Front Cover
 Title Page
 Table of Contents
 List of tables and figures
 Technological developments and...
 Theory and methodology
 Cost functions and technology
 Empirical results
 Appendix A: Data
 Back Cover

Group Title: Bulletin - University of Florida. Agricultural Experiment Station - 863
Title: Modeling technical change in the frozen concentrated orange juice processing industry
Full Citation
Permanent Link: http://ufdc.ufl.edu/UF00027757/00001
 Material Information
Title: Modeling technical change in the frozen concentrated orange juice processing industry
Series Title: Bulletin Agricultural Experiment Stations, University of Florida
Physical Description: ii, 57 p. : ill. ; 23 cm.
Language: English
Creator: Shonkwiler, J. S ( John Scott )
Stranahan, H. A
Publisher: Agricultural Experiment Stations, Institute of Food and Agricultural Sciences, University of Florida
Place of Publication: Gainesville
Publication Date: 1986
Subject: Orange juice industry -- Mathematical models -- Florida   ( lcsh )
Orange juice industry -- Research -- Florida   ( lcsh )
Genre: government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
non-fiction   ( marcgt )
Bibliography: Bibliography: p. 51-57.
Statement of Responsibility: J.S. Shonkwiler and H.A. Stranahan.
General Note: "September 1986."
Funding: Bulletin (University of Florida. Agricultural Experiment Station) ;
 Record Information
Bibliographic ID: UF00027757
Volume ID: VID00001
Source Institution: Marston Science Library, George A. Smathers Libraries, University of Florida
Holding Location: Florida Agricultural Experiment Station, Florida Cooperative Extension Service, Florida Department of Agriculture and Consumer Services, and the Engineering and Industrial Experiment Station; Institute for Food and Agricultural Services (IFAS), University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: aleph - 000882861
oclc - 15147094
notis - AEJ0814

Table of Contents
    Front Cover
        Front Cover
    Title Page
        Title Page
    Table of Contents
        Page i
    List of tables and figures
        Page ii
        Page 1
        Page 2
    Technological developments and R & D in the FCOJ industry
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
    Theory and methodology
        Page 9
        Page 10
        Measuring the technical dimensions of R & D
            Page 11
            Page 12
            Page 13
        The effect of R & D on input usage
            Page 14
            Page 15
            Page 16
            Page 17
            Page 18
            Page 19
    Cost functions and technology
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Estimation method
            Page 28
    Empirical results
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
        Page 47
    Appendix A: Data
        Page 48
        Page 49
        Page 50
        Page 51
        Page 52
        Page 53
        Page 54
        Page 55
        Page 56
        Page 57
    Back Cover
        Back Cover
Full Text


The publications in this collection do
not reflect current scientific knowledge
or recommendations. These texts
represent the historic publishing
record of the Institute for Food and
Agricultural Sciences and should be
used only to trace the historic work of
the Institute and its staff. Current IFAS
research may be found on the
Electronic Data Information Source

site maintained by the Florida
Cooperative Extension Service.

Copyright 2005, Board of Trustees, University
of Florida

~~September 1986

J I If i LPIu VJ I

Bulletin 863

DEC 8 1986

I.F.A.S. Univ. of Florida

Modeling Technical Change in
the Frozen Concentrated
Orange Juice Processing Industry

J. S. Shonkwiler and H. A. Stranahan

Agricultural Experiment Stations
Institute of Food and Agricultural Sciences
University of Florida, Gainesville
J. M. Davidson, Dean of Research





J.S. Shonkwiler and H.A. Stranahan

Food and Resource Economics Department
University of Florida



LIST OF TABLES AND FIGURES ............................... ii

INTRODUCTION ...............................o.............. 1

IN THE FCOJ INDUSTRY...................................... 3

THEORY AND METHODOLOGY.................................... 9

Measuring the Technical Dimensions of R & D........... 11

The Effect of R & D on Input Usage................... 14

COST FUNCTIONS AND TECHNOLOGY............................. 20

Estimation Method ................................... 28

EMPIRICAL RESULTS......................................... 29

SUMMARY........................................... ...... 44

APPENDIX A: DATA.......................................... 48

REFERENCES...................................... .......... 51


Table Page

1 U.S. Citrus Per Capita Consumption................. 4

2 Parameter Estimates for the Translog
Cost Function...................................... 33

3 Test Statistic for Restricted Models............... 35

4 Estimated Allen Partial Elasticities
of Substitution (AES).............................. 37

5 Estimated Input Price Elasticites.................. 37

Figure Page

1 Ahmad's Induced Innovation Model.................. 16

2 Florida FOB FCOJ Movement,
Million Concentrate Gallons........................ 41


The Florida citrus industry utilizes over 80 percent of

Florida oranges for frozen concentrated orange juice (FCOJ) or

related products and is the second largest producer of orange

products in the world (Gunter, 1984). Many factors are

involved in the growth of the Florida FCOJ industry. Among

them are numerous product improvements that have resulted from

investment in research and development (R & D) by private

industry and the Florida Department of Citrus (FDOC). The

Florida Department of Citrus is a self-financed and state-regu-

lated organization that has supported a major proportion of

FCOJ research conducted since 1940.

The citrus processing subsector has devoted substantial

resources toward technological advancement. However, no stud-

ies of the structure of production in the FCOJ industry have

been published. Therefore, little information exists regarding

the degree of technological change in the industry and the

results from R & D activities. This study attempts to model

the underlying production relationships of the FCOJ industry

during the period 1956-80. Using the dual relationship between

production and cost functions, a translog cost function and

corresponding share equations are estimated.

Estimation of the translog cost function in conjunction

with the share equations allows analysis of homotheticity of

the production structure, computation of input substitution and'

price elasticities as well as evaluation of the effects of

technical change on an input's share in total cost.

Usually, the arguments of a cost function are input prices

and output; however, McFadden (1978) shows that a fixed input

may be introduced into the cost function as well. This input

may be any factor which characterizes the state of technical

progress or which describes or influences the production tech-

nology. Since R & D is an input aimed exclusively at product

and process innovation and has been shown to be of significant

influence in productivity and production function studies, a

measure of the quantity of Florida citrus research is intro-

duced into the cost function.

In this manner, technical change can be represented in a

more relevant manner rather than that from using a time trend

or other deterministic functions to approximate temporal

changes in technology. That is, R & D enters the cost function

as a specific quantity affecting the evolving structure of

costs. The purpose of the inclusion of R & D and the time

trend exclusion is to measure and identify the specific cost

reducing effect of a variable aimed exclusively at product and

process innovation.

Since the quantity of R & D is used to represent technical

change, certain inferences about the value of R & D can be made

when the translog cost function is employed. Following Diewert

(1974) and Lau (1976), the shadow price of R & D can be

obtained by partial differentiation of the cost function with

respect to the quantity of research. Assuming a constant rate

of growth, a continuously compounded average rate of return

associated with Florida citrus processing research can then be


This study proceeds by considering some technological

developments and the role of research and development in the

Florida FCOJ industry. Next, methodological issues are

addressed in terms of theoretical models used to represent

technological change and investment in R & D. The third sec-

tion reviews the translog cost function and its value in the

present context. Then the empirical model is presented and

analyzed in terms of the previously discussed methodology. The

study concludes with some observations regarding the relevance

of the findings and possible shortcomings in the approach



In 1935 the Florida State Legislature passed a set of laws

generally referred to as the Florida Citrus Code in order to

protect the health, welfare and stability of the industry. The

FDOC was established under these guidelines to foster industry

coordination through stimulating demand, promoting quality

standards and establishing a research program for Florida


An impetus to industry growth occurred in 1945 when the

scientific research staff at the FDOC patented frozen concen-

treated orange juice. This technological breakthrough has been

a key component in the industry's expansion and changing struc-

ture. Per capital consumption of citrus products has grown from

just over 22 pounds in 1920 to almost 118 in 1980 (Table 1).

