the returns at an earlier period Again, the only exception was the case in which the spread rate is lowered to 0% by means of using the control strategy. These results highlight the importance of the sanitation strategy suggested by University of Florida researchers at the Tropical Research and Education Center (TREC) E arly detection (permanent scouting) and elim ination of diseased tissues and vectors are of paramount importance Note that this model will still be useful once scientists improve their understanding of biological relationships between the disease, the vector, and the host O nce all required relation ships are fully understood, it will be possible to use th is model jointly with the disease optimization model proposed in the first essay
94 Table 4 1 Potential direct impact from a Laurel Wilt outbreak on the Florida avocado industry Considered l oss 100% reduction in production 75% reduction in production 50% reduction in production Industry potential sales loss 30,000,000 22,500,000 15,000,000 Decline in property value** 326,250,000 244.688,000 163,125,000 Disease management costs*** 0 4,525,000 4,525,000 Total direct loss 356,250,000 271,713,000 182,650,000 *Based on three potential losses of avocado sales ** Based on the value of a mature avocado tree ***Monitoring fungicide and labor costs. Source: Excerpted from Evans et al. ( 2010 ).
95 Table 4 Considered impact 100% loss 75% loss 50% loss Industry sales 30,000,000 22,500,000 15,000,000 Output impacts 54,266,259 40,699,694 27,133,129 Employment impacts 546 409 273 Labor income impacts 19,674,272 14,755,704 9,837,136 Indirect business tax 1,862,415 1,396,811 931,207 Source: Excerpted from Evans et al. ( 2010 ).
96 Table 4 3 Scenarios considered with respect to LW control strateg y Scenario Cost increase LW incidence at first detection, Spread rate Net price Do nothing 0% 1% 100% 0.15 0% 10% 100% 0.15 Fully effective 5% 1% 0% ** 0.13 5% 10% 0% ** 0.13 10% 1% 0% ** 0.12 10% 10% 0% ** 0.12 Low effectiveness 5% 1% 50% 0.13 5% 1 0 % 50% 0.13 10% 1 % 50% 0.12 10% 1 0 % 50% 0.12 Intermediate effectiveness 5% 1% 25% 0.13 5% 10% 25% 0.13 10% 1% 25% 0.12 10% 10% 25% 0.12 *It is assumed partial effectiveness of the control strategy. Control strategy drives laurel wilt spread rate from 100% to either 50% (low effectiveness) or 25% (Intermediate effectiveness) ** It is assumed full effectiveness of the control strategy, d riving laurel wilt spread rate from 100% to 0%
97 Table 4 4 Period at which net returns become negative according to age at LW initial infection assuming 5 % cost increase and =1%* *Total costs increase due to treatment Do nothing =100% p=0.15 Low effectiveness =50% p =0.13 Intermediate effectiveness =25% p=0.13 Fully effective =0% p=0.13 1 5 5 9 42 2 5 6 10 42 3 5 7 11 42 4 6 8 12 42 5 7 9 13 42 6 8 10 14 42 7 9 11 15 42 8 10 12 16 42 9 11 13 17 42 10 12 14 18 42 11 13 15 19 42 12 14 16 20 42 13 15 17 21 42 14 16 18 22 42 15 17 19 23 42 16 18 20 24 42 17 19 21 25 42 18 20 22 26 42 19 21 23 27 42 20 22 24 28 42 21 23 25 29 42 22 24 26 30 42 23 25 27 31 42 24 26 28 31 42 25 27 29 32 42 26 28 30 33 42 27 29 31 34 42 28 30 32 34 42 29 31 33 35 42 30 32 34 36 42 31 33 34 37 42 32 34 35 37 42 33 35 36 38 42 34 36 37 39 42 35 37 38 39 42 36 38 39 40 42 37 39 39 40 42
98 Table 4 5 Period at which net returns become negative according to age at LW initial infection assuming 10 % cost increase and =1%* Do nothing =100%,p=0.15 Low effectiveness =50%, p=0.12 Intermediate effectiveness =25%, p=0.12 Fully effective =0%, p=0.12 1 5 5 8 41 2 5 6 9 41 3 5 7 10 41 4 6 8 11 41 5 7 9 12 41 6 8 10 13 41 7 9 11 14 41 8 10 12 15 41 9 11 13 16 41 10 12 14 17 41 11 13 15 18 41 12 14 16 19 41 13 15 17 20 41 14 16 18 21 41 15 17 19 22 41 16 18 20 23 41 17 19 21 24 41 18 20 22 25 41 19 21 23 26 41 20 22 24 27 41 21 23 25 28 41 22 24 26 29 41 23 25 27 30 41 24 26 28 31 41 25 27 29 32 41 26 28 30 32 41 27 29 31 33 41 28 30 32 34 41 29 31 32 35 41 30 32 33 35 41 31 33 34 36 41 32 34 35 37 41 33 35 36 37 41 34 36 37 38 41 35 37 37 39 41 36 38 38 39 41 37 39 39 40 41 *Total costs increase due to treatment
