small farmers' decisions: utility versus profit … papers/pert vol. 5 (2...pertanika 5(2):...

Pertanika 5(2): 141-153(1982)

Small Farmers' Decisions: Utility Versus Profit Maximization

MOHD. GHAZALI MOHAYIDINFaculty of Resource Economics and Agribusiness

Universiti Pertanian Malaysia, Serdang, Selangor, Malaysia.

Key-words: Risk; decision making; crop selection; quadratic programming; mean-variance; expected uility.

RINGKASAN

Sikap petani terhadap risiko dimodel dengan menggunakan fungsi-fungsi nilai-faedah Cobb-Douglas,transendental, exponensial negatif dan ukuran-bersama. Pengamatan petani-petani mengenairisiko tanaman-tanaman alternatif juga disukat dan algorithm programan quadratik digunakan untuk mendapat sempadan

jangkaan min-varians (E-V) paling cekap bagi tiap-tiap petani. Sempadan E~V init seterusnya, digunakanbersama-sama fungsi-fungsi nilai-faedah untuk menentukan rancangan ladang yang optimum. Rancangan-rancangan ladang yang memaksimumkan jangkaan-untung juga ditentukan. Keputusan analisis menunjukkanbahawa model ukuran-bersama membuat ramalan yang hampir tepat dengan gelagat petani yang sebenarny a.Modal jangkaan-untung sebaliknya ialah peramal yang paling lemah sekalL Ini membuktikan bahawa risikomemainkan peranan di dalarn membuat keputusan dan petani-petani bertujuan memaksimumkan nilaifaedah dan bukan keuntungan sahaja. Oleh yang demikian, program-program yang lebih berkesan adalahprogram-program yang mengurangkan risiko dan ketidakpastian yang dihadapi oleh petani-petani.

SUMMARY

Farmer's risk attitudes are modelled using the Cobb-Douglas, transcendental, negative exponential,and conjoint measurement utility functions. The farmers' perception of the riskiness of alternative crops arealso measured and a quadratic programming algorithm is used to derive the most efficient expected mean-variance (E-V) frontier of each farmer. The E-V frontiers are then used in conjunction with the utilityfunctions to determine the optimal farm plans. Farm plans that maximise expected profit are alsodetermined.

The results reveal that the conjoint measurement utility model predicts actual behaviour better thanthe other models. The expected profit model, on the other hand, is the worst predictor. This indicates thatrisk does play a role in decision-making and that the farmers are utility maximizers rather than profitmaximizers only. Therefore, more effective programs would be those that tend to reduce risks anduncertainties faced by the farmers.

INTRODUCTION districts, and states; the labour supply and creditavailability vary from farm to farm; the input

Agricultural production in Malaysia is and product prices vary from place to place; andundertaken mainly on smallholdings ranging from the farmers have differing experience with newless than one-half hectare to about 25 hectares. technologies and new practices. The fanners areThe situation in agriculture is very complex. The also faced with differing market conditions,soil characteristics and the area topography vary Thus the technical production coefficients ofmodestly from farm to farm and vary more each farmer and the economic relationshipsimportantly among farms in different villages, among factors and products confronting him

Key to author's name: M. Ghazali

141

M. GHAZALI

differ to some degree - perhaps modestly, perhapsgreatly - as each of these farmers considers theadoption of new technology brought to his atten-tion or made available to him by governmentprograms or policies. The entire scenerio is furtherconfounded by the differences in attitudes of eachfarmer towards the risk of adopting the newtechnology and his perception of the riskiness ofthe new innovation. Thus, almost every develop-ment program or policy that may be conceivedfor agriculture cannot be appraised as to its profit-ability or productiveness within itself. It can onlybe done in terms of the response it evokes amongthe farmers who come in contact with the programor policy.

In the present study, the basic concern iswhether risk and uncertainty affect the processof decision-making regarding crop selection,which in turn may affect policy prescriptions andthe effectiveness of policy tools. Since the majoractors of this study are the small farmers, attentionis concentrated on analysing their risk preferencesand their perceptions of risk. The study wascarried out in the districts of Muar and PerakTengah in the Malaysian Peninsula. Even thoughboth districts are major fruit producing areas,the local agriculture is still dominated by rubber.

An accurate estimate of the domestic consump-tion of fruits and fruit products is extremelydifficult because of the lack of data. A projectionon the demand for and supply of fruits indicatesthat there is and will be a shortfall in the supplyfor many more years to come unless domesticproduction is stepped up vigorously. At present,the country is importing large quantities of fruitsand fruit products to supplement the local market.

