xt7tmp4vk19c https://exploreuk.uky.edu/dips/xt7tmp4vk19c/data/mets.xml   Agricultural Experiment Station, Department of Agricultural Economics, University of Kentucky 1974 journals kaes_research_rprts_21 English University of Kentucky Contact the Special Collections Research Center for information regarding rights and use of this collection. Kentucky Agricultural Experiment Station Research Report 1 : September 1974 text Research Report 1 : September 1974 1974 2014 true xt7tmp4vk19c section xt7tmp4vk19c A MULTIPERIOD LINEAR PROGRAMMING-SIMULATION
MODEL OF THE FARM FIRM GROWTH PROCESS
Ying I. Chien and Garnett L. Bradford
O
RESEARCH REPORT 2I : September I974
University of Kentucky : : College of Agriculture
Agricultural Experiment Station :·: Department of Agricultural Economics
Lexington

 J x
x * a
’

 CONTENTS
Page ~
Preface ............................................ 2
List of Tables ........................................ 3 L
List of Figures ........................................ 4
Introduction ......................................... 5
Concepts Pertinent to Farm Firm Growth Studies ...................... 8
The Model: Conceptual Framework ............................. 9
The Model: Operational Form ................................ 13
The Study Farm ....................................... 18 »
Analysis of Results ...................................... 20
Summary and Conclusions .................................. 36
References .......................................... 39
Appendix A: Multiperiod Linear Programming Model .................... 41
Appendix B: Flow Chart of the Simulation Model ...................... 53
1

 PREFACE
This report concerns results of research conducted by the authors at the University of
Kentucky in 1971 and 1972 and are based in large part on the work conducted by senior author T'
as a part of his Ph.D. dissertation.
The authors contend that prior to undertaking this investigation that considerable effort,
with varying degrees of success, had been expended by agricultural economists in developing and
using farm firm growth models of either of two general types: (l) optimizing (mostly LP, etc.), _
or (2) descriptive—accounting (mostly computer simulation). The primary thrust of our ‘
investigation was not to refine the two techniques or approaches but, rather, to link the best
features of the two into a single, computer-operational model. Thus, the first portion of the 4
report is devoted primarily to conceptual and theoretical matters--literature review, constructing `
the combination model and discussing its features. The second portion is devoted largely to
empirical matters--testing, using and experimenting with the model on a Central Kentucky beef
i cattle farm.
l
A
T
_ 2
l
l _k.·

 LIST OF TABLES
of
lor Table Page
Ht 1, Estimates of Initial Expected Values for Yields and Prices, and Coefficients of
mc; Expectation ....................................... 14 t
  2. Farm Enterprise Organization and Financial Situation ofthe Case Farm,_]anuary 1967
{est and December 1970 ............................,..... 19
h
En; 3. Farm Enterprise Organization Generated from the Growth Model ........... 25
C; 4. Summary of Simulated Financial Outcomes for the Study Farm ............ 27
5. Means and Variations of Total Assets and Net Worth as Simulated by the Growth , '
Model .......................................... 28
6. Comparison of Simulated Farm Enterprise Organizations, Three Alternative Production
Systems on the Study Farm 1971 through 1974 .................... 31
7. Output Data Generated By the Growth Model for Net Worth at the End of 1974 . . . 34
8. Output Data Generated By the Growth Model for '1`otal Assets at the End of 1974 . . 34
9. Statistics for Analysis of Variance for Total Assets at the End of 1974 ......... 35
10. Statistics for Analysis of Variance for Net Worth at the End of 1974 ......... 35
Appendix A
Table 1
A Two—Year Version of the Multiperiod Linear Programming Tableau for the Study
Farm .......................................... 47
3

 LIST OF FIGURES
i Figure Page
l Conceptual Process Model of the Farm Firm Growth .................. 12
2 Actual and Simulated Mean Values of Total Assets at End of Year ........... 23
3 Actual and Simulated Mean Values of Net Worth at End of Year ............ 23
4 Actual and Simulated Mean Number of Beef Cows in the Herd at End of Year ..... 24
5 The Projected Time Paths for Total Assets Under the Three Operating Alternatives . . 32
mr
[ 6 The Projected Time Paths for Net Worth Under the Three Operating Alternatives . . . 32 bc
lar
Appendix B Tm
Figure 1 t€<
Flow Chart of the Simulation Model .......................... 53 i¤l
stx
fa1
co
fa:
is
A1
qu
ag
re
ax"
fir
cc
sti
wi
Y
.»
i
r , 4
4,27.