Furthermore, the increase in consumption of processed products

has more than offset the decrease of fresh citrus (Gunter,


Table 1. U.S. citrus per capital consumption

1920 1940 1960 1980

Fresh* 22.2 52.1 30.7 26.3
Processed 10.4 52.2 91.2

Total 22.2 62.5 82.9 117.5

Source: Gunter, 1983.
*Excludes lemons and limes.

The success of processed citrus can be attributed in part

to the quality standards governing processed orange juice which

ensure a homogeneous product, development of alternative pro-

duct forms, the relatively stable real price of FCOJ and a

S large scale marketing program (Myers, 1978). At the core of

these developments has been citrus processing research. Scien-

tific research has affected the quality, development and cost

structure of the processed product forms. Economic and market-

ing research has guided the marketing strategy and affected the

industry pricing structure.

The Florida citrus sector has demonstrated adeptness in

its ability to stimulate demand and satisfy consumer prefer-

ences. However, the continuing success of the citrus industry

is intimately tied to the state of technology. Many of the

past achievements in the citrus sector can be attributed to

both private and publicly funded scientific research. A new

aseptic processing and packaging technology in the 1960's made

possible the introduction of a single strength ready-to-serve

chilled orange juice. Due to changing lifestyles, the conven-

ience provided by this product and an effective marketing

strategy, ready to serve chilled orange juice has experienced a

substantially greater increase in demand than that for FCOJ

during the last 15 years.

In addition to new product improvements, scientific

research has also yielded several cost reducing production

technologies. Low temperature pan evaporators used universally

within the industry before 1960 have for the most part been

replaced by high speed evaporators. These evaporators are

almost six times more energy efficient and are able to process

a higher quality orange juice in about five percent of the time

needed for pan evaporation (Lykes-Pasco, no date). Along these

same lines, more efficient juice extraction equipment has

increased the amount of juice produced from each orange by 26

percent (MacDowell et al., 1962).

Technology has permitted not only greater processing effi-

ciency but a greater utilization of the entire orange. Before

1950, the remnants of processing such as pulp, rind and pulp

wash were discarded as waste. Today there is virtually no

waste from processing oranges. The citrus industry processes

the rind and pulp for use in cattle feed and more recently they

have been used as high fiber filler for flour and hotdogs.

Methods for capturing essential oils and essence recovery have

improved the amount and quality of citrus flavorings produced.

In this case scientific research has allowed a more efficient

utilization of citrus by-products.

Although several of the larger firms in the Florida citrus

processing industry engage in scientific and marketing

research, few employ an economic research department. The

FDOC's Economic Research Department provides information

concerning long and short-term supply and demand conditions in

the United States and abroad. In addition, the department is

responsible for answering specific questions posed by industry

members and addressing legislative matters affecting the


The Economic Research Department in conjunction with the

Market Research Department is responsible for monitoring trends

in consumer behavior that may affect citrus marketing strate-

gies. By studying the demand for citrus products and analyzing

price elasticities or substitutability among product forms, the

effects of changing prices and their impact on the industry are

investigated. Since returns to the grower and processor are

often highly dependent on retail price and volume, improved

knowledge of prices and quantities transacted at the retail

level guides the industry's decision making in matters such as

inventory control, product allocation and pricing decisions.

The Marketing Research Department is responsible for moni-

toring the effectiveness of advertising and promotional pro-

grams. Since nearly 87 percent of the FDOC budget as well as

numerous private funds are allocated to generic and brand

advertising, comprehensive consumer profiles and demographic

outlines are necessary for efficient allocation of promotional

funds. Analyses of consumer preferences are carried out

through continuous and large scale testing by the Market

Research Department. In both national and international

studies, this department has investigated buyer response to

color, brix-acid ratios, pulp content, bitterness tolerance and

packaging convenience.

One of the objectives of consumer testing is to identify

new market potential. The success of alternative market strat-

egies can mean an expansion of demand for the Florida citrus

sector. It is in this arena that new product forms and con-

cepts are tested for consumer acceptance. The market research

performed can greatly reduce the uncertainty associated with

new product introduction. In short, this additional informa-

tion aids in increasing the probability of success of new pro-


Recently the industry has introduced an aseptically pack-

aged, shelf-stable orange juice product. Although several

problems still remain involving taste and color volatility, the

Market Research Department foresees an important institutional

market for this new product form which could greatly expand

demand in the future (DeJager, 1984). In these and other

scenarios it is clear that market strategy and industry

revenues are largely dependent on technological developments.

Several of the larger firms in the industry also spend

considerable resources on market research departments.

Recently several product innovations in the processed orange

juice subsector have been designed to further differentiate the

market. For instance, new product introductions include a low

acid FCOJ and an orange juice with a high pulp content. Also,

multiple sizes and different packaging forms have been designed

to suit specific market segments.

In addition to extensive support for R & D programs, the

FDOC aids Florida industry members in the legal and political

arena as well. The Florida citrus industry is highly regulated

by the state. Laws govern the processing and distribution of

oranges, the amount of pressure used in juice extraction and

the prohibition of additives in orange juice. The increasing

importation by northern U.S. processors of Brazilian juice,

which is not regulated by Florida's quality standards, has

caused concern among industry members. Recently, the industry

Shas worked closely with the Food and Drug Administration in

order to detect poor quality orange juice which may be

adulterated through dilution with water, sugar, acids or pulp

wash. Several Florida citrus organizations have been involved

in these and other political and legal matters affecting the


The Florida citrus processing subsector invests substan-

tial resources in post-harvest R & D. In fact, over $6 million

in private and public funds were allocated to citrus processing

research in Florida during 1981 alone (Florida Department of

Citrus, 1956-80; United States International Trade Commission,


Few agricultural sectors have the extensive data and

information network or the research base that is available

within the Florida citrus sector. The technological advance

experienced by the industry is the result of several factors,

not the least of which is the close coordination among the

various research departments and industry members. Clearly

economic, marketing and scientific research has aided the

organizational and technical efficiency within the sector.


In neoclassical economic theory, at the micro level the

firm transforms inputs into output via the technological

relationships inherent within a production function

(1) Y f(XX2...Xn)

where Y is output and K1.. Xn are inputs into the production

process. The efficient transformation of inputs into outputs

is determined by the state of technology. The entrepreneur or

producer utilizes the product mix, determined by available

technology, in order to maximize profits. In doing so he

simultaneously chooses a position on his production function.

This product mix also depends upon the supply and demand condi-

tions in the factor and product markets. If the markets for

input supplies are perfectly competitive, then factor prices

are exogenous to the firm. Similarly, if the product market is

competitive, product prices are also exogenous.

As output increases due to proportional increases in

inputs, the entrepreneur moves along the production function.

Using Euler's Theorem and a homogeneous production function, it

can be shown that proportional growth in output is equal to the

weighted share of proportional input growth along a production

function. The residual of output growth less the share

weighted input growth is seen as technical change (Nelson,

1981). If technology allows a more efficient employment of

inputs such that an equal quantity of inputs yields greater

output, the production function will shift outward; hence,

technical change has occurred.