Realizing that there is a good market potentialfor local fruit, the government has taken severalsignificant steps to promote the development ofthe fruit industry. Some of the steps taken includeraising the amount of financial assistance to farmersand raising tariffs on imported fruits. The govern-ment also provides some of the essential supportingservices, such as extension and marketing.

Despite these programs, most of the farmersare still hesitant to commit themselves to fruitproduction. The reasons are diverse; however, itis hypothesized that one of the major factorsinhibiting the farmers from participating in thegovernment programs is risk and uncertainty. Inother words, the hypothesis is that the farmersare maximizing utilities rather than profits.

ANALYTICAL FRAMEWORK

Farmers' Utility FunctionsPerhaps the most widely accepted model of

individual behavior under uncertainty is based onthe expected utility theorem (Anderson et al.,1977), which takes into account the risk attitudesand beliefs of the decision-maker. There are severalmethods of eliciting farmers' utility functions. Inthis study, two methods were used: (i) certainty -equivalent (Francisco and Anderson, 1972) and(ii) conjoint-measurement (Garrod and Miklius,1981).

In the certainty-equivalent technique, the riskattitude of each farmer was ascertained within therange of losing his entire annual income and gainingtwice the amount of income. The fanner wasconfronted with a hypothetical decision problemwhich was set to present a real-world situationfaced by him in his agricultural environment. Anexample of the hypothetical problem is as follows:

The farmers' crop is maturing well and by thenext month it will be ready for harvest. Whilethe farmer is waiting anxiously for the harvest,an agricultural officer breaks the news that aparticular type of disease is spreading veryrapidly and is expected to reach his area verysoon. At the speed the disease is spreading, hehas a fifty-fifty chance of harvesting his crop.If the disease strikes before the crop can beharvested he will lose the entire crop and thushis annual income (assume sunk costs equalzero). However, if he manages to harvest beforethe disease strikes, he will be able to sell hiscrop at a higher price (say double the normalprice) because many other farmers' cropswould have been completely destroyed. Whilehe is in this uncertain situation, somebodycomes to "pajak" his crop, that is, offers topay cash now in return for the rights to harvestthe crop. What will be the sum of money offeredat which he would find himself indifferentbetween selling and not selling?

If the farmer found it difficult to answer, theinterviewer would act as the "pemajak" and startto bargain with the fanner until a point was reachedwhere the farmer was just willing to sell his crop.This value x2 was recorded as the certainty-equiva-lent of the uncertain prospect of losing this entireincome 'a' and gaining twice this annual income'b ' (Figure 1).

Once the first set of information was obtained,a new problem with equally-likely outcomes wasset-up using X! as one of the uncertain outcomes

142

SMALL FARMERS' DECISIONS: UTILITY VS PROFIT MAXIMIZATION

and one of the previously mentioned extremes(a or b) as the other. If 'a' was selected first, thenthe certainty-equivalent for the uncertain prospectof 'a' and 'x i ' was determined using the aboveprocedure. Taking this as problem 2 (Q.2), theprocess was repeated until Q.7 was answered bythe farmer.

crops and theii associated riskiness, measured interms of variance. Specifically, the main concernwas to evaluate the joint effect of the two variables,mean and variance, on the ordering of the depen-dent variable, utility. The analysis could be extendedto include other attributes, but this was not withinthe scope of this study.

Q.3. (a, x 2 ) =

Q.2. (a,

Fig. 1. Questioning Procedure for Obtaining Certainty-Equivalents.

Q.7. (x5, b) =

Cross-check questions were also asked to as-certain whether the fanner's answers were internallyconsistent. This was done by finding the certainty-equivalent of the uncertain prospects of x2 and x 5 .The value of the certainty equivalent should be x :

or very close to it. These data were then used in aregression model to estimate Bernoullian typeutility functions. Alternative forms of the utilityfunction were specified, i.e., Cobb-Douglas, trans-cendental, and negative exponential.

The conjoint measurement technique, whichwas the second technique used to estimate utilityfunctions, has shown a lot of promise in marketingresearch. This technique "starts with the consu-mer's overall or global judgements about a set ofcomplex alternatives. His or her original evaluationsare then decomposed into separate and compatibleutility scales by which the original global judge-ments (or others involving new combinations ofattributes) can be reconstituted" (Green and Wind,1975). Once the overall judgements are separatedinto their psychological components, a decision-maker would have valuable information about theattributes of a product. He would also have theinformation about the value of various levels ofany single attribute. Conjoint measurement, whichis concerned with the joint effect of two or moreindependent variables on the ordering of a depen-dent variable, was used to explain the decision-makers' selection of crops.