99 Table 4 6 Period at which net returns become negative according to age at LW initial infection assuming 5 % cost increase and =1 0 %* Do nothing =100%,p=0.15 Low effectiveness =50%, p=0.13 Intermediate eff ectiveness =25%, p=0.13 Fully effective =0%, p=0.13 1 5 5 6 41 2 5 5 7 41 3 5 6 8 41 4 6 7 9 41 5 7 8 10 41 6 8 9 11 41 7 9 10 12 41 8 10 11 13 41 9 11 12 14 41 10 12 13 15 41 11 13 14 16 41 12 14 15 17 41 13 15 16 18 41 14 16 17 19 41 15 17 18 20 41 16 18 19 21 41 17 19 20 22 41 18 20 21 23 41 19 21 22 24 41 20 22 23 25 41 21 23 24 26 41 22 24 25 27 41 23 25 26 28 41 24 26 27 29 41 25 27 28 30 41 26 28 29 31 41 27 29 30 32 41 28 30 31 32 41 29 31 32 33 41 30 32 32 34 41 31 33 33 35 41 32 34 34 35 41 33 34 35 36 41 34 35 36 37 41 35 36 37 37 41 36 37 37 38 41 37 38 38 39 41 *Total costs increase due to treatment
100 Table 4 7 Period at which net returns become negative according to age at LW initial infection assuming 10% cost increase and =10% Do nothing =100%,p=0.15 Low effectiveness =50%, p=0.12 Intermediate effectiveness =25%, p=0.12 Fully effective =0%, p=0.12 1 5 5 6 39 2 5 5 6 39 3 5 6 7 39 4 6 6 8 39 5 7 7 9 39 6 8 8 10 39 7 9 9 11 39 8 10 10 12 39 9 11 11 13 39 10 12 12 14 39 11 13 13 15 39 12 14 14 16 39 13 15 15 17 39 14 16 16 18 39 15 17 17 19 39 16 18 18 20 39 17 19 19 21 39 18 20 20 22 39 19 21 21 23 39 20 22 22 24 39 21 23 23 25 39 22 24 24 26 39 23 25 25 27 39 24 26 26 28 39 25 27 27 29 39 26 28 28 30 39 27 29 29 31 39 28 30 30 32 39 29 31 31 33 39 30 32 32 33 39 31 33 33 34 39 32 34 34 35 39 33 34 35 36 39 34 35 36 36 39 35 36 36 37 39 36 37 37 38 39 37 38 38 38 39 *Total costs increase due to treatment
101 Table 4 8 NPV according to age of initial infection and control strategy scenarios, assuming c ontrol strategy increases costs 5 %, and =1% *NPV is calculated from planting to the period in which net returns become negative Do nothing =100%,p=0.15 Low effectiveness =50%, p=0.13 Intermediate effectiveness =25%, p=0.13 Fully effective =0%, p=0.13 1 5737 5217 3015 11404 2 5117 4520 1951 11405 3 4467 3493 820 11406 4 3220 2272 315 11413 5 1761 991 1406 11429 6 293 239 2428 11458 7 1095 1375 3364 11487 8 2359 2410 4219 11516 9 3509 3351 4996 11543 10 4554 4207 5702 11567 11 5504 4985 6344 11589 12 6367 5692 6928 11610 13 7153 6335 7458 11628 14 7866 6920 7941 11644 15 8515 7451 8379 11660 16 9105 7934 8778 11673 17 9641 8373 9140 11686 18 10129 8772 9470 11697 19 10572 9135 9769 11707 20 10975 9465 10041 11717 21 11341 9765 10289 11725 22 11674 10038 10514 11733 23 11977 10285 10719 11740 24 12252 10511 10901 11746 25 12502 10716 11061 11752 26 12730 10902 11198 11757 27 12937 11071 11313 11762 28 13124 11216 11411 11766 29 13295 11338 11495 11770 30 13439 11437 11562 11774 31 13556 11520 11616 11777 32 13652 11589 11661 11780 33 13729 11644 11697 11782 34 13791 11687 11725 11784 35 13840 11719 11747 11786 36 13878 11744 11764 11788 37 13908 11763 11775 11789
102 Table 4 9 NPV according to age of initial infection and control strategy scenarios, assuming control strategy increases costs 10 %, and =1% Do nothing =100%,p=0.15 Low effectiveness =50%, p=0.12 Intermediate effectiveness =25%, p=0.12 Fully effective =0%, p=0.12 1 5737 5590 3844 9237 2 5117 5030 2908 9238 3 4467 4145 1894 9239 4 3220 3067 865 9246 5 1761 1918 130 9262 6 293 808 1064 9291 7 1095 220 1921 9320 8 2359 1156 2703 9349 9 3509 2008 3414 9376 10 4554 2782 4061 9400 11 5504 3486 4648 9422 12 6367 4126 5182 9442 13 7153 4708 5668 9461 14 7866 5236 6109 9477 15 8515 5717 6511 9492 16 9105 6154 6876 9506 17 9641 6551 7207 9519 18 10129 6913 7509 9530 19 10572 7241 7783 9540 20 10975 7539 8032 9549 21 11341 7811 8259 9558 22 11674 8057 8465 9566 23 11977 8282 8652 9573 24 12252 8486 8822 9579 25 12502 8671 8968 9585 26 12730 8839 9093 9590 27 12937 8993 9204 9595 28 13124 9123 9294 9599 29 13295 9233 9368 9603 30 13439 9328 9429 9607 31 13556 9403 9479 9610 32 13652 9463 9518 9613 33 13729 9509 9547 9615 34 13791 9543 9572 9617 35 13840 9569 9590 9619 36 13878 9591 9603 9621 37 13908 9606 9613 9622 *NPV is calculated from planting to the period in which net returns become negative