Technology can be described as the method of combining

inputs to arrive at a specified output. The advance of techno-

logy has been viewed as either an exogenous factor affecting

the growth of output or as a decision variable within the pro-

duction structure dependent upon the firm's investment in

knowledge or R & D (Nelson, 1981). In the latter context the

supply of, or possibly demand for, technical change is depend-

ent upon the knowledge and techniques available to the firm.

R & D can be viewed as an investment directed toward augmenting

organizational and technical efficiency, which consequently

affects the production opportunities of the firm. Along these

most basic lines of causation, the innovations resulting from R

& D at the micro level yield economic and productivity growth

as well as resource savings at a more aggregate level.

Measuring the Technical Dimensions of R & D

Despite their limitations, various studies have shown that

definitive relationships exist between R & D and the amount of

innovative activity originating from an industry (Kamian and

Schwartz, 1975) or between R & D and productivity increase

(Mansfield, 1972). Theory and application have not ended at

this point. Many factors in addition to R & D have been asso-

ciated with technical change and productivity advance.

Increases in capital intensity, advancement in human capital,

urbanization and the learning process have been found to

interact and complement the advances in technology (Nelson,


For example, the productivity index approach has been used

to estimate the relationship between technological developments

and research investment. Consider a model which relates pro-

ductivity growth and expenditures on R & D (Griliches, 1980).

(2) Q = Tf(C,L)

(3) T = g(K,O)

(4) K = I w Rt-

where Q is the value of output, C and L are capital and labor

inputs, respectively, T is the state of technological

knowledge, K is the amount of productive research knowledge in

existence at time t, 0 is other inputs affecting the state of

technology, wi measures the effect of past R & D in period t-i

on knowledge in time t and Rt-i is R & D expenditures in period


Equation 4 may be interpreted as the distributed lag of

past R & D. In order to empirically estimate the system, equa-

tions 2 and 3 are specified as Cobb Douglas forms and 0 is an

exponential trend. This reduces the system to

(5)t 8 (1-8)
(5) Qt= AeXt Kt Ct Lt(1)

In equation 5, A is a constant term and A is interpreted as the

rate of disembodied technical change.

Disembodied technical change generally refers to techno-

logy generated and affecting the production process from exter-

nal sources. Conversely, embodied technical change refers to

embodiment of technology in capital and labor inputs. Differ-

entiating equation 5 with respect to time and writing it in

implicit form yields a productivity equation (Griliches, 1980).

(6) P = -8 -- (1-8) = + a
where P is a measure of productivity and where Q, C, L and

where P is a measure of productivity and where Q, C, L and K

represent the derivatives with respect to time of output, capi-

tal, labor and current knowledge (i.e. x ).
Q dt Q
The variable describing the relationship between R & D
and technology is difficult to estimate because of the unknown

wi values. Several factors influence the lag structure between

R & D investment and the resulting increase in technology.

These include the time lag between R & D expenditure and the

invention of a new process, between invention and commercial

development of the technique and the replacement or depre-

ciation of this technology by a newer and more productive pro-

cess (Griliches, 1980). Evidence suggests that lags between R

& D and the realized benefits tend to be shorter in industries

where R & D is focused on applied and development work rather

than basic research, which is longer term and more uncertain

(Mansfield, 1980).

Evenson (1967) first used this approach in conjunction

with alternative lagging schemes for R & D. By minimizing the

residual sum of squares associated with various R & D lag

structures, he found the impact of R & D on aggregate agricul-

ture was best described by an inverted V-shape lag with a mean

lag of 5 to 7 years. Other econometric evaluation of returns

to research have generally ignored the lag of the impact of R &

D on productivity in the econometric formulation of the model.

The lag, however, is taken into account based on the nature of

the sector being considered by adjusting the calculations of

the marginal product or internal rate of return associated with

R & D (Bredahl and Peterson, 1976; Griliches, 1964).

The Effect of R & D on Input Usage

Although substantial literature addresses the problem of

measuring the returns to R & D, few studies have investigated

the influence of research on input usage. Because R & D expen-

ditures may characterize the pace of technological change,

knowing the effects of R & D on factor employment may be as

important as knowing the benefits associated with the invest-

ment. Although limited empirical analysis has focused on the

effect of R & D on factor shares, several studies have investi-

gated the impact of technical change on factor utilization.

Both relative factor prices and the technical characteristics

of the production process influence factor usage.

The technical characteristics affecting production possi-

bilities can be broken down into five categories (Nadirl,

1970). These categories include 1) the efficiency of the pro-

duction process, 2) biased technical change, 3) the elasticity

of substitution, 4) the economies of scale and 5) homotheticity

of the production process.

The efficiency of the production process includes such

factors as organizational or managerial efficiency, which af-

fects all factors of production equally. An increase in pro-

duction efficiency may be interpreted as neutral technological

change since capital and labor requirements per unit output

would decrease proportionately. Factor biased technical change

occurs when a cost saving process is adopted that reduces the

employment of one factor of production relative to other fac-


Economies of scale will govern the quantity of inputs

required at different levels of production. Neutral economies

of scale (a homothetic process) would increase factor require-

ments proportionately among inputs as output expands. Con-

versely, a nonhomothetic production process may increase one

factor requirement proportionately more than other factor

requirements as output expands.

The elasticities of substitution of the production process

may influence the degree to which changes in factor prices

affect factor usage. For instance, a given change in relative

factor prices will have a greater effect on factor utilization:

the greater the elasticity of substitution between the two

factors, ceteris peribus. This occurs because the entrepreneur

will more easily substitute the cheaper factor for the more

expensive one in the production process (the greater the elas-

ticity of substitution) in order to minimize cost. However,

with a small elasticity of substitution, production possibili-

ties would not allow easy substitution between the factors.

Hence, there would be less response of the factor ratio to

relative price changes.

The elasticity of substitution between factors may also

influence the ability of the firm or industry to capture the

benefits of embodied technical change. For instance, the abil-

ity of the entrepreneur to fully realize the quality improve-

ment embodied in a new machine may depend upon the production

process and the extent to which it allows increased utilization

of capital at the expense of labor or other inputs.

These technical characteristics of the production process,

in addition to relative price changes, clearly affect factor

utilization through time. Although few empirical studies have

explored the role of R & D in factor bias, research enters the

theoretical framework via the R & D processes that generate

technical possibilities. Syed Ahmad (1966) developed an

induced innovation model based on an innovation possibility

curve (IPC). The IPC is the envelope of all unit isoquants

that describe the set of potential processes available to the

entrepreneur given an exogenous R & D budget (Figure 1).

11IPC t

Pt+l Labor

Figure 1. Ahmad's induced innovation model.
Source: adapted from Syed Ahmad (1966).

The IPCt describes all innovation possibilities available to

the entrepreneur during time t. The It is the cost minimizing

innovation process given factor prices Pt. In period t+1 the

IPC shifts inward to IPCt+1 and the entrepreneur will adopt the

processes on innovation isoquant It+1 given constant factor

prices Pt. The shift in IPC may be neutral or non-neutral at

constant factor prices. If the IPC shift is neutral and factor

prices change to Pt+l the optimal innovation choice would be

I't+,. A neutral shift in IPCt+I, in conjunction with the rise

in the price of labor (Pt+l), results in labor saving innova-

tion possibilities. R & D influences, albeit indirectly, the

technological advances of the firm. The position of the IPC is

determined by the amount and direction of the R & D resources

allocated to the production of new improved techniques.