The major attributes of concern in this studywere the expected net incomes derived from the

Five cards were used to elicit the informationrequired to apply conjoint measurement. Differentnet income levels from a hectare of fruit holdingover a period of four years and their chances ofoccurence were written on each card:

Card 1 : 2 out of 4 years, the net income is$4500 and2 out of 4 years, the net income is$5500




Card 5: 1 out of 4 years, the net income is- $500 and3 out of 4 years, the net income is$8000

Each farmer was asked to rank these cardsaccording to his preference. The reasons for thepossibility of variations in income from differentfarms growing the same crops in the same area wereexplained to farmers before ranking of the cards.Some of the reasons given were pest, diseases,weather, and theft. The interviewers were instructed

143

M GHAZALI

to make sure that the ranking was based on thefanner's preference concerning the mean andvariance of income.

Computation of the utility scales of each attri-bute was carried out by a mathematical programmingformulation of monotonic (or order-preserving)regression (Garrod, 1979). Monotonic regressionhas been applied to all conjoint measurement andalso to certain types of multidimensional scalingproblems. Pekelman and Sen (1974) developedmodels that minimize the number of discordantpairs; Srinivasan and Shocker (1973) used a linearprogramming formulation to minimize the sum ofthe differences between discordant pairs; and bothJohnson (1975) and Kruskal (1965) used squareddifferences between discordant ranks in their lossfunctions. Concordance in this case was defined as"the event where the sign of the difference betweenthe estimated rank order of any pair of observationsis the same as the sign of the difference betweenthe true or initial ranks." Garrod (1979) has provedthat the mathematical programming formulationof monotonic regression generally yields moreconcordant results than the other techniques andthat it will always yield results at least as concor-dant. For this reason, this formulation was used inthe analysis.

Farmers' Perception of RiskIn the second stage of the analysis, the fanners'

degree of beliefs or subjective probabilities werequantified and their perception of the most efficientproduction frontiers were developed in the formof Mean-Variance (E—V) frontiers using a quadraticprogramming algorithm.

Probability distributions are used to describethe stochastic or probabilistic behavior of randomvariables. The states of nature depend on one ormore random variables. Hence, an assessment ofthe subjective probabilities of states usually requiresknowledge of the decision-maker's degree of beliefabout the underlying random variables. A varietyof methods are available for estimating theseprobabilities. Anderson et al., (1977) recom-mend the 'gross method' of eliciting subjectiveprobabilities of income levels directly from thedecision-maker. However, this method is quitesensitive to interview technique. This often resultsin inconsistencies in the decision-makers' responses.Many decision-makers, particularly farmers, do notthink in terms of probabilities. Thus they may notbe able to implicitly evaluate production responsesof different enterprises under various environmentalconditions, consider their price expectations, andcombine all this information to come up withprobability distributions.

The technique adopted for the purpose ofestimating the farmer's perception of risk in thisstudy was to elicit the components for the approxi-mation of the frequency distributions of incomesfrom various crops. Problems of pest and weatherthat the farmer perceived as being associated withmajor and moderate crop damage were first dis-cussed. 'Good,' 'medium/ and 'poor' seasons werethen defined according to the extent of damage.The farmer was then asked to respond to thequestion: "How many years out of ten do youexpect the seasons to be good, medium, and poor?"He was also asked to indicate the output and priceshe expected to get in each of these seasons. Thedata obtained from this technique were then usedto calculate means, variances, and covariances ofdifferent crops to be used as input data for quad-ratic programming to derive E-V frontiers.

Programming FrameworkAttempts to incorporate risk in mathematical

programming formulations in a whole-farm plan-ning problem include quadratic risk programming.Risk is considered only in relation to the activitynet revenues that are assumed to follow a multi-variate normal distribution. Choice of the utility-maximizing set of Xj values is a type of portfolioanalysis where the optimal portfolio is some vectorof X = X| , . . . , Xj , . . . x n that maximizes utilitysubject to the following resource constraints:

n2 ahj Xj { < = > } bh , (h = 1 , . . . , m),

where bh = the quantity of the h^resource, and

ahj = the technical input-output coeffi-cient specifying the amount of theh t h resource required to produce aunit of the j t h activity.

A more common approach like the one deve-loped by Wolfe (1959) is to divide the analysis intotwo stages. The first stage is to make use of aparametric programming procedure to determinethe efficient E-V set of portfolios or the E-Vfrontier. The second stage is to ascertain the utilitymaximizing member of this set.

In this study, the objective function was tominimize

144


subjected to a parametric expected profit constraintn2 E(c:)x; — F = 0 ,(/? = — F to Emax),

j = 1 J

j =

where:

ahjXj

1

0;

bh , (h = 1, . . . , m), and

= covanance of the per unitrevenues of activities i and j ,

net

V = variance of profit of current plan,E(Cj) = expected net revenue per unit of

activity j ,F = fixed costs, and

j3 = parameter which measures theexpected profit of current farmplans for the values ranging from—F to Emax (the maximumpossible expected profit regardlessof variance).