103 Table 4 10 NPV according to age of initial infection and control strategy scenarios, assuming control strategy increases costs 5%, and =10%* Do nothing =100%,p=0.15 Low effectiveness =50%, p=0.13 Intermediate effectiveness =25%, p=0.13 Fully effective =0%, p=0.13 1 6009 5740 5070 7958 2 5573 5366 4507 7962 3 4900 4839 3734 7966 4 4041 3926 2737 8034 5 2710 2750 1591 8191 6 1255 1442 366 8474 7 194 179 799 8762 8 1541 997 1887 9053 9 2765 2067 2876 9318 10 3877 3039 3775 9558 11 4889 3924 4592 9777 12 5808 4727 5335 9976 13 6644 5458 6010 10156 14 7404 6122 6624 10320 15 8095 6726 7182 10470 16 8723 7275 7690 10605 17 9294 7774 8151 10729 18 9813 8228 8571 10841 19 10285 8640 8952 10943 20 10714 9015 9298 11035 21 11104 9356 9613 11119 22 11459 9666 9900 11196 23 11781 9947 10160 11265 24 12074 10203 10397 11329 25 12340 10436 10612 11386 26 12583 10648 10808 11438 27 12803 10840 10978 11486 28 13003 11015 11129 11529 29 13185 11166 11259 11568 30 13342 11299 11368 11603 31 13473 11410 11458 11636 32 13580 11500 11535 11664 33 13672 11572 11597 11688 34 13746 11629 11646 11709 35 13806 11674 11685 11727 36 13853 11709 11718 11742 37 13889 11739 11742 11755 *NPV is calculated from planting to the period in which net returns become negative
104 Table 4 11 NPV according to age of initial infection and control strategy scenarios, assuming control strategy increases costs 10 %, and =10%* Do nothing =100%,p=0.15 Low effectiveness =50%, p=0.12 Intermediate effectiveness =25%, p=0.12 Fully effective =0%, p=0.12 1 6009 6113 5580 5795 2 5573 5739 5136 5799 3 4900 5349 4481 5804 4 4041 4555 3620 5871 5 2710 3497 2597 6029 6 1255 2325 1484 6311 7 194 1186 421 6600 8 1541 121 574 6891 9 2765 847 1478 7155 10 3877 1727 2301 7396 11 4889 2526 3048 7614 12 5808 3253 3728 7813 13 6644 3914 4346 7993 14 7404 4515 4908 8158 15 8095 5062 5418 8307 16 8723 5558 5882 8442 17 9294 6010 6304 8566 18 9813 6420 6688 8678 19 10285 6793 7037 8780 20 10714 7132 7354 8872 21 11104 7441 7642 8956 22 11459 7721 7904 9033 23 11781 7976 8142 9102 24 12074 8208 8359 9166 25 12340 8418 8556 9223 26 12583 8610 8735 9275 27 12803 8784 8897 9323 28 13003 8942 9036 9366 29 13185 9086 9154 9405 30 13342 9206 9254 9440 31 13473 9305 9340 9473 32 13580 9384 9408 9500 33 13672 9446 9461 9525 34 13746 9494 9506 9545 35 13806 9534 9541 9563 36 13853 9566 9567 9579 37 13889 9588 9588 9592 *NPV is calculated from planting to the period in which net returns become negative
105 Table 4 12 D ecision rules for the model with LW Period at which net return becomes negative and NPV calculations ( considered simultaneously ) Control strategy =1% C.I.= 5% =1% C.I.= 10% =10% C.I.= 5% =10% C.I.= 10% Fully effective =0% No immediate R.T. R.T. year 43 No immediate R.T. R.T. year 4 1 No immediate R.T. R.T. year 4 1 No immediate R.T. R.T. year 39 Interm Effectiveness =25% R.T. immediately >3 R.T. 8 years later R.T. immediately >4 R.T. 7 years later R.T. immediately >6 R.T. 5 years later R.T. immediately >7 R.T. 4 years later Low effectiveness =50% 5 R.T. immediately >5 R.T. 4 years later R.T. immediately >6 R.T. 4 years later R.T. immediately >7 R.T. 3 years later R.T. immediately >8 R.T. 2 years later Do nothing* >6 R.T. 2 years later >6 R.T. 2 years later C.I.: Increase in total costs due to LW control strategy *In the do nothing scenario, growrs do not incurr in extra costs R.T. Remove all orchard trees Interm.: Intermediate
106 Figure 4 1 Disease incidence along time according to the considered laurel wilt possible spread rates (Gompertz)
107 Figure 4 2 Period at which net returns become negative according to age at LW initial infection assuming 5 % cost increase and =1%
108 Figure 4 3 Period at which net returns become negative according to age at LW initial infection assuming 10 % cost increase and =1%
109 Figure 4 4 Period at which net returns become negative according to age at LW initial infection assuming 5 % cost increase and =1 0 %
110 Figure 4 5 Period at which net returns become negative according to age at LW initial infection assuming 10 % cost increase and =1 0 %