 C
.8 A MULTIPERIOD LINEAR PROGRAMNHNG-SIMULATION MODEL
12 OF THE FARM FIRM GROWTH PROCESS
23 ’
by
23
Ying I. Chien and Garnett L. Bradford*
24
32 During the past three decades one of the become necessary for the acquisition of
most dramatic changes in U.S. agriculture has additional resources because self-owned
32 been the continuous trend toward fewer and and/or intemally generated capital will likely
larger farms. This revolution has been due be insufficient for expansion over time?
mostly to the adoption of new production Consequently, will farmers and capital lending
technology and the substitution of capital agents be interested in quantifying the
53 inputs for labor. Changes in market and farm potential for growth of the farm firm under
structure have brought about the necessity for different capital market structures? (3) How
farm businesses to be large enough to remain may the impact of the variability of such
competitive and to earn ample income for factors as prices and yields be expected on the
family needs. firm growth potential? Information pertaining
to these and other related questions is
necessary for future farm adjustment.
The Problem To answer such questions, fruitful
models of the farm firm growth process need
This trend toward fewer and larger farms to be developed. Farm firm growth models
is likely to continue, even if at a slower rate. which were most popular or most often
Accompanying the trend, are a number of employed during the l960’s may be classified
questions about which farmers, into three types: multiperiod linear
agribusinessmen, policy makers, and programming, recursive linear programming,
researchers are concerned. Pertinent examples and simulation models} Of these three, the I
are: (l) What growth patterns of the farm multiperiod linear programming (MLP)
firms are to be expected when farmers technique has been the most widely
contemplate alternative farm management employed. Although it has been considered to
strategies? (2) As a farm business expands, be an efficient and flexible tool for analyzing
will greater reliance on borrowed funds farm firm growth problems, its solution still
remains questionable vis-a-vis the reality of
*Assistant Professor of Business Administration, Morehead 1-__-__-Zl-
Statc University and Associate Professor of Agricultural 1For a more complete review of the applications of these
Economics, University of Kentucky, respectively. models to farm firm growth, see Irwin [1968].
5

 b
-i actual farm operations Critical shoitcomrngs (5) Multrperiod linear programming model
which have been cited may be outlined: cannot (by itself) adequately handle and
i predict financial variables such as total
L (1) The MLP model, as its name implies. assets or total net worth
explicitly provides a simultaneous (6) It is difficult to incorporate
i solution for all periods in the planning "qualitative` factors into an MLP model.
horizon It does not, therefore, account For example, it seems reasonable to
for the sequential nature of production assume that farmers' decision rules for (2
or marketing decisions. Consequently. asset investment depend not only on
the farm firm growth process generated easily quantrfred economic factors but
by this kind of model may not be also on thc necessity of assets in terms of
compatible with the real world setting in timeliness of asset services
which farms typically operate
(2) Multiperiod linear programming is an The recursixe linear programming
Optimizing m0d€l, $0 li 1€S¤iiS Hi 21 global approach was first employed by T Heidhues (E
r optimum by solving the system of the (1966] to solve growth problems for farm
model for all periods simultaneously firms This approach deals with the dynamics
This characteristic may render the model of decrsron making by using a sequential
to be less satisfactory when one rs optimizing procedure to describe how plans
interested in descriptive or predrctive for a gtven time period are related to past
economic analysis rather than expectations and performance.Consequently,
‘ ‘ p r e s c r i p t r v e ` ` (m a k i n g it is applicable to a wide variety of dynamic
recommendations for resource or output problems in the field of posztzve economic
s adjustments) analysis.
(3) This model, like the standard linear Since recursive linear programming (”
pr0gI‘&mmmg appi0&Ch, €&!I1€5 the approach employs conventional linear
assumption that all inputs and products programming to solve problems sequentially,
are perfectly divisible. Clearly, for most it suffers the drawback of the divisibility
farm firms many items come in problem and the incapability of adequately
indivisible umIS» FOI example. ii fEilm€Y handling and predicting financial variables. ln
CZI1 DOI bllv 3 0,75 HHH of U21€i0! Oi sell any event, it seems that this approach is not
0.5 head of beef cattle entirely satisfactory for application to firm
(4) Multiperiod linear programming is a growth studies, because expectations about
dynamic-certainty model; perfect future condrtrons and possible outcomes in
knowledge about input output and price the future periods are not taken into explicit
CO€ffiCi€I’ltS is assumed {O €X1$[ OVEI all Cgngidggrgugn
periods The assumption of certainty Computer simulation becomesarelevant
usually imPi1€S Ih€ HOUOH that and useful tool for analyzing f1rm—growth
j €XP€Ci¥1'€i01'1S of ih€ fU¤1i€ 6-16 economic problems when the researcher faces sl
. single-valued and C01f€Ci and, h€¤€€, one or more of the followrng situations [see F
C renders the model to be inadequate and Naylor, 1971, pp 5.9] _ tl
( unrealistic. This assumption can, h
h0W€V€F, be relaxed, 6 g i S R- ]0h¤S0¤, (1) It may be either impossible or extremely S
et. al, [1967] have employed the MOIIIC costly to observe actual behavior Of F
~ Car1<> M€ih0d I0 allow CYOP Y1€1d$ LO processes of an economic system. For 3
vary in his multiperiod linear example, certain data on farm firm 1
i PYOgT&mm1U§m0d€1— growth patterns under different r
l
r
l  