The movement or direction of the shift of the IPC may not

be random. Binswanger (1978) maintains that technological

opportunities will follow the path of least cost. Research

projects that decrease use of high priced inputs will have

greater benefits than those that reduce use of low priced

factors. The cost minimizing entrepreneur will therefore

direct R & D toward the savings of the more expensive

factors. Along these lines, R & D will influence the techno-

logical advances of the firm and hence factor usage.

Although.R & D has been incorporated into the theoretical

framework (Binswanger, 1978), empirical analysis of factor bias

has focused on isolating the effects of price ratios, scale and

technical change on factor utilization. Recent studies have

utilized cost functions to analyze the forces affecting the

demand for inputs (Lopez, 1980; Kako, 1978). Several develop-

ments in cost function specification allow for a variable elas-

ticity of substitution and nonconstant returns to scale (Caves

et al., 1980). Furthermore, by Shepard's Lemma the factor

demand for the ith input is easily computed by taking the first

partial derivative of the cost function with respect to the ith

Factor price. These characteristics of the cost function have

Permitted several studies to investigate the effects of techni-

cal change, variability or scale effects on factor usage.

Binswanger (1974B) employs the translog cost function to

measure the effects of technical change (although it can be

generalized to other factors) on factor usage through time or

among cross sections. He defines factor bias as follows

dSi I < factor i saving
(7) --- x -= 0 factor neutral
S> factor i using

where Si is the ith factor's share in total cost and T is the

index of technical change. By assuming a neutral effect of

output on factor shares (a homothetic production technology),

the ith share is specified as a function of factor prices and

technical change. The effect of technical change on factor

bias is reflected by the parameter on the time variable. Bins-

wanger (1974B) notes that this approach is valid only when time

affects factor shares at constant logarithmic rates. If the

parameter in the share equation on time were zero, this would

imply that technical change or time alone is not a significant

variable influencing factor shares. Therefore, T would have a

neutral effect on the ith share. Binswanger (1974B) found that

technical change has a significant and positive effect on capi-

tal and a negative effect on labor for aggregate U.S. agricul-


In a similar study, Kako (1978) used the parameter esti-

mates and Allen elasticity of substitution derived from the

estimation of a translog cost function to investigate the

demand for inputs in Japanese rice production. Assuming a

constant returns to scale production technology, a change in

the level of factor demand was specified as a function of fac-

tor price variability, technical change and scale of output.

The effect of technical change on input demand was calculated

by subtracting the changes in input usage due to scale and

price from the observed changes in input levels. It was found

that output and price changes were the main factors behind

increased machinery usage, whereas technical change and wage

rate changes were the major components influencing the decline

in labor employment.

Lopez (1980) estimated a set of derived demand equations

corresponding to a generalized Leontief cost function for Cana-

dian agriculture. Using a similar methodology, variation in

relative prices, technical change and scale were found to be

the major factors affecting input demand. More importantly,

when the underlying production technology was not constrained

to linear homogeneity of inputs, technical change was no longer

significantly related to factor usage. This highlights the

importance of allowing for a nonhomothetic production struc-

ture. The changes in factor shares attributed to technical

change may be negligible where scale effects are considered.

Lopez's (1980) results are consistent with the Lau and

Tamara (1972) study, which utilized a nonhomothetic production

function to model the Japanese petrochemical industries.

Although technical change did not appear to be a significant

influence in the nonhomothetic specification when homotheticity

was imposed, technical change became a significant variable

affecting production. These and other studies have documented

the value of the cost function approach in specifying flexible

models of production that can accommodate technical change,

Specification of a sufficiently flexible cost function

permits analysis of homotheticity of the production relation-

ship, computation of input substitution and price elasticities

and evaluation of the effects of R & D on an input's share in

total cost. Therefore, this approach provides valuable

information for assessing the structure of production and the

effect of technical change on production relationships. For

these reasons it is the methodology chosen for the subsequent



It is well known that production relationships may be

derived from a cost function via duality. As often occurs at a

disaggregated level, productivity and input quantity data are

either unavailable or difficult to measure. Many times in firm

or subsector studies cost and price information is more accu-

rate and easily obtained than data on input levels. Further-

more, at a micro level the specification of input prices as

exogenous appears more realistic than input quantities which

may be varied in response to price changes. Since input

prices, total cost and cost share data are obtainable in the

Florida citrus processing sector, a translog cost function in

conjunction with share equations was estimated.

The cost function depends upon output, prices and the

underlying production function and is, by definition, the solu-

tion to minimizing input expenditures subject to producing a

prespecified level of output.

(8) C(Y,P) = Min[E PiXi : f(X) > Y]
X i

where Pi are prices of the inputs, Xi, and f(X) describes the

production technology available for combining inputs to yield

output Y. The industry or firm will minimize the cost of a

given level of output by choosing the optimal level of inputs

conditional on the input prices.

It can be shown (McFadden, 1978) that, if there exists a

well defined production technology strictly convex in input

structure, the same information is contained in a unique cost

function. Conversely, if the cost function satisfies several

regularity conditions, then duality ensures that there exists a

well defined production possibility set.

Modeling cost requires few a priori restrictions on the

structure of production unlike empirical estimation of produc-

tion or value added functions. Brown et al. (1979) show that a

priori restrictions of homogeneity of inputs or separability

may distort the scale economies or marginal cost of inputs

associated with the production technology. The cost function

is homogeneous in factor prices irrespective of the homogeneity

of inputs because doubling of all prices will double cost. In

addition, the elasticities of substitution are easily computed

using the estimated parameters and cost share data. In the

translog case, both the elasticity of substitution between

inputs and economies of scale are allowed to vary. Binswanger

(1974A) notes that neutral and non-neutral economies of scale

and efficiency differences can be handled conveniently using

the cost function. Accordingly, the parameter estimates will

not be biased as a result of these problems.

Only homogeneity in input prices and equality of cross

price derivatives (symmetry) must be imposed a priori. Other

conditions that ensure regularity such as monotonicity and

concavity in input prices, nondecreasing in output and nonnega-

tivity in prices and output must be checked at each data point.

If any of these restrictions are not satisfied, the cost func-

tion does not describe a well-behaved underlying production

technology over the sample observations.

The cost function usually has output and input prices as

arguments. However, the variable cost function may also

include a "fixed" input Z.

C = C(Y,P,Z)

In this context, the firm or industry minimizes cost of a given

output Y with respect to input prices and the level of the

"fixed" input Z. Following McFadden (1978), the variable cost

function is a form of the restricted profit function. The

variable Z may characterize the state of technical progress or

degree of learning or can contain environmental or behavioral

parameters. In short, the variable Z may be any factor that

describes or influences the production technology.

The variable Z may also be interpreted as a fixed factor

that cannot be varied in the short run. Caves et al. (1981)

employ this methodology to incorporate fixed capital structures

in a translog cost function. They assume that the firm mini-

mizes the cost of a subset of inputs conditional on the levels

of the remaining inputs Z. This "variable" cost function still

contains all the information describing the underlying techno-


The first derivate of the cost function with respect to

input Z can be interpreted as the negative of the shadow price

of Z (Lau, 1976; Diewert, 1974).

(10) ac(YP,Z) (Y,P,)
az -i i

At the margin, an input Z decreases the total cost of producing

Y, given the cost minimizing levels of input usage. The

implicit market value (or imputed value) of input Z is the

amount that an extra unit decreases total cost.