111 CHAPTER 5 CONCLUSIONS Diseases in perennial crops are a major threat for growers due to the fact that they may kill their trees and turn a profitable operation into a non profitable one very quickly. This is the case in the empirical applications presented here, p ud ricin del cogollo (PC) on Colombian oil palm plantations and Laurel Wilt (LW) on South Florida avocado orchards. When one considers diseases from an orchard perspective, it is yield per unit area and by increasing production costs. Commonly when an outbreak takes place it is the growers who are left to bear the brunt of costs associated with disease control and they must employ one or various efficient and cost effective tacti cs which explains why t h is work focuses on the perspective. Disease management strategies in perennial crops may include avoidance, exclusion, eradication, protection and treatment of diseased plants, which are not mutually exclusive strategies However deciding on a particular course of action can be extremely challenging especially in situations where the crop in question is perennial. Among the factor s that add a great deal of complexity when making decisions regarding a specific control str ategy, we mentioned: 1) perennial crops involve a long term investment that requires a substantial amount of initial capital outlay 2) perennial crops usually require a number of years before trees reach maturity, and 3) once established it is costly to u ndo this type of operation. Complicating matters further is the fact that diseased trees may still bear fruit albeit at lower yields and reduced quality. The former sets a dilemma for growers, since
112 they may prefer to attain some short term revenue at the cost of allowing the source of infection to remain in the fields. Most studies in the literature dealing with perennials have focused on assessing yield reductions and/or economic damages caused by pests. Little research has been done focusing on develop ing a decision making framework that would assist growers in choosing a particular approach or management strategy in situations where a pest is present in an orchard. The model proposed here is intended to help fill that gap. Consequently this research i s aimed at developing a framework that would facilitate economic evaluation of disease management in perennial crops. The literature review presents different approaches to disease management from the economics discipline Through the literature review th ere were found appealing features from the so called O ptimization M odels for dealing with pest management in agriculture. It must be highlighted that Optimization models maximiz e the revenue by choosing a certain control strategy. Some of the concepts borrowed in order to build the proposed models are potential output, abatement and damage functions. Potential output refers to the amount of product that may have been obtained in the absence of the disease. Abatement is a concept referring to the effectiveness of the disease control strategy. Damage functions link biological and economic systems. A lso found were the reduced form damage function approach and the structural damage function approach. The former assumes that yield loss due to disea se attack is a function of an exogenous pest population, while the latter endogen e izes the pest population. By endogeneizing the pest population a crucial element can be added to our model namely time. By
113 considering the disease orchard dynamics it was possible to arrive at more powerful insights for disease management in perennial s In this case, net revenue through time should be thought of as the NPV of the operation. Two models are proposed here and are intended to maximize the NPV of the orchard by choosing the optimal replanting/ period of destruction of all orchard trees due to negative net returns The first model is intended to determine the optimal replanting period that maximizes the NPV of an orchard without disease This model constitutes the in the Faustmann Rotation problem for determining the optimal rotation period This