 7
sdel
and conditions (e.g., the f1rm’s investment to economic analyses, G. F. Patrick and L. M.
otal policy, resource situations, etc) simply Eisgruber [1968] first applied this tool to a
do not exist. Computer simulation could farm firm growth study, followed by H. R.
‘ate be an effective means of generating data llinman and R H. Hutton [1971] as well as
»dcl_ which can describe possible growth by ll D Hal] Amir) [,_ Walker []97o]_
to patterns of the firm In spite of its potential as a tool for
for (2) The system in study may be so complex analyzing many economic problems, t
on that it is impossible to describe rt computer simulation, when applied to
but mathemalleally in such a way that dynamic farm planning or farm firm growth
is Of analytical solutions may be Obtalnable studies, also has several deficiencies. This is -
and single-valued PY€d1€tlOh$ Can be primarily because simulation models lack
made. Many deC1Si0nS made by farm linkage in over all farm planning for each time
ning 0P€Yat0Y$l`allmt0 this category period within the planning horizon. They
hues (3) While Some aspects of the system(s) of typically provide purely a sequential rather
farm lht€l€$t maY be descnbable m a than a simultaneous solution to the farm firm
mics mathematlcal model, Om? may ¤0t be growth problem. Yet any given period of
ntial able to obtain a solution to the model by time, the farm operator seems likely to draw a
ilans ahalYtl€al t€€hhl€l¤€$t C<>mPUt€¤‘ blueprint (at least in his mind) for an over-all
past Simulation methods haV€ been (simultaneous) farm planning over a number
m]y_ demonstrated to be efficient techniques of years, The formulation of this dynamic
amic of numerical analysis for solving farm planning is based on the operator’s
omic complex mathcmatlcal Pl'0hl€m$ ahd expectations which, as stated in the
stochastic models. subsequent section, plays an important role in
ming (4) Conducting experiments to test the planning.
(near validity of mathematical models wlnch
rally, describe the behavior of the system may
may be impossible or too expensive. For ()bjeerives of the Study
mcly example, it is difficult to conduct
:S_ In experiments with actual farms I0 Out of the examination of the past farm
S not examine the effects of different firm growth models grew the awareness that a
firm production alternatives on the farm firm research effort should be directed toward
bout growth. However, experimentation on developing a farm firm growth model which V
BS in the computer provides researchers an incorporates the “best” features of these
phd, efficient tool to handle problems of this models. Thus, the primary objectives of this
sort. report deal with research techniques. More
zvam specifically, these objectives are:
Owth In addition to the foregoing four
faces situations where computer simulation has (l) To structure a farm firm growth model
[SCC potential, it has been pointed out that this which is in conformity with economic
technique is also useful and appropriate in theory and consistent, to the extent
handling multiple goals, indivisibilities, possible, with reality.
Tmcly sequential decisions within the planning (2) To develop and apply, based on the
W Or period, concepts of organizational, managerial conceptual model noted in objective fl),
For and behavioral theories [see Halter and Dean, operational farm firm growth models
firm 1965 and Hutton, 1966]. Recognizing the which are capableaof depicting and
Cmnt relevance of computer simulation technique analyzing the farm firm growth process.