An optimal solution vector Xo* was initiallyobtained when j3 = —F. As j3 was increased, thelevels of activities in the optimal solution changedlinearly with 0 until one of the constraints was metor one of the activities was driven to zero. The"change-of-basis;' occurred at this point. When j3was further increased, the levels of activities wouldalso vary with 0. This change was also linearuntil another change-of-basis was met. In this waya sequence of critical values of ]3 denoted as ft,jSg, . . . . were obtained along with a sequence ofchange-of-basis solutions. For the k t h change-of-basis solution, the expected value Ek and thevariance Vk of the total net revenue were computedrespectively as follows:

The above parametric procedure was used toobtain the set of solutions that yielded minimumvariance for given levels of expected incomesubjected to the specified constraints. The solu-tions then represented the E-V efficient set. Theoptimal solution could either be left to the decision-maker's discretion or could be determined ifutility function expressed in terms of mean-variance was determined (Figure 2).

Variance of

expected

Utility functions

Expected hcome. E

Figure 2: Expected Utility Maximization.

Predicting Actual BehaviorIn the third stage of the analysis, the farmers'

attitude toward risk and their perception of riskwere brought together in the E-V space (Figure 2).The ability of the behavioral models or the utilityfunctions were then tested to determine how closethey were in predicting the actual behavior of thefarmers in terms of selecting various crops. A chi-square test was used to test the performance ofeach models. In Figure 2, suppose point p repre-sents the mean and variance of the actual incomeobtained from the present plan, the test is todetermine how well points c, b, and a (whichrepresents profit maximization point) predictpoint p - the closer the better.

j = 1Cjxk j - F

n n= 22

* *7ij x ki * k j

where: xkj * = value of Xj at the k th change-of-basis solution.

For the value of 0 between any two change-of-basis solutions, the corresponding activity levelswere determined by linear interpolation.

RESULTS OF ALTERNATIVE SPECIFICATIONSOF THE DECISION MODELS

The Certainty-Equivalent TechniqueThe method of eliciting risk preferences of

the farmers using the certainty-equivalent techniquewas described in the preceding section. Thefarmers were asked a set of hypothetical decisionproblems and the certainty-equivalents for a seriesof risky prospects were ascertained. These valueswere then used to derive the farmers' utilityfunctions.

145

M. GHAZALI

Arbitrary utility values were first assigned tothe two extreme income values of 'a' and 'b\ Theutility values adopted for this case was 0 and 100.Using the expected utility rule, the expectedutility of each certainty-equivalent was obtained.As an example, suppose U(xi) is the utility ofXi, the uncertainty-equivalent of the risky prospectwith equally likely outcomes of 'a' and V, then

U(Xl) = P(a)U(a) + P(b)U(b)

where P(a) and P(b) are the probabilities of 'a' andlb' occurring. With a fifty-fifty percent chance,

U(Xi )= ]/2(0)= 50

Similarly, the expected utility of x2 (Figure 1) iscalculated to be

U(x2) = V2 Vi

= 75

The expected utilities of all the other certainty-equivalents were calculated in a similar manner.The expected utilities, including the two extremevalues, were then regressed on the correspondingcertainty-equivalents, using several functionalrelationships1 that include:

a. The Cobt>Douglas function : U(W) = AWC

b. The transcendental function :

U(W) = AWbecW

c. The negative-exponential function :

U(W)= 1 - e " ° W

where U(W) is the utility of wealth, W.

The Conjoint Measurement TechniqueThe questioning procedure for obtaining

the raw data has already been presented. Anexample of the ranking of the raw data by thefarmer is shown in Table 1. The alternative orstimulus with mean 5875 and standard deviation3681 is the most preferred, followed by thealternative with mean 5000 and standard deviation1000, and so on down the columns. These resultsbecome the input data for monotonic regression.2

In this analysis, the following values werechosen: e = 1, bx = 1, and the initial value ofb2 = 0 .

TABLE 1An example of raw data and ranks for the monotonic

regression problem

Alternative

Expected AverageIncome

58755000612560005000

Stimuli

StandardDeviation

3681100023821732

500

Rankby a

as GivenFarmer

1

2

34

5

In the first function where the slopes bt = 1and b2 = 0, the value of the objective function is2.00; the optimal weight for the first attribute(mean) is 0.0366, and for the second attribute(standard deviation) the optimal weight is—0.0227(Table 2)3. These values indicate that this parti-cular farmer preferred a higher mean income and alower variance. These results are characteristicof a risk-averse individual.