model provides an effective tool for growers to tackle the crucial question of when to replant, which is by no means an easy one. In fact, for both Colombian oil palms and South Florida a vocado o rchards this was an unsolved question. The second model seeks to determin ing the optimal amount of control and the optimal period of destruc tion of all orchard trees due to negative net returns after a disease is detected in the orchard. This model It is assumed that there exists a strategy for controlling the disease Also, it is assumed that the proc ess by which the disease spreads is known and that there is available information on the control strategy effectiveness. Given that these functions were known it was possible to build an Optimal Control model of the bang bang type for PC threatening Colombian oil palm plantations Note that the at the disease first detection is a parameter entering the second model. Since s cientific information on the empirical applications
114 presented here PC and LW, state that oil palm and avocado orchards are susceptible to being infested at any age, it is possible to obtain a solution for each possible orchard age. It is important to highlight that results from both models are comparable. As mentioned above they use the same yield functions, time units and area units. This is very important because it allows one to determine the difference s between disease free and with disease scenarios, which may constitute a very powerful tool for policy making decisions such as mandatory host destruction With this tool one can determine: What would be a fair retribution for grower s who are mandated to destroy their trees Assess the economic impact of the disease. Determine the threshold of disease incidence after which it would be bet ter to remove all trees from the orchard Comparisons among control strategies cost effectiveness. When using a dynamic framework there are two tools of great importance : discount rate and prices. This work considers sensitivity analyses o f both in orde r to consider risk in our results, s ince it is known that price relates positively to NPV, while discount rate relates negatively to NPV. However, when analyzing the FOC (from maximizing NPV by choosing T) there was found a result that at first sight s eemed to be counterintuitive. We refer to the relationship between price and optimal replanting period in the w ithout disease model. Nonetheless, one must keep in mind that the disease free scenario assumes the grower will stay in business for future rotat ions with identical features. This result makes sense considering that a higher price has a larger effect on increasing the marginal cost of waiting an extra period than it does on the marginal benefit of waiting an extra period.
115 The models we present he re are deterministic in the sense that they assume time invariant biological relationships between disease and yield, while also assuming that disease spreading rates and treatment effectiveness are known. In a ddition, the proposed framework requires a great deal of good quality information on prices, costs and parameters, so the results obtained are useful for growers as well as policy makers. However, note that even lack ing information on LW such as management strategy spread rate, and treatment ef fectiveness, it was possible to build a With disease model to determine the optimal period of destruction for all orchard trees due to negative net returns while allowing grower s to maximize their NPV. We do so by using an asset valuation model that uses S outh Florida avocado production information to simulate LW attacks. In th is case, it was assume d that LW control strateg y effectiveness and costs increase if an active control plan is followed. Even with the limited information on LW due mainly to its rece nt discovery, it was possible to propose a tool that considers the interaction between disease and avocado production. Specifically, we consider age at first detection and profitability (cost increase, control effectiveness and yield) to establish proper orchard removal rules. Even more important, it was determine d that the maximum cost for any control strategy can be cost effective. In terms of future research, we suggest t he further develop ment of this framework by including varying prices based on spati al and temporal dynamics of the disease different levels of technology ado ption, and diverse yield scenarios Additionally, it would be of extreme importance to incorporate the social dimension of the problem in these analyses. This could be done by assuming that there