 8
To achieve these objectives, certain general, 1S thought of as an increase in the
criteria for the modelbuilding must be met. firm size which may be measured in terms of
First, the model should be, in some sense-, any number of several variables, e.g., volume (EI
dynamic and stochastic That rs, account of output, quantity of resources, and U
should be made of the fact that firm growth magnitude of accumulated worth, etc. To
does not take place in an environment of However, the fact that several or all these dn
certainty and statics. Second, research effort tariables may not change in the same cn
should be directed toward constructing a direction- some may increase and some others P]
descriptive model so that the farm frrm decrease presents difficulty in measuring the lll
growth process may be depicted and net change in the srze of the firm. {0
l analyzed. Finally, the model should be In this report, firm growth is measured Oi
operational in the sense that obtainable by primarily in terms of three variables: (1) an lh
means of mathematics and/or computer increase in total assets, (2) an increase in net I
operations. Accordingly, the MLP—srmulatron worth (equity), and (3) an expansion in the Sd
model discussed in this report is applied on a particular productive enterprises (e.g., beef  
r test or preliminary basis to a Central cow herd size) There are several reasons for CX
Kentucky Beef Cattle Farm. This application choosing these three variables as measures of hc
is discussed in the concluding sections. firm growth. The use of total assets allows ti]
one to recognize the fact that ultimately firm ar
growth must arise from the acquisition of tc
CONCEPTS PERTINENTTO FARM additional assets to meet the need for cv
FIRM GROWTH STUDIES expanding the farm business. Change in net bc
worth is a reasonable base of evaluation when bc
Before the model is presented, certain we examine growth of the firm as a whole. A
definitions and concepts of farm firm growth change in net worth reflects increases in assets tc
will be delineated. The terms —farm firm and and/or decreases in liabilities. The level of and fu
firm growth——are defined in this section, and the change in net worth are, therefore, good ul
the dynamic nature of farm firm growth is indicators of growth capacity of the firm. pl
briefly discussed. Consideration of change in the size of major C(
farm enterprises (such as beef cows) is A
particularly appropriate when financial P]
Definitions variables fail to reflect the growth of the farm sk
. firm. ,
Firm·household interrelationships are gg
not to be ignored Thus, a "fa.rm f1rm," as O1
defined in this report, is a business entity The Dynamics of Firm Growth tc
_ which is primarily concerned with the M
creation of net returns and the satisfactron of Like feeding of livestock and raising of W
j certain levels of family living by means of crops, the growth process of a farm firm does rc
_ producing agricultural products From this not take place in a static environment. In the el
definition, it follows that the farm firm rs a actual growth process, the firm’s actions for
, decision making unit on both the production decision and planning at any given period of C,
side and consumption side. time obviously are interrelated closely both C,
The concept of firm growth can be with the past and the future. It is, therefore, d
I illusive. At present there is no widely essential that research on firm growth it
_ _ accepted unique definition. Firm growth, in somehow account for its dynamic nature. fl
I
'  