Kendall's tau coefficient of rank order correla-tion and the Spearman's coefficient or rankcorrelation (rho) were used to measure the degree

TABLE 2An example of results of monotonic regression

when b! = 1 and b2 =0

Ranks Given by a Farmer

1

2

3

4

5

Predicted Ranks

1

2

4

5

3

Optimal weights wi =.0366;w2 =—.0227Value of loss function (objective function) = 2.00

Measure of Concordance

1. Spearman's coefficient of rank correlation = .7

2. Kendall's tau coefficient = -6

3. Number of concordant pairs = 84. Number of pairs with ties = 05. Number of discordant pairs = 2

1 The utility functions for all the farmers are shown in Table 3.2 A detail discussion on monotomic regression can be found in Garrod (1979).3 The conjoint measurement functions for all farmers arc shown in Table 3.

146


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147

M. GHAZALI

of association between the actual and predictedranks. The values of .7 and .6 for the Spearman'srho and Kendall's tau respectively indicate thatthere was a moderately strong association betweenthe initial ranks and the estimated ranks. Alsopresented in the table is a count of the number ofconcordant, discordant and tied pairs. There areeight concordant pairs and two discordant pairs;none of the pairs are tied.

The problem of multiple vectors of w corres-ponding to the same minimum value of the lossfunction was partially alleviated by parametricallyvarying the initial value of b2 from 0 to b2 = W.The values selected were 0, .1 , .5, and I. Para-metrically varying b2 did not show any improve-ment in the number of concordant pairs or in thevalue of the optimal weights in this example. Thisalso held true for most other cases.

The Probability DistributionsThe response functions were estimated for

individual crops rather than for a heterogeneous

aggregate for the total farm. Price and yieldexpectations were combined to get an estimateof the expectation of gross returns per hectarefor the individual crops. An illustration of thistechnique is shown in Table 4.

The average yields and prices in the threedifferent seasons were calculated for all cropsbelonging to each of the farmers. Rubber wasconsidered the least risky crop. Farmers expectedno fluctuation in the income level generated bythis crop over the years. They did, however,expect some monthly fluctuation. In the courseof the interview, the farmers were also asked togive their opinion on inflation. The general responsewas that even though they expected an increase inthe price level, as far as their products were con-cerned, prices would remain fairly stable. Regardingthe price of inputs, particularly fertilizer andplanting materials, they believed that prices wouldincrease but they expected the government to stepin and stabilize the prices they would have to pay.

TABLE 4Expected output, prices and incomes of one crop per hectare

SeasonsClassification

GoodMediumPoorAverage *

No. of Yearout of ten

3

4

3

ExpectedOutput

(Kilograms)

59901122625

2433

ExpectedPrice

(M$/Kilogram)

.55

1.101.651.10

ExpectedIncome

(M$)

3295123410312676

*Average expected output is computed using the formula

E(Y) * YJPJ where Yj = output in j 1 * 1 season

P. = probability of the j t h type of season

Average expected price and average expected income are computed in similar manner.

TABLE 5Activity gross margin per hectare (M$)

Type of growingseasons

Good

Medium

Poor

Average

Durian

3295 (n

1234 (n

1031 (n

1791

(Xi)

= 3)

= 4)

= 3)

Cropping

Duku(X2)

1754 (n= 1)

1261 (n = 7)

1124(ns 2)

1283

Activities*

Rambutan

2377 (n =

1373 (n =

589 (n =

1439

(X3)

= 3)

= 4)

= 3)

Rubber

1266 (n

1266

(X4)

= 10)

*n = number of years out of ten.

148


The E-V FrontierThe farmer's subjective probability distribu-

tion of prices and yields were incorporated in theestimation of the expected net returns and thevariances. The figures were obtained by thetechnique discussed in the preceding section andan example of the elicited gross margins perhectare from one farmer are shown in Table 5.

A closer look at Table 5 reveals that this parti-cular farmer perceived the presence of good,medium, and poor seasons for all the fruit cropsbut not for rubber. He believed that the incomefrom rubber was not subjected to annual fluctua-tion even though he expected monthly variations.