Equation 11 presents a translog formulation of a cost

function inclusive of McFadden's variable Z (represented by the

variable R). Although it is possible to estimate the cost

function alone, by jointly estimating the cost function and

share equations, additional information and hence greater effi-

ciency are provided without introduction of additional parame-

ters. By Shepard's Lemma, the share of the ith input in total

cost is computed by the partial logarithmic differentiation of

the logarithm of the cost function with respect to the loga-

rithm of the ith input price (equation 12).

(11) InC = a0 + 11nY + 6 InR + X Y InPi

+ 1/2 E y ijlnP lnP + E y InPilnY + E YirlnP InR
ij i jr i

+ 1/282(InY)2 + 3nYlnR + 1/262(inR)2

(12) ainC 8c i XPE Y nP
81nPi x C EXP Si + ijP

+ YiynY + YirlnR
iy ir

where R is the fixed input, or input describing the technology

and Si is the share in total cost of the ith input.

The translog cost function is a second order approximation

to an arbitrary cost function. By imposing the proper restric-

tions it can be used to approximate any cost function (Bins-

wanger, 1974B). In terms of equation 11, a Cobb Douglas

formulation would require all Yij = 0 (ij), Yir = 0, Yiy = 0,

82 = 0, 03 = 0 and 62 = 0.

Other restrictions on the production structure may also be

examined by testing the corresponding parameters. The cost

function will be homothetic if it can be written as

(13) C(Y,P) = Q(Y) x C(P)

where C(P) is a non-negative, linear homogeneous, nondecreasing

and concave function of P (Lopez, 1980). Accordingly, equation

11 will be homothetic if all Yiy = 0. This is a relatively

restrictive assumption since it implies that the changes in

factor usage, reflected in the share equations, will be inde-

pendent of scale. Likewise, linear homogeneity or constant

returns to scale can be imposed by the additional restriction

82 = 0, 81 = 1, since returns to scale in the translog cost

function are measured by the inverse of the first derivative of

the logarithm of cost with respect to the logarithm of output.

(14) n )-nY

As discussed previously, several studies have rejected homo-

theticity of the production structure and have concluded that a

priori imposition of the restrictions either substantially

altered the results of the study or was decisively rejected

(e.g. Brown et al. (1979) in the U.S. railroad industry, Denny

and May (1978) in Canadian manufacturing and Lau and Tamara

(1972) in the Japanese petrochemical industry). The translog

flexible functional form allows for testing of linear homogene-

ity or homotheticity rather than a priori imposition of these


Use of the translog cost function also facilitates easy

computation of the Allen elasticities of substitution (AES) and

factor demand elasticities. The AES between factors i and j

measures the impact of a change in the price of the jth factor

on the quantity demanded of the ith factor when output is fixed

but quantities of other factors are allowed to vary. In terms

of the translog cost function the AES can be calculated via

equations 11 and 12 (Binswanger, 1974A). The AES depends upon

the shares of the ith and jth inputs and therefore vary at each


1 2
(15) r = (- ) (Y + S2 Si)

(16) r = (1-- ) Yi + 1 for all i*j
ij Si iij

The price elasticities of factor demand, which measure the

impact in the jth factor price on the demand for the ith factor

holding output and other factor prices constant, are also eas-

ily computed as follows (Binswanger, 1974A).

(17) nii ii/i) + i 1

(18) n = (YiI/Si) + Sj for all i*j.

The AES and price elasticities give important information

on the relationship between factor inputs. As discussed pre-

viously, the elasticity of substitution may affect the factor

substitution possibilities of the producer and hence influence

factor bias through time. Kako used the AES in this context,

in order to calculate the total substitution effect of factor

prices in Japanese agriculture. He was able to differentiate

the substitution from the scale effects in order to arrive at

the contribution of technical change to factor bias.

If R & D as a representation of technical progress is

found to be a significant factor affecting the cost structure

of the Florida citrus processing industry, then the shadow

price of research will be reflected by the negative of the

first derivative of the cost function with respect to the quan-

tity of research (equation 10). This explicitly defines the

decrease in cost attributable to a one-unit increase in the

quantity of research, which is interpreted as the market value

of research. A measure of the returns to processing research

was estimated by using the dollar value of one unit of research

and the corresponding decrease in citrus processing cost attri-

butable to a one-unit increase in R & D.

The quantity of research and development conducted in the

citrus processing sector as a proxy for technical change will

also affect the cost shares of inputs via the citrus structure.

Research may induce factor bias by providing technologies that

augment labor or capital usage. It is also conceivable that

R & D could affect input usage neutrally through organizational

or other innovation. Binswanger (1978) points out that a cost

minimizing producer will have the tendency to adopt the least

cost path of technological opportunity. For the Florida citrus

processing industry this may imply that the adoption of the new

technology will increase (or decrease) the requirements of one

factor relative to another.

Estimation Method

In estimation of the translog cost function with the cit-

rus share equations, one share equation must be dropped because

only n-i share equations are linearly independent due to the

homogeneity restrictions (Binswanger, 1974B). Additionally,

the additive specification of the error terms results in a

singular variance matrix since the share equations sum to one.

Assuming that optimal behavior is represented by utilizing

share Si* in the production of Y, then the relationship of the

observed share Si will be Si = Si* + Vi, where Vi is the error

in the ith share equation. If E(Vi) = 0 and E(ViVj) = Eij the

residuals will reflect error in the optimizing behavior since

Si is stochastic.

Iterative seemingly unrelated regression (ITSUR) was used

to estimate the cost function and share equations. Under this

method the parameters are estimated using

(19) s8 (X'(E1 x I )X) -I'(E x I )Y
sur n n

where X is the matrix of exogenous variables in the system, Y

is the vector of endogenous variables, In is the identity mat-
rix of dimension n and E is the inverse of the estimated

variance covariance matrix of error terms. ITSUR repeats the

estimation of the parameters and corresponding error covariance

matrix until both the parameter vector and covariance matrix

coverage to stable values. Under this method the parameters are

consistent and efficient. Most importantly, this method

ensures that the parameter estimates are invariant to the share

equation dropped from the system.


A translog cost function in conjunction with the share of

labor and share of materials equations for the Florida citrus

processing sector was fitted to the data for the years 1956-


(20) InC = a0 + 11nY + 61 nR + E YilnPi

3 3 3
+ 1/2 E Y ij lnP InP + i Yiy nPilnY
i=1 j=1 i=1

3 2
+ E YirlnPilnR + 1/2 82(lnY)

+ 1/2 62(InR)2 + 31nY InR

(21) S1 Y1 + j YjlnP + Y1ylnY + Y1rlnR
j=1 j

(22) Sm Y + Z Y lnP + YyInY + Y InR
m ., mj j my mr

where Pi is the price of labor (L), materials (M) and other

inputs (0), and i,j = l,m,o; Y is total output of FCOJ from

Florida processors; C is total cost of processing FCOJ; Si is

the share of labor (L) and materials (M) in total cost; and R

is the quantity of research.

The quantity of R & D is the average of the deflated

expenditures of R & D lagged one and 6 years. Since both

applied and basic research activities are undertaken in the

industry, with an average lag for R & D payoffs of 6 months to

2 years for applied and 5 to 9 years for basic R & D (Attaway,

1984), the average of a 1-year and a 6-year lag is used to

approximate the impact of R & D expenditures on the current

citrus cost structure. Griliches (1964) used similar reasoning

in calculation of his R & D variable where he lagged R & D

expenditures one and 6 years (additional information on data

sources and calculations is contained in the Appendix).