 9
15:;, It is because entreprenuers or farm andfinancial management overlap. It is quite
umc operators can never be very certain about the obvious that the rate of firm growth depends
and future that expectations play an important heavily. upon the firm’s capacity of
ctc. role in planning. The fact that expectations, production which may be expanded through
qhcsc and hence planning, may be in error the uacquisition of additional resources. The
iam: emphasizes the importance of the recursive ability of acquiring resources at any period of
[hers processes oi learning and obtaining time is largely dependent upon the availability .
, the information which greatly influence the of funds which may be obtained from both
’ formulation of expectations. Such processes internal and external sources, viz., disposable
umd of learning and obtaining information reveal income in excess of needs for consumption, a
) an that expectations stretch over time. tolerable amount of saving and funds
I net While the firm manager may stick to the borrowed from loan agencies. When the
1 the same expectations over a certain period of availability of factors of produciton is not. in
beef time, it is likely that new expectations arise as the form of fractional sized units, the timing
S for time lgoes by. Accompanying each new of investmenttbecomesimportant to the firm.
CS Of experience, expectations are changing and, Investments in buildings, machinery and
Hows hence, different at every successive pointpof equipment sewe as an example. When capital
firm time. In otherwords, the process of learning is limited, such lumpiness of many inputs
and obtaining information may be considered complicates investment planning which
in Of to be continuous. As time goes by, the certainly affects production choices and,
for evidence changes continuously as more facts hence, the rate of growth.
I net become known and, hence, the prospect may
when be changing over time accordingly.
)1€‘ A Since expectations in one period relative THE MODEI.: CONCl·ll"l`I’.r\I. FRAMEWORK
lsscts to economic and environmental conditions in
fend future periods might be held with great The conceptual model of the farm firm
srwd uncertainty, the production and investment growth process rests upon two theoretical
flfm‘ plans which are based on expectations must notions, viz., Hick’s notion [1946] and that
mq gf continuously be adjusted or revised with time. of Modigliani and Cohen [1961] regarding
S) _ls Adjustment of production and investment the dynamic planning behavior of the firm.
mcml plans toward "desired" or "optimal" levels Pragmatically, it takes into consideration that
farm should continue with time as knowledge is the model should be capable, at least to some
gained over time. However, owing to various extent, of "implementing" farm operations l
reasons such as lack of knowledge, durability into a "real-world setting." A brief review of
of capital inputs, uncertainty of prices and these two notions is presented in the
technology, the firm may carry out following subsection.
adjustments slowly and gradually. In other
ng Of words, there may exist lagged adjustment in
ldocs 1”eSp0nse to changes in the economy and Theoretical Background
in the environment.
is for The dynamic nature of firm growth also In his "Value and Capital," Hicks
Od Of Can be, in addition to that inherent with [1946] developed adynamic decision-making
b¤th expectations, recognized from the fact that model of the firm under certainty. According .
€fOf°» decisions concerning production and to his view, just like in static theory, the firm
fowth investment are closely interdependent as the is to choose from among alternative available
¤- firm grows over time. In other words, business courses of action the one which is most

 10
conducive to the achievement of its goal. period the firm is supposed to faee with the
Hicks [p. 193] expressed his idea by arguing maximization problem subject to certain Pl
that ". . . the decision which confronts any constraints over some definite horizon. It also O"
particular entrepreneur at any date . .. may implicitly indicates that definite estimates of bf?
be regarded as the establishment of a parameters associated with these constraints BF
production plan." He comments further [p. are obtainable through anticipations. lat
194] that ". . . just as the static problem of F. Modigliani and K. Cohen [1961] m
the enterprise is the selection of a certain set contend that in reality "economic men" do  
of quantities of factors and products, so the not generally behave expressly in the way Wl
dynamic problem is the selection of a certain implied by the Hicks' concept. They indicate be
production plan from the alternatives that are that the discrepancy between the conclusion gr
0pen.” From this proposition, he concludes of Hicks’ analysis and observed behavior may gh
that the decision problem faced by the firm at be explained in two ways. First, uncertainty is I  
any given point of time is the selection of the involved in the real world, and the existence [ll
best plan over the planning horizon. The most of uncertainty tends to shorten considerably 0
' fundamental way of selecting the preferred the horizon over which it is useful to form
production plan involving costs and returns in anticipations or to formulate plans. Secondly,
future periods is that of the capitalized value Hicks’ model which assumes rational behavior
of the stream of surplus--Hicks called it"the1r on the part of business firm cannot
capitalized value of the production plan." In adequately account for the actual behavior.
establishing this criterion, he [pp. l94·95] Modigliani and Cohen argue further that CC
contended that: "while it is perfectly true that in terms of the pl
pay-off function the single current move of 1
In statics, we were content to think of the static model is replaced by the entire set (
the entrepreneur maximizing his surplus of moves over the horizon, it does not
of receipts over costs; this caused no necessarily follow that, as in the static model, (2
special difficulty. But when the problem the firm must choose now its entire course of
is looked at dynamically, it becomes action." Therefore, they propose [p. 20]: (3
clear that the entrepreneur can expect,
not a single surplus, but a stream of . . . the decision problem confronting the
surpluses, going on from week to week. entrepreneur at a given point of time is .
If two streams were such that every most usefully regarded not as that of ISA
surplus in the one stream was greater selecting the best possible plan of al
than the corresponding surplus in the operations over the horizon, but rather, P
other stream, then there would be no as that of selecting the best possible first 2;]
question which stream was the larger. move only.
But if this condition is not fulfilled (and  
[ there is no reason why it should be According to Modigliani and Cohen, the bi
Q fulfilled always, or even often), we used "best possible" not only refers to the first m
¤ y some criterion to enable us to judge period but refers to the entire maximization al
_ whether one stream is to be reckoned problem over the horizon. In this sense, this ,1,
[ larger than another. formulation is similar to the Hicks’ notion. A
  _ However, there is conceptual difference in
· The implication of the Hicks’ that their formulation places major stress on
* formulation is that at the beginning of each the first period (or sub-period) of the  
’ 1
l
 + g
 .   — i
l l  