A quadratic programming model was used toestimate the E-V frontier for each farm.4 The sizeof operation was limited by the total amount ofland available. The total labor available for farmwork was computed by summing the number ofdays per year each family member was expectedto contribute. Fertilizer was limited by the maxi-mum amount of funds the farmer was willing tocommit to fertilizer. The amount of non-farmincome the farmer received was also incorporatedinto the quadratic programming. Inclusion of thenon-farm income did not alter the shape of the

E-V frontier, but it could affect the optimalfarm plan since it did shift the frontier. Fixedcosts were not included in the analysis becausethe values were negligible for this type of fanningoperation. Table 6 shows examples of the inputdata used in the quadratic programming frame-work. Means and variances of income for individualcrops on each farm were estimated subjectively,but it proved impossible to obtain subjectiveestimates of covariances (or correlations) directlyfrom the farmers. It was also not possible to usehistorical covariances among crops since data werenot available. Therefore, an assumption was madethat the income correlation among differentfruits was .5. It was also assumed that rubberincome was not correlated with those of variousfruits.

Optimal Farm PlansEach of the alternative behavioral models and

the profit-maximization hypothesis was then usedin conjunction with the E-V frontier, described inthe preceding section, to derive the optimal farmplans.

Utility functions (except the conjoint measure-ment function which was already defined in termsof mean and variance) were respecified as func-

TABLE 6The quadratic programming data requirement (for one farmer)

The Objective Function (covariance metrix):

x,x2

X3

x4

aA small number, 1, is used as variance of rubber income for operational purposes.

The Technical Coefficients and Constraints:

Xi

1084427

91146

381218

0

X2

91146

30643

64082

0

x3

381218

64082

536051

0

Land (hectares)

Labor (man-days)

Fertilizer (Kilograms)

Miscellaneous ($)

Expected income ($)

X i

1

203

80

64

1791

x21

175

27

40

1283

x31

67

9

30

1439

x41

423

19

40

1266

< 5.25

< 1500

< 567

< 500

= X

The E-V frontier solutions were obtained using a quadratic programming routine developed by Dr. Peter V. Garrod,Department of Agricultural and Resource Eonomics, University of Hawaii at Manoa.

149

M. GHAZALI

tions defined in terms of the mean and varianceto estimate the optimal farm plans. Assuming anormal or approximately normal distribution, theCobb-Douglas utility function was written use:

U= {\V0+ E(w)] b + b(b-l)

and the negative exponential utility function as:

u =where:

E(w)] -cVar(w)/2,

Var(w)/2;

the transcendental utility function as:

U = (Wo + E(w)] bec{W + E(w))

4- U2bc

[W + E(w)}

+ C2 Var(w) /2 ;

WQ = initial wealth,

E(w) = expected gain or loss of wealth, and

Var(w) = variance of wealth.

Profit maximization implies a linear utilityfunction. This implies vertical indifference curves.Therefore, the profit maximizing farm plan wasthe extreme right of the E-V frontier (point a inFigure 2).

TABLE 7The Chi-square goodness-of-fit and the estimated probability of income profile of actual and predicted plan being equal

FarmerNo.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

a. CD

b. TR

c. BW

d. CM

e. PM

C D a

3.084

.628

3.579

3.072

.796

7.621

12.645

3.770

66.936

6.266

10.693

9.345

16.135

3.081

7.341

1.779

.328

12.761

1.022

5.648

Calculated Chi-Square

TRb

3.088

.628

3.580

3.037

.798

7.621

12.650

3.793

66.936

6.270

10.690

5.993

16.132

.728

2.722

1.784

.328

12.763

1.022

5.652

BWC

3.082

.628

3.578

3.078

.786

7.621

12.624

3.793

66.973

6.266

10.678

5.990

16.132

3.070

2.722

1.784

.311

12.761

.966

5.650

= Cobb-Douglas utility model.

= Transcendental utility model.

Value f

CM<*

3.088

.628

3.580

7.137

.646

7.628

12.650

3.794

66.936

6.270

6,220

5.990

16.135

3.081

2.722

1,784

.063

12.761

.742

5.648

= Negative exponential/Binswanger utility

= Conjoint Measurement.

= Profit maximization model.

PMe

3.090

.850

3.582

7.137

.798

7.628

12.652

3.794

69.363

6.270

10.690

9.345

16.135

3.081

7.344

1.784

.328

12.763

1.022

5.652

modeL

CD

.•0835

.7182

.0615

.0840

.6683

.0060

0

.0214

0

.0314

0

0

0

.0836

.0072

.3764

.8073

0

.6012

.0191

Estimated Probability6

TR

.0833

.7182

.0615

.0855

.6682

.0060

0

.0213

0

.0134

0

.0159

0

.6885

.0995

.3750

.8073

0

.6012

.0191

BW

0.836

.7182

.0161

.0837

.6713

.0060

0

.0213

0

.0314

0

.0160

0

.0841

.0995

.3750

.8123

0

.6719

.0191

CM

.0833

.7182

.0615

.0080

.7129

.0060

0

.0213

0

.0134

.0138

.0160

0

.0836

.0995

.3750

.8860

0

.6844

.0191

PM

.0832

.6523

.0614

.0080

.6682

.0060

0

.0213

0

.0134

0

0

0

.0836

.0071

.3750

.8073

0

.6012

.0191

f. underlined values show the best predictor of actual behavior.

g. underlined valued show the predictor with the higher probability that the actual and predicted plans are equal.