116 is a Central Planner solving for the NPV maximization problem using parameters sensitive to envi ronmental concern s about specific control strateg ies This dissertation makes an important contribution to the literature since there is little information on optimal replanting age when disease is present in perennial crops. In a ddition, the results here in are informative for growers in terms of providing a specific moment in time at which replanting makes economic sense under different price scenarios with and without disease This i s an un re solved question for productive oil palm plantations in Colombia
117 APPENDIX A MODELS USED TO PARAMETERIZE THE MODELS ON PUDRICI"N DEL COGOLLO Empirical functions: empirical functions and parameters were calculated from the available information The following present s each model used for parameterizing the PC model. Net price Fruit price was calculated from the Crude Palm Oil price series (Fedepalma 2011) between January 2001 and December 2010. Production costs were estimated from CEPLV records. Potential yield (Kg/ha/month) Estimated model: where expected yield and ( orchard age in terms of months) Table A 1 OLS estimates of the effect of age and age squared on yield Parameter Estimator 27.2652*** (0.2664) 0.0668*** (0.0006) Intercept ( 320.4161*** (23.0151) N 398 F test 5383.95 R squared 0.34 = p < 0.10, ** = p < 0.05, and *** = p < 0.001 where p is the p value Standard error is in parenthes e s
118 Damage function. Yield in the presence of PC Estimated model: where and is the number of PC cases detected Table A 2 OLS estimates of the effect of number of diseased trees and number of diseased trees squared on potential yield Parameter Estimator 0.0033*** (0.00035) 0.00002*** (4.8130E 06) Intercept 1.00035*** (0.0029) N 734 F test 503.409 R squared 0.57935 *=p < 0.10, ** = p < 0.05, and *** = p < 0.001, where p is the p value Standard error is in parenthes e s
119 Costs of PC control strategy (Colombian Pesos/ha) Estimated model: where represents the monthly costs of the PC control strategy and is the number of PC cases treated Table A 3 OLS estimates of the effect of number of treated trees on PC control costs Parameter Estimator 6,332*** (5.3389) Intercept 50,900*** (443.0940) N 143 F test 1406702 R squared 0.99 = p < 0.10, ** = p < 0.05, and *** = p < 0.001 Standard error is in parenthes e s
120 Estimated model: where is PC new cases and represents PC cumulative cases. Note this is a regression with no intercept term ( forced to the origin ). Table A 4 OLS estimates of the effect of cumulative PC cases on new PC cases Parameter Estimator 0.2020*** (0.01448) Intercept 0 (forced) N 22 F test 194.5988 R squared 0.90 = p < 0.10, ** = p < 0.05, and *** = p < 0.001 Standard error is in parenthes e s
121 APPENDIX B MODEL USED TO PARAMETERIZE THE MODEL ON LAUREL WILT (NO DISEASE SCENARIO) Potential yield (Kg/ha/month) Estimated model: where represents the expected yield and is the orchard age expressed in terms of months Table B 1 OLS estimates of the effect of age and age squared on yield Parameter Estimator Intercept ( 3599.9522*** (1254.2564) 1355.5938*** (141.0865) 30.3932*** (3.3371) N 40 F test (p value) 46.53 R squared 0.7155 = p < 0.10, ** = p < 0.05, and *** = p < 0.001 where p is the p value Standard error is in parenthes e s
122 Table B 2 Parameters used for the model Planting density per acre (number of trees) 87 Discount rate (percentage) 10% Sales charge (per pound) 0.05 Pick, haul and pack (per pound) 0.12 Price received by grower on tree (per pound) US$ 0.32 Stump removal cost (per tree) 150 Cost of a new tree 20 Cost to plant a new tree 10 Source: http://agecon.centers.ufl.edu