 11
the ·
tain planning period. In other words, it emphasizes revised. From this argument, it is therefore,
also on the choice of the first move? which cannot reasonable to assume that the farmer
,5 Of be postponed and, hence, must be made at a formulates, at the beginning of each period, a
aims given point in time. This approach treats the long-run plan with the aim only of providing
later sub-periods of the planning period in himself with a basis for farm operation for the
,61] much less detail than the first sub-period. It current year. In terms of the Modigliani and
., do also stresses the point that the decision-maker Cohen’s notion, the farmer may be supposed =
way will have to revise his planswhen information to try to get the best possible first move
icatc becomes available through time, even if he has which cannot be postponed and, hence, must
{sion great, confidence. I.ong-run plans are, be carried out at a given point of time. We
mav therefore, not necessarily made up in order to may, therefore, call this kind of long-run plan I
ny {S be implemented, but only to utilize all the an expected or ex ante plan. , i
[ence available information to make the best plan U Having formulated an ex ante plan in his
mbly for the current period. mind, the lmanager then takes laction to
form implement it for the current period (year).
ndly Actual outcomes may turn out to be (
. ° Construction of the Conceptual Model significantly different from the prospects, due
(aww to various reasons. The mono-period plan
mimi As sketched in Figure 1, a general (derived from the ex ante long-run plan) may
ivwn conceptual model of farm firm growth be, due to various factors such as
that process may be described in three phases: psychological inertia and institutional factors,
)f th? adjusted during the course of implementation.
vc O (l) Formulation of expectations and the ex Actual prices and yields may deviate
ic Set ante long-run plan, significantly from the expected levels. The
i gc? (2) Implementation of the current actual investment decision process, at a given
Ec 2,} mono-periodic plan, and point in time, may not be the same as that
_ (3) Reformulation of expectations and the decision made in the long-run planning. Such
` ex ante long-run plan. phenomena, however, may be incorporated in
a research model by employing computer
fg this At any given period of time the manager simulation techniques and the concept of
Imc 15 is, in Hicks’ concept, assumed to have in mind behavioral (or flexibility) constraints.3 One of
mt Of a long-run plan; that is, over a certain the merits of computer simulation is that the
in Of planning horizon, hc plans for his goals to be model can be designed to allow for stochastic 4
,ath_cr’ achieved. This plan is formulated on the basis V81`i¤bl€$· Thus. when Stochastic elements are
eflmf of single-valued expectations about prices and involved in th€ mods]. T€P€3t€d Uials
yields. This plan is, however, not likely to be (1‘€P·li€8U0¤5) aff? madf? P0$$ibl€ bY thc
carried out for the entire planning horizon €0mPUt€T sim¤l¤t1<>¤ techniquc $0 35 to
“· Fhs because expectations, being a "subjective ¤V€1'&g€ Out thi? €ff€Ct$ Of “‘·mu$u8·1
C flrst m&tt€r,” are subject to errors. As experiences happenings" occurring for any single
Zatmfl are gained and new information becomes Y€Pll€3tl0¤·
c» fhls available, expectations are changed over time. At tht? €¤d Of th€ Pmduction P€Yl0di ths
IOUOIT Accordingly, the iorigqun plan must bg current mono-periodic plan becomes a
nce in
ess on
lf thc   . . 2 · · - -
Nvdlglnm and Cohen [p. 16] called the action carried out Th¢ ¤d¢¤ is °"8“““Y dw to Hcndcrwn (1959» PP·
by the firm in any period its move in that period. 242‘260)·