150


Prediction of Actual BehaviorThe final step in this analysis was to test the

ability of the models, to predict actual behavior(i.e., the actual cropping pattern at the time of thestudy). It is obvious that the actual plan has manydimensions, including sizes of various crops,levels of various inputs, average income fromdifferent crops, etc. However, the income distri-bution for each plan — Le., its mean and variance— is perhaps the best factor to characterize theplan. So, the test to determine which models bestdescribe actual behavior was made within the E-Vspace. The Chi-square goodness-of-fit test wasused. It was calculated by comparing the meanand variance of the income from the optimal planpredicted by each of these models with that of theactual plan. The results of the Chi-square test areshown in Table 7.

The Chi-square values were then used tocalculate the probability of obtaining the twodifferent distributions at random when in factthey have the same mean and variance. This meansthe higher the probability level, the better is theprediction.

The conjoint measurement model was the bestpredictor in seven cases. The next best predictor ofthe actual farm plan were the transcendental, thenegative exponential, and the Cobb-Douglas utilitymodels; and finally the profit maximization model.For the classical behavior assumption of profitmaximization, the probability of "correctly''predicting actual behaviour is essentially or veryclose to zero in 15 of the 20 cases analysed.

Therefore, the results of the analysis showthat Bernoullian utility maximization explainsactual farmer behavior more accurately thanprofit maximization.

POLICY IMPLICATIONS AND AREAFOR FURtHER RESEARCH

What is the best way to get the numeroussmall farmers to participate in the programs ofthe fruit development plan in the prescribedway so as to contribute to the attainment of theplan goals and targets? It has been observed onmany occasions that a significantly large numberof farmers still fail to participate in governmentprograms to develop the fruit industry when itappears that it is to the economic advantage ofthe farmers to participate. Hence a conventionalwisdom has gained widespread acceptance amongsome people that the small farmers stubbornlyand irrationally resist change. This, of course, maynot be true. Firstly, a small farmer typically lacks

technical information concerning the technicalchange that may be involved, and he has had littleor no experience with it; hence he is inclined tomove slowly with respect to adopting the techno-logy. Secondly, adoption of new technology may,in fact or in the mind of the fanner, involve con-siderable risk, and often, he can not afford to takethe chance. For both of these reasons one couldnot say that the farmer acts irrationally.

It would be ideal if the government programscould reach the individualized operation ofthousands of farms and direct the pattern ofoperation in each of these farms so as to maximizethe expected utility of each farmer. This, of course,is next to impossible. However, it is believed thatthe attainment of development goals and targetscan be achieved via the inducement approach; itwould be far easier and more productive to providea general incentive in terms of a temporarilyincreased price, or factor subsidy, etc. aimed atincreasing farm profit and to let each farmer, withthe aid of a good information program, work outthe most efficient pattern of operation for hisparticular farm according to his preference.

In light of the above, a consideration of a fruitdevelopment plan must contain within it a rela-tively large and effective production educationprogram to convey to farmers relevant and reliabletechnical information concerning the new techno-logy or production program so that they makerational decisions with respect to adoption orparticipation. Where research for technologicaldevelopment is concerned, effort has been concen-trated on propagating and developing fruit clonesthat are high yielding and at the same time haveshorter maturity periods. Another importantfeature of these crops that has not been researchedis the variability in production which is irregularand unpredictable. Research on developing clonesthat have lower variability and irregularity of pro-duction but at the same time provide an acceptableyield and a short maturity period is highly relevantfor the development of the fruit industry.

The fruit development plan may be comple-mented by economic programs which providebetter marketing and credit facilities, input subsi-dies, planting materials, technical information,and non-farm job opportunities which allowgreater pooling of risks at the household leveL

Agricultural price support has been used quitesuccessfully in the production of rice as part of anincomes policy. This policy is likely to be moreappropriate in cases where price uncertaintydominates. In this study, however, the extent of

151

M. GHAZALI

price and yield uncertainties are not examined in-dividually; thus it would not be appropriate torecommend price support policy. This issue,therefore, requires further research before anyform of conclusion can be made.