123 Table B 3 Costs per acre of producing avocado in South Florida Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 30 Year 35 Year 40 CULTIVATION COSTS Fertilizer 174 218 261 305 348 566 696 696 696 Fungicide 44 44 131 131 131 219 261 261 261 Herbicide 174 174 174 150 150 150 150 150 150 Insecticide 10 22 44 65 87 109 131 131 131 Pruning 44 44 61 174 174 174 296 296 296 Irrigation 35 35 35 35 50 50 50 50 50 Mowing 513 513 313 287 200 200 200 200 200 Total cultivation cost (I) 994 1048 1018 1146 1139 1467 1783 1783 1783 FIXED COSTS Land rent 500 500 500 500 500 500 500 500 500 Supervision 155 155 155 155 155 155 155 155 155 Overhead 300 300 300 300 300 300 300 300 300 Total fixed cost (II) 955 955 955 955 955 955 955 955 955 SALES CHARGE (III) 0 0 127.5 340 680 765 850 658 509 PICK, HAUL AND PACK (IV) 0 0 306 816 1632 1836 2040 1579 1221 TOTAL COSTS (I)+(II)+(III)+(IV) 1949 2003 2406 3257 4406 5023 5628 4974 4468 Source: http://agecon.centers.ufl.edu
124 LIST OF REFERENCES Alamo, C., E.A. Evans, A. Brugueras Trade Implications of the Introduction of Black Sigatoka ( Mycosphaerella Fijiensis Journal of Agricultural and Applied Economics 39: 5 17. Batra L. vision, and Nutritional Studies of Mycologia 59 (6): 976 1017. American Journal of Agricultural Economics 84 (2): 279 291. Carls American Journal of Agricultural Economics 52 (2): 216 223. Europe an Journal of Lipid Science and Technology 109 (4): 307 314. Journal of Environmental Economics and Management 29: 25 41. Elements of Dynamic Optimization Prospect Heights IL: Waveland Press Inc pp. 161 204. Clark, C Mathematical Bioeconomics: The Math of Conservation 3 rd ed. Hoboken, NJ : John Wiley & Sons Inc pp. 223 251. A nnual M eeting, Orlando FL, 27 29 July Circular No. CIR1034 Laurel Wilt University of Florida EDIS No. HS1136. European Economic Review 52 (5): 892 918.
125 Duarte, E., and L. Gutterman. 2007. d e Los Costos d e Produccin d el Aceite d Unpublished, Fedepalma. Evans, E. Choices (2): 5 9. Evans, E.A. and J. Crane. 2009. o f t he Replacement Costs o f Commercial a nd Backyard Avocado Trees i University of Florida EDIS No. FE8 25 Profitability Analysis for Florid FE837 Hortechnology 20 (1): 235 238. Fedepalma. 2008. Anuario Estadstico 2007. Bogot: Fedepalma. 2012. Anuario Estadstico 2011. Bogot: Fedepalma. Fraedrich, S.W., T.C. Harrington, R.J. Rabaglia, M.D. Ulyshen, A.E. Mayfield III, J. Hanula, J.M. Eickwort, and D.R. Miller. Ambrosia Beetle Causes a Lethal Wilt in Redbay and Other Lauraceae in the Plant Disease 92 (2): 215 224. Oleagineaux, Gras Et Lipi des 12 (2): 121 124. Associations of Redbay Ambrosia Beetle (Coleoptera: Curculionidae: Scolytinae ), Exotic Vector of Laurel Wilt Killing Redbay Trees in the Southeaste rn Journal of Economic Entomology 101 (4): 1276 1286. Harrington, T C, and S W Wilt Fungus and Other Mycangial Fungi from the Redbay Ambrosia Beetle, Xyleborus Glabaratus topathology 100 (10): 1118 23. Raffaelea Lauricola a New Ambrosia Beetle Symbiont and Pathogen on the Lauracea Mycotaxon 104:399 404. t, Caused by Raffaelea lauricola on Xylem Function in Avocado, Persea americana Forest Pathology 42 (3): 239 245.
126 nted at USDA Integrating Risk Assessment and Economics for Regulatory Decisions, Washington D.C. 7 December. Kendra, P.E., Niogret, J., Montgomery, W.S., Sanchez, J.S., Deyrup, M.A., Pruett, G.E., Ploetz, R.C., Epsky, N.D., and Heath, R.R. 2012. Temporal Analysis o f Sesquiterpene Emissions f rom Manuka a nd Phoebe Oil Lures a nd Efficacy f or Attraction o f Xyleborus Glabratus ( Coleoptera : Curculionidae : Scolytinae ) J ournal Econ omic Entomology 105 (2) :659 669. io temporal Analysis of Xyleborus Glabratus (Coleoptera: Curculionidae: Scolytinae Environmental Entomology 37 (2): 442 452. D. Leonard, and N. van Long. Optimal Control Theory and Static Optimization in Economics Cambridge: Cambridge University Press, pp. 221 262. America n Journal of Agricultural Economics 68 (2): 261 273. V irus American Journal of Agricultural Economics 83: 556 569. Revista Palmas 31 (1): 43 53. Martinez, G., N. Arias, G. Sarria, G. Torres, F. Varn, C. Norea, S. Salcedo, H Aya, J. Ariza, R. Aldana, L.C. Martinez, O. Moya, and C. Burgos. 2009. Manejo Integrado De La Pudricin Del Cogollo (PC) De La Palma De Aceite Bogota: SENA SAC. Mayfield III, A.E., J.H. Crane, and J. : A Threat to Redbay, Avo Florida EDIS No.HS1137 Journal of Economic Theory 40 (2): 229 249. puesta De Evaluacin Del Impacto Econmico De La PC En