 12
rea
gm
cx;
cx;
· . _ _ an<
Given: Formulating Expectations ho
of Prices and Yields to E
Farm Firm's Goals be Prevalent in Periods t, 3i
and (t+l),..., (t+kI ra
Initial Farm Firm
V Situation in Period t
Adjusting and lmple- Formulating an Ex Ant; aa
menting Mono-period Multiperiod Production- ““
Plan for Period t Investment Plan for a Th
Horizon of (k+l) Years. PP
(On the basis of expec— kv
tations) aH
fox
lcv
cw
nu
foi
· ful
Analyzing Results and Revising and Reformulating Ed
Adjusting Resource Expectations of Prices and 52
Conditions Yields to be Prcvalent in
A Periods (t+1), (t+2),..., CX
(t+k+1) 2*
wl
l
g Figure l. Conceptual Process hbdel of the Farm Firm Growth Z*
  YX
Q
Y · Y·
Q . re
l  
 ’ j _
l. 2
M   
..§,_\ j l

 13
realized or ex post plan. The farmer has Zt is the actual level of the variable during
gradually accumulated knowledge and period t,
experiences, and then must revise his B is the coefficient of expectation.
expectations and adjust or reformulate
another ex ante long-run plan over a new Eql1¤tl0r1 (l) HIHY be rewritten 2-Si
horizon.4 Repeating the process year after
year, a time path of farm firm growth may be Z*t Z B Zt-1 ‘*' (1 ‘ B) Z*t-1 (2) ,
traced out.
Expanding equation (2) by iteration gives the
following expression:
THE MODEL: OPERATIONAL FORM t _
Z*t:(l·l’)‘ Z’6+,>3,¤0-¤>1·1 Zta <3>
Expectation Model
where
In this study, farmers’ expectations
about prices and yields are hypothesized by i denotes the most recent time period
using Nerlove’s expectation model [1958]. (year) for which levels of the variable (Z)
The basic idea underlying this model is that were known, and
people’s notions of the expected "normal" t denotes the "current" time period
level of economic variables, such as prices, is (year).
affected by their actual past values. However,
for any given manager (decision maker), past The nature of this model is readily
levels of economic variables do not necessarily apparent from equation   Given the
exert their influence equally. In other words, coefficient of expectation, B, the weights
m0r€ recent prices are H partial result of decrease as the actual data get older. It also
forces expected to continue to operate in the implies that Nerlove’s model is a type of
future; the more recent the price, the more it adaptive, error-learning behavior of
is likely to express the operation of forces expectations. lt is the nature which makes the
relevant to "normal" levels [Nerlove, 1958, p. model appeal to this study. Presumably,
52]. Mathematically, the model may be farmers base expectations on their memories.
expressed as: The further one goes back in time, the more
vague his memory should be. Therefore, the
Z*t: Z*t-1+5 lZ*t-ll weights [the B(1 - B)l;l coefficients decline `
as data get older.
0 i B   1 (1) The initial expected values for yields and
prices (2*) are 5-year averages (1961—65),
where computed from Costs and Returns [USDA,
1950-1965] and from Prices of Products
. Z*t is the expected "normal" level of a Bought and Sold by Kentucky Farmers [Card
variable (e.g., price or yield) during and Koepper, 1970]. However, the average
period t, yield of corn was adjusted upward by 20
A ` l ` l percent to make it more consistent with the
study farm records (Table 1). _
"`_“""“"_ Expectation coefficients for yields and
4** mw **<··*¤>·· *¤ ¤¤w =¤=¤=¤<*=·¤ im ¤f¤¤*·=rv¤¤d¤¤¤¤¤ prices are assumed to be 0.7 and 0.9,
. year, but the current yearisexcluded because it is no longer _ .
,d,v,m_ respectively. On the basis of commonly
accepted "thumb rules" and a priori

 14
TABLE I kn
frc
ESTIMATES OF INITIAL EXPEC'I`ED VALUES FOR EO;
YIELDS