In the area of crop insurance as a policyalternative to dealing with the undesirable con-sequences of risk aversion, various studies haveshown that pure insurance schemes based onindividual loss assessment are likely to have lowbenefit-cost ratios, particularly in countries withlow levels of income and small landholdingsbecause the administrative costs of assessingindividual losses become very high (Roumasset,1978). Furthermore, the relevant efficiency issueis not whether risk preferences change the alloca-tion of resources, but whether risks are appro-priately spread throughout the economy (Arrow,1971). There is also the possibility that where riskpreferences are derived from market imperfectionslike the differences in buying and selling prices,they serve a positive role in the efficient allocationof resources (Roumasset, 1978). In developingcountries where the insurance schemes seemed tohave worked, they are better described as incomesupport and distribution schemes towards poorareas rather than insurance schemes (Binswanger,1979). The prospect of crop insurance at thismoment appears bleak; however, to the extentthat one believes that it may be an affective toolto reduce risk, further research is warranted.

The biggest problem encountered during thesurvey was related to the process of eliciting thesubjective risk preferences of the farmers, and thismay have some effect on the results. If similartechniques were to be used in future researchwork, the problem could be alleviated by providingmore intensive training to the interviewers so thatthey could explain more clearly the nature andrequirement of the scheme to the farmers andbecome more alert in recognizing inconsistentanswers.

The conjoint measurement utility functionappears to work quite well in explaining farmers'attitudes towards risk and thus may be considereda good prospect for similar work in the future. Theconjoint measurement if carried out in more detail,may become a good tool in explaining the decision-making process of small farmers.

Research dealing with subjective probabilitydistribution has gained momentum in recent years.In this study, an approach combining personalprobabilities of certain 'disasters' such as pestoutbreaks with expected outcomes of yield and

prices is used. This approach appears to work quitewell, i.e., most farmers are able to specify thenumber of good, medium, and poor years out often as well as the associated yields and prices.Future studies dealing with subjective probabilitydistributions may consider using and improvingthis approach.

Because it considers only two moments of thedistribution of returns, there has been strongcriticism of the E-V approach. However, a cruderepresentation of risk may be better than ignoringit altogether. The analysis can be extended tohigher moments if required, though at somecomputational cost.

In the final analysis, planners for the fruitindustry must develop methodological innovationsfor dealing with uncertainty in complex croppingsituation and formulate research, projects, pro-grams, and policies that are tailored to its specialcharacteristics but which constitute tolerablesolutions to the difficult issues of its development.It is hoped that a recognition and understandingof these special characteristics and issues will leadto a more effective development plan for the fruitindustry.

REFERENCES

ANDERSON, J.R., DILLON, J.L. and HARDAKER, J.B.(1977): Decision Analysis in Agricultural Develop-ment. Ames. Iowa State University Press.

ARROW, K.J. (1971): Essays in the Theory of RiskBearing. Chicago. Markham Publishing Company.

BINSWANGER, H.P. (1979): Risk and Uncertainty inAgricultural Development: An Overview. In Rou-masset, J.A., Boussard, J.M. and Singh, I. (Eds.)."Risk, Uncertainty and Agricultural Development."Laguna. Southeast Asian Regional Centre for Gra-duate Study and Research in Agriculture.

F R A N C I S C O , E.M. and A N D E R S O N , J.R., (1972):Chance and Choice West of the Darling AustJ. agri. Econ. 16(2): 82-93.

GARROD,P.V.(1979): A General Program for MonotonicRegression, (mimeograph). University of Hawaii.

GARROD, P.V. and MiKLIUS, W. (1981): A Method forEstimating the Value of Transport Service Attributes.Paper presented at WAEA Annual Meeting ofLincoln. Nebraska. July 19-21, 1981.

GREEN, P.E. and W I N D . , Y. (1975): New Way to Mea-sure Consumers' Judgements. Harvard Bus. Rev. 54:

JOHNSON, R.M. (1975): A Simple Method for PairwiseMonotone Regression, Psychometrika. 40,(2): 163-168.

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KRUSKAL, J.B. (1965): Analysis of Factorial Experi- ROUMASSET, J.A. (1978): The Case Against Cropments by Estimating Monotone Transformations of Insurance in Developing Countries. Philippinesthe Data,//?, statist. Soc. Series B. 27: 251-263. Rev. Bus. andEcon. I.

MALAYSIA MINISTRY OF AGRICULTURE. (1975): SRINIVASAN, V. and SHOCKER, A. (1973): LinearReport of the Committee on Fruits and Vegetable. Programming Techniques for MultidimensionalVol. 1. Kuala Lumpur. Ministry of Agriculture Analysis of Preferences. Psychometrika. 38(3):Printing Office. 337-369.

PEKELMAN, D. and SEN., S.K. (1974): MathematicalProgramming Models for the Determination ofAttribute Weights. Management Science. 20(8):1217-1229. (Received 2 February 1982)

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