Empirical estimation of the cost function requires a pri-

ori imposition of homogeneity in input prices and symmetry.

Equation 20 uses 24 free parameters. Homogeneity of input

prices is defined as. follows.

(23) C c(Y,R,AP) Xc(Y,R,P)

In equation 21, homogeneity implies the following restrictions.

(24) E Y = 1, Y = 0, E Y = 0, E ir = 0
i ij i it
i i 1j i

i Y = 0 for all i and j

The second order partial derivatives of the cost function

with respect to input prices generate symmetry constraints.

a(2nC a21nC
(25) alnPi DnP ij = anP. lnP- ji iJ

Symmetry and homogeneity restrictions reduce the number of free

parameters to 15. In addition to these restrictions, the

regularity conditions mentioned previously require the cost

function to be nondecreasing in output and input prices at each


aC ac
> 0, c- > 0 for all i

The translog cost function will be nondecreasing in output and

input prices if both the derivative of the logarithm of cost

with respect to the logarithm of output and the predicted

shares are greater than zero, at each observation.

The cost function will be concave in factor prices pro-

vided the Hessian matrix of second order price derivatives is

negative semidefinite at each data point. This requirement is

satisfied by the translog formulation if the matrix of esti-

mated substitution elasticities is negative semidefinite at all

data points.

Results from the estimation of the full or unrestricted

translog model are presented in Table 2. The results show that

few parameters are significantly different from zero at

conventional levels. The exception appears to be the interac-

tion terms of R & D with input prices and output with input

prices (i.e. Yir and Yiy, respectively).

The R2 values associated with the share of labor and share

of materials equations are .76 and .72, respectively, and are

somewhat higher than the fits found in other studies that

estimate the share equations alone (Binswanger, 1974A). This

result is most likely due to the additional information

provided by estimation of the cost function in conjunction with

the share equations. Multicollinearity is not an unusual

result considering the large number of variables that are

fitted to 25 observations. Such results suggest restricting

some of the flexibility inherent in the specifications.

Although homogeneity of factor inputs may be imposed to

further restrict the flexibility, it was thought to be an
overly restrictive assumption due to the significance of Ym

and Y Additionally, as Lopez noted, when the production
technology is constrained to input homogeneity, it is not unu-

sual to find technical change to be a significant factor

affecting input usage. Although this finding is not entirely

applicable to this study (since R & D is a more specific varia-

Table 2. Parameter estimates for the translog cost function
(estimated asymptotic standard errors in parenthe-

Model 1 Model 2
Variable Unrestricted Restricted

Intercept a0 -16.20 1.09
(36.49) (1.60)
InY 8 5.24 .494
(7.60) (.162)
InR 1 -7.47 .432
(6.59) (.168)
InP1 Y1 -.0186 -.009
(.297) (.284)
lnPm Y .299 .293
m (.429) (.413)
InPo Y0 .719 .715
(.329) (.320)
(InP1)2 11 -.0342 -.0307
(.072) (.068)
InPllnPm Ym .0362 .0353
(.064) (.062)
InP1lnP Ylo -.002 -.0046
S(.021) (.020)
(lnPm)2 Y -.148 -.1265
m (.084) (.08)
InPmlnPo Y .112 .0911
nmP o (.057) (.052)
(lnP0)2 Y -.110 -.0865
00 (.052) (.047)
InRlnP1 Y .054 .054
S (.024) (.023)
InRlnPm Yr -.194 -.184
S (.042) (.040)
InRlnPO Y .141 .131
or (.035) (.033)
InYlnP1 Y -.009 -.009
Iy (.013) (.012)
InYlnP Y .096 .088
my (.038) (.036)
InYlnPO Y -.087 -.0795
oy (.035) (.033)
(lnR)2 6 -1.09 0
(lnY)2 B2 -.616 0
InRlnY B3 .919 0

ble associated with citrus technology than a time trend which

may encompass many factors), it is better to avoid the bias

that has resulted from imposition of homogeneity in other


Accordingly, Binswanger (1974B) notes that leaving out a

factor that does not affect shares neutrally will bias the

estimation of the parameters in the share equations. If the

factor does affect the shares neutrally (in this case, if all

Tiy = 0), then leaving this variable out of the regression will

not bias the results.

Instead, the quadratic terms of the R & D and output vari-

ables as well as the interaction of R & D and output were

dropped (i.e. 2 -, = 0, 83 = 0). This method was chosen

because the variables appear to be collinear and because, in

the study where share equations are estimated without the

accompanying cost function, these variables would not

explicitly enter the analysis. This specification makes the

model more in line with previous studies measuring the impact

of technical change on factor shares. Secondly, the input

price interaction variables appear to be collinear, and this

result may suggest further restrictions on the Yij

parameters. However, without a priori knowledge of the input

demands in the citrus processing sector (i.e. knowledge of the

prices that affect the cost share of the ith input) setting any

given Yij = 0 would yield, at best, an arbitrary result.

The restrictions 62 = 0, 82 = 0 and 73 = 0 were tested

with a likelihood ratio. As seen in Table 3, the restrictions

could not be rejected at the 95 percent confidence level. The

second column of Table 2 reports the estimated coefficients for

the resulting (restricted) model.

The restricted model was used in further analysis. Note,

however, that due to the fact that the restricted model is

based on a test, the estimators are pretest estimators. Hence,

the standard tests of significance may not be strictly valid

(Judge et al., 1980).

Table 3. Test statistic for restricted models.

Critical Level
Test Number of of X at .05
Statistics Restrictions = r Significance

3.45 3 7.81

aLikelihood ratio test: R = determinant of the restricted
covariance matrix, U = determinant of the unrestricted covari-
ance matrix and N is the number of observations (Judge et al.,
1980) [ln(R) ln(U)] x N ~ x (r)

Both the restricted and unrestricted translog cost func-

tions satisfy the conditions required for regularity at each

observation. These requirements include monotonicity and con-

cavity in factor prices, and nondecreasing in output.

As mentioned in the Appendix, the shares of other inputs

in total cost consist predominantly of expenditures on mainte-

nance, depreciation, warehousing and manufacturing overhead

costs. It is assumed in the analysis, therefore, that the

share of other inputs represents the expenditures on working

capital and capital equipment and structures in total cost.

The ij values alone have little intuitive meaning;

therefore, it is better to interpret them in the context of

factor demand and substitution elasticities (Binswanger,

1974B). The estimated Allen partial elasticities of

substitution and factor demand elasticities evaluated at the

means of the data along with their estimated asymptotic

standard errors for the restricted model are presented in

Tables 4 and 5, respectively. Note that by

definition ai = ji; of course, in general, this result does

not hold for the demand elasticities (i.e. n ij Ii).

All of the own factor demand and substitution elasticities

have the correct sign. The own partial elasticities of substi-

tution have little economic meaning; however, note that the own

factor demand elasticities for both materials and other inputs

are significant and less than one in absolute value. This

result suggests that the factor demands for materials and capi-

tal are inelastic. Since both materials and capital are impor-

tant factors in the production of FCOJ, this is not an unlikely

result. The demand elasticity for labor is marginally greater

than one in absolute value. This may imply, other things being

equal, that a rise in the price of labor would lead to a

decrease in the share of labor in total cost. However, since

1 llis not significantly different from zero at conventional

levels this result is tenuous.