127 Mosquera, M., and E. Garca. Revista Palmas 26 (2): 11 19. Mumford, J.D., and G.A. Norton. 1984. Annual Review of Entomology 29: 157 174. Oliveira, M., D. Escobar, N. Rojas, J. Moreno, C. Quintero, and A. Tibocha. 2011. Cuadernos Fedesarrollo 37: 1 93. Pea, J.E., Crane, J.H., Capinera, J.L., Duncan, R.E., Kendra, P.E., Ploetz, R.C., McLean, S., Brar, G., Thomas, M.C., and Cave, R.D. 2011. Chemical Control of t he Redbay Ambrosia Beetle, Xyleborus Glabratus, a nd o ther Scolytinae ( Coleoptera : Curculionidae ) Florida Entomolo gist 94 (4) : 882 896. Ploetz, R. Plant Disease 91 (6): 644 663. Ploetz, R.C., J.M. P rez Martinez, E.A. Fungicidal Management of Laurel Wilt o f Avocado Plant Disease 95 (8): 977 982 Ploetz, R.C., J.M. Prez Martnez, J.A. Smith, M. Hughes, T.J. Dreaden, S.A. Inch, and Y. Fu. 2011. Plant Pathology 61 (4): 1 8. Rabaglia, R.J., Dole, S.A. and Cognato, A.I. 2006. Review o f American Xyleborina ( Coleoptera : Curculionidae : Scolytinae ) Occurring North o f Mexico With a n Illustrated Key Ann als of the Entomol ogical Soc iety of Amer ica 99 (6) : 1034 1056. Salifu, A.W., K.A. Grogan, T.H. Spreen, and F.M. Roka. meeting, Birmingham AL, 4 7 February. Pest Species with Barrier Z Ecological Applications 8 (3): 833 845. Proce edings of the Florida State Hor ticultural Society 2003 Florida State Horticultural Society, pp. 289 294. Torres, G., G. Sarria, and G. Martinez. 2010. Identificacin Temprana y Manejo De La Pudricin Del Cogollo En La Palma De Aceite Bogot: SENA U.S. Department of Agriculture, National Agricultural Statist ics Service. 2013. Avocado Price Received, Measured in Tons. http://quickstats.nass.usda.gov/results/
128 University of Florida Tropical Research and E ducation C enter. 2006. Agricultural Economics Extension: Interactive tools Tree Value Analysis. http://agecon.centers.ufl.edu/TreeCostAvocado.htm. 2012. Agricultural Economics Extension: Interactive tools Tree Value Analysis. http://agecon.centers.ufl.edu/TreeCostAvocado.htm Valderrama, M., and H. Mondragn. 1998. Desarrollo y Equidad Con Campesinos Bogot: Tercer Mundo Editores.
129 BIOGRAPHICAL SKETCH In 1999, Mauricio Mosquera obtained a B.Sc. degree in Economics from the Universidad Nacional de Colombia. His research project was focused on studying the effect of the Structural Adjustment in the 1990 s on Colombian peasants. Once he graduated as an Economist, he decided to pursue a Master s degree at the Universidad Nacional de Colombia He obtained his M.Sc degree in Economic Sciences in 2002. His research project focused on determining if GMO potatoes would be cost effective in Colombia. In January 2000, while pursuing his Master studies he was hired at the Contralora General de la Repblica (the Colombian Governments O ffice in charge of contro lling spending by P ublic institutions). There, he worked on evaluating a gricultural policy for almost three years. In June 2002, he was hired by the Colombian Federation of Cattle Ranchers (Fedegan) where he joined the Planning Office team. There he participated in two main projects: Updating the Cattle Index Prices and on the proposal of the Development Plan for the Colombian Bovine Sector 2003 2020 Since October 2003, he has work ed for Cenipalma ( the Colombian Oil Palm Research Center) ; his work i s oriented towards suppo rt ing Colombian oil palm decision makers (managers) to determ ine if technologies adapted or generated by Cenipalma a re cost effective. Mauricio was the Leader of the Impact Assessment team until he came to the Uni versity of Florida to pursue his Ph D Stu dies in 2009 He received his Ph.D. from the University of Florida in spring of 2013