The positive values of the off-diagonal elements in Tables

4 and 5 suggest that the inputs are substitutes. Conversely,

negative values would have indicated complementarity among

inputs. The substitution between inputs is best evaluated by

utilizing the AES rather than the n j. This occurs because the

factor demand elasticities reflect the relative importance of

the input's share in total cost whereas those of the AES do not

(Binswanger, 1974A).

Table 4. Estimated allen partial elasticities of substi-
tution (estimated asymptotic standard
errors in parentheses)

Labor Material Other

Labor -7.28 1.53 .921
(3.24)a (.940) (.350)
Materials -1.83 1.50
(.394) (.290)
Other -2.02

aSE(ij x SE ( j)

Table 5. Estimated input price elasticitiesa (estimated
asymptotic standard errors in parentheses)

Labor Material Other

Labor -1.06 .69 .368
(.467) (.427) (.137)
Materials .221 -.821 .59
(.135) (.176) (.114)
Other .133 .683 -.816
(.050) (.130) (.117)

an measures the effect of a change in the price of the input
in the jth column on the quantity demanded of the input in the
ith row. SE (ni) = x SE (Ti)
-j S i j

The estimated substitutability between materials and other

inputs is statistically significant asymptoticallyy) and large.

This relationship may reflect the industry trend to substitute

away from the relatively more materials intensive packaged FCOJ

to the relatively more capital intensive bulk FCOJ in recent

years. The estimated AES corresponding to labor and other

inputs is also significant and close to one. If it is assumed

that capital and warehousing are reflected by the other inputs

category, then this is consistent with the citrus industry's

continual mechanization over the last 40 years. Both packaged

and bulk processes have become increasingly capital intensive

as illustrated by the trend to substitute capital for labor in

the washing, transporting and packaging stages of production.

Finally, the estimated AES associated with labor and mate-

rials also suggests that these inputs are substitutes. How-

ever, the small magnitude of alm relative to its estimated

standard error makes analysis of this variable inconclusive.

The parameters Yiy reflect the way in which output has

affected input shares at constant logarithmic rates through

time. It can also be viewed as the impact of output over time

on the factor shares. The parameter Y suggests that as out-
put has increased over time the share of materials has

increased. Considering that approximately 60 to 70 percent of

the citrus processing industry's output consists of packaged

FCOJ it is not unusual to find that expansion in output induces

an increase in the materials share of total cost (on average).

The parameter y indicates that as output increases at
constant logarithmic rates over time the share of capital in

total cost decreases. Accordingly, these results imply that

the citrus processing industry has a nonhomothetic production

structure. Furthermore, economies in capital usage exist. As

output increases, on average, proportionately less capital cost

is incurred per unit of output.

The parameter Yly is close to zero and smaller than its

estimated standard error. This implies that labor's share in

cost is unaffected (or affected neutrally) by output expansion.

The same proportion of labor cost in total cost is incurred, on

average, for any scale of output.

The partial derivative of the log of cost with respect to

the log of output at the means of data was calculated to be .77

with an associated standard error of .09. This implies an

estimated economy of scale at 1.28 (equation 14). This value

reflects large economies of scale, which may be partly

responsible for the high industry concentration rate observed

among Florida citrus processors. In the 1970-71 season only 10

industry members processed almost 68 percent of Florida FCOJ.

At the selling level, the market share increases further. In

addition, there has been little variation in the breakdown of

market shares of specific firms in the industry (Ward and

Kilmer, 1980). Therefore, it appears that the large economies

of scale are in accord with the high market share concentration

observed in the industry.

The economies of scale in capital usage (i.e. oy > 0)

may contribute to the large returns to scale observed in the

production technology. Undoubtedly. the large freezer ware-

housing facilities, computerized processing and high volume

packaging equipment and manufacturing overhead amount to a

substantial fixed investment for industry members. It seems

reasonable that these inputs, which are represented in the

other inputs share category, would reflect increasing returns

to scale and may contribute to the large economies of scale

observed in this study.

The parameters Yir in the share equations, which were all

considerably larger than their estimated standard errors.

reflect the way in which research has affected the input shares

in total cost at constant logarithmic rates through time.

These results are related to several factors in Florida

citrus processing R & D and trends affecting the industry

structure. As noted previously, a major trend in the Florida

citrus industry has been increased bulk processing and ware-

housing of FCOJ (Figure 2). R & D has been an important

component in the growth of bulk. R & D is responsible for

initiating new technologies that have lowered the cost of

warehousing and shipping of bulk as well as creating and

stimulating the demand for ready to serve orange juice, a major

product form of bulk FCOJ.

Although FCOJ processing of bulk and packaged FCOJ entails

equivalent procedures for the most part, after processing, the

packaged FCOJ operation becomes a relatively more material



18.7 9%

S40.3 95.7 46%
15% 20.5

1971-72 1984-88

Figure 2. Florida FOB FCOJ movement million concentrate
gallons. Source: Gunter (1985).

intensive process whereas bulk FCOJ requires relatively more

capital and labor expenditure per gallon. Therefore, both bulk

and packaged FCOJ production requires labor; however, a rela-

tively greater proportion of total cost per gallon is spent on

labor in bulk processing and storage than for packaged FCOJ


Given the phenomenon of increased bulk production, which

utilizes proportionately more labor and less materials than

packaged FCOJ, that research has induced an increase in labor

usage and a decrease in materials usage is not an unexpected

outcome. Accordingly, by considering the relative magnitudes

of the parameters on R & D in the share equations, the results

imply that, on average, R & D has induced a small increase in

labor's share in total cost and a larger decrease in material's

Share in total cost through time.

The parameter Yor corresponding to R & D and other inputs

in the share equation suggests that, on average, R & D has led

to an increase of capital's share in total cost through time.

This result may be related to the phenomenon described above,

where R & D aiding the growth of bulk FCOJ has increased

warehousing's and capital equipment's shares in total cost. On

the other hand, the direct effects of R & D should be accounted

for as well. R & D has affected the technological

possibilities of citrus processing at all stages of production,

especially in terms of increasing the mechanization of both

bulk and packaged FCOJ. Although the value of Yor is difficult

to interpret, the relatively larger Yor indicates that R & D,

on average, has induced a greater increase in capital's share

of cost than labor's share of cost through time.

The measure of the shadow price of the quantity of

research calculated at the means of the data was $1536 with an

associated standard error of $672 (equation 10). This measures

the imputed market price of one unit of R & D or the decrease

in total cost attributed to one unit of R & D applied over six

years. The mean total cost of one unit of research as

calculated in this study was $92.60. Dividing the total cost

savings attributed to one unit of R & D by the amount spent on
1535 9
the R & D ( 92.9 ) yields an average cost savings of $16.58

today per dollar of research investment one and 6 years

previously. Not surprisingly, this result is similar to previ-

ous production function studies. Peterson (1967) calculated a

marginal product of $18.52 associated with poultry research in

the U.S.. Griliches (1964) found a $13.28 marginal product

associated with the value of aggregate agriculture and Bredahl

and Peterson (1976) estimated a marginal product of $14.09 per

dollar of research in cash grain production in the United


If it is assumed that R & D yields continuous benefits on

average (versus benefits that pay off annually or quarterly),

then the application of one dollar of research investment allo-

cated over one and 6 years to citrus processing has yielded a

continuously compounded average rate of return of 57.4 per-


This rate of return is somewhat higher than those calcu-

lated using the productivity index approach. Comparison of the

relative rates of return are not entirely analogous, however.

The productivity index studies focus on industry-wide (two-

digit Standard Industry Classification) R & D, which could be

viewed as an average rate of return over the entire food and

kindred product industry, whereas the present study analyzes

the Florida citrus processing sector alone.

The results show that the translog cost function may yield

important information about the effects of R & D at a disaggre-

gated or subsector level. The cost function also yields impor-

1The formula used for calculation of returns to research
assumes constant rates of growth (.5ei + .5ei = 16.58 where i
is the interest rate).

tant information regarding the relationship among inputs via

S calculation of the substitution and price elasticities. When

the cost function and share equations are estimated as a sys-

tem, the factors affecting the input's share in total cost may

also be analyzed.

The results suggest that R & D, and thus technical change,

has had an important impact on the Florida citrus industry's

cost structure. In addition, the evidence implies that the

underlying production structure is nonhomothetic. Both

research and output have a significant impact on factor shares.

In short, the scientific, marketing and economic research

performed in the Florida citrus processing sector has affected

the cost of producing FCOJ directly and via the inputs' shares

in total cost over the last 25 years.


Using the duality relationship between production func-

tions and cost functions, a translog cost function and corre-

sponding share equations were estimated in order to measure the

technological relationships in the FCOJ industry. While the

cost function usually has input prices and output as arguments,

McFadden shows that a fixed input may be introduced into the

cost function as well. This input may include any factor which

characterizes the state of technical progress or which

describes or influences the production technology. In this

study the quantity of Florida citrus research was introduced

into the cost function. Following Diewert and Lau, the shadow

price of R & D was obtained by partial differentiation of the

cost function with respect to the quantity of research. Assum-

ing a constant rate of growth, a continuously compounded aver-

age rate of return associated with Florida citrus processing

research was calculated. In addition, estimation of the trans-

log cost function in conjunction with the share equations

allows analysis of the effects of R & D and, hence, technologi-

cal change, on input shares in total cost.

As in any econometric study, it is important to analyze

the production structure and account for all possible factors

affecting the endogenous variables (given the empirical limita-

tions of data measurement and accuracy). A common practice is

to enter time into the production or cost function in order to

characterize the technology or technological change occurring

in an industry. In the present study, however, since R & D

enters the cost function as a specific quantity affecting cost,

its impact is more clearly delineated than a time trend varia-

ble, which may characterize and encompass the effects of

various factors. The purpose of R & D's inclusion and the time

trend exclusion is to measure and identify the specific cost

reducing effect of a variable aimed exclusively at product and

process innovation.

The parameters on the interaction term of research and

input prices (Yir) reflect the way in which research has

affected the input's share in total cost at constant logarlth-

mic rates through time. The results imply that, on average,

S research has had a positive effect on labor and other input

usage and a negative effect on materials usage.

The measure of the shadow price of the quantity of

research calculated at the means of the data was $1535.90 with

an associated standard error of $672. This is the imputed

market value of one unit of research applied over one and 6

years previously. By considering the price of one unit of R &

D, the decrease in total cost today attributed to a one-dollar

increase in R & D expenditures one and 6 years ago is $16.58.

Assuming constant rates of growth and continuous compounding,

this yields a 57.4 percent rate of return to citrus research.

Of course there are several factors that may bias the

estimated shadow price of research. There is a possibility

that R & D from sources outside the citrus industry may have

affected the citrus cost structure through organizational or

capital-embodied technical innovations. Although it is assumed

that R & D entering the citrus sector through purchased inputs

will be reflected in the input price, for the most part, expen-

ditures not incorporated in the industry R & D variable or

input price may tend to bias the returns to research upward.

Conversely, technological innovation attributable to

research conducted within the Florida citrus industry may have

spillover effects into other food processing sectors. (This is

a pertinent factor in this case because the Brazilian citrus

industry, the world's largest FCOJ exporter, has imported most

of its processing technology directly from the Florida citrus

industry.) Equally important, the change in the quality of

FCOJ resulting from industry R & D will not be reflected in the

output measure. These are benefits from R & D that are not

measurable within the scope of this study. Because the input

and output variables do not explicitly account for these fac-

tors, the actual returns to citrus research may be larger than

the estimated returns.




Output is total movement of FCOJ from Florida

processors. This quantity includes annual retail,

institutional and bulk sales of Florida processors on an

equivalent 420 to 450 Brix basis. Bulk FCOJ is warehoused

directly after processing whereas retail and institutional FCOJ

is packaged in various forms and later warehoused (Florida

Citrus Mutual 1956-1980).

Total Cost

Total cost is calculated as the sum of the cost per gallon of

processing bulk multiplied by the quantity of bulk plus the

cost per gallon of packaged FCOJ multiplied by the quantity of

packaged FCOJ. All data were calculated on an equivalent 420

to 450 Brix basis. Since data were not available for bulk

processing costs before 1962 and bulk sales represented less

than 10 percent of output during this time period, total cost

for 1956-1962 was calculated as total cost per gallon of

packaged FCOJ multiplied by total movement. Data were

available from Florida Citrus Mutual.

Price of Labor

Price of labor is the average hourly earnings of production

workers on private nonagricultural payrolls in the two-digit

SIC, Food and Kindred Products classification (United State

Department of Labor 1956-1980).

Price of Materials

The price of materials is the producer price index for

converted paper and paper-board products, 1967 = 100.00 (United

States Department of Labor 1956-1980).

Price of Other Inputs

Since a large proportion of cost, other than materials and

labor, is encompassed in warehousing and capital expenditures

such as maintenance, depreciation, manufacturing overhead and

warehousing, the Moody's triple A bond interest rate is used as

a proxy for the price of other inputs. In this analysis, the

interest rate reflects the price of capital and the cost of

warehousing FCOJ (Economic Report of the President 1983).

Share of Labor

The total labor expenditure is the product of the labor

expenditure per gallon of processing bulk FCOJ multiplied by

the quantity of bulk, plus the labor expenditure per gallon in

processing packaged FCOJ multiplied by the quantity of packaged

FCOJ. All data were calculated on an equivalent 420 to 450

Brix basis. The total expenditure on labor is divided by total

cost to arrive at the share of labor. Before 1962 when bulk

processing data were not available, the share of labor in

packaged FCOJ is used (Florida Citrus Mutual).

Share of Materials

The share of materials is the expenditure per gallon of

materials multiplied by the quantity of packaged FCOJ and

divided by total cost of processing (Florida Citrus Mutual).


The quantity of research is calculated using the Florida

Department of Citrus R & D expenditures, state Research and

Extension expenditures on citrus processing R & D and a proxy

for R & D conducted by private industry. The FDOC allocation

to economic, marketing and scientific research and Florida

processing R & D expenditures were obtained. A time series

reflecting private R & D was developed using data for private

citrus R & D in the state from the United States International

Trade Commission (USITC) and the National Science Foundation

(NSF) series (both 1983) on private company R & D, conducted in

food and kindred product industries. The USITC data were

correlated with the NSF series and extrapolated back to 1947 in

order to arrive at a proxy for private R & D. The quantity of

research variable is constructed by summing the Florida

Department of Citrus and the proxy for private R & D

expenditure, dividing by the GNP implicit price deflator (1972

= 100.00), and taking the average of this variable lagged one

and 6 years.


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This publication was produced at a cost of $1011, or 67 cents per copy, to
model production relationships in the frozen concentrated orange juice

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Agricultural Experiment Stations are open to all persons regardless of race,
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