13

THE ADEQUACY OF A CROP PLANNING MODEL FOR DETERMINING INCOME, INCOME CHANGE, AND CROP MIX

Lars Brink and Bruce McCarl’

Plans generated by linear programming models for crop planning often must be assumed to be repeatable year after year, with the spring and fall operations in one year being determined simultaneously in the model. In reality, spring operations are influenced by the fall operations that were or were not done the previous year. Linear programming models have also been the subject of numerous suggestions that risk aversion be modeled explicitly by various techniques. This paper analyzes how the usefulness of a linear programming crop planning model is affected by (1) the fact that cropping activities are related between years but the model covers only one year, and (2) the explicit incorporation of risk aversion. The procedure is to compare results from the planning model with results from a model variant that does not assume repeatability and results from simulated decision making. Three uses are investigated: prediction of farm income, farm income change, and crop acreages. The consideration of previous fall operations in planning improved the prediction of income and acreages, but the prediction of income change from making a machinery investment was not improved. The explicit incorporation of risk aversion did not improve the ability of the model in any of its uses.

I1 faut souvent supposer que la planifiction engendrte par des modhles B programmation lineaire puisse h re rtpkt6e d’une an& sur I’autre puisque les activitts du printemps et celles de I’automne sont determinks simultanhent dans le modtle. En realitt, les activitts du printemps sont influenctes par les activitts de I’automne qui ont ou n’ont pas ttC effectukes durant l’annke prkedente. De nombreuses suggestions ont aussi CtC fakes pour que I’aversion pour le risque soit modhliste explicitement par des techniques diverses. Cet article analyse comment I’utilitt d’un modkle i programmation lintaire utilid pour la planification de la rkolte est affectte par (1) le fait que 14 activitts de mise en culture se rapportent entre deux annkes, mais que le modile embrasse m e annk seulement, et (2) I’incorporation explicite de I’aversion pour le risque. La methode B suivre est de comparer les rkultats du modtle A planification avec les rtsultats d’une variante d’un modtle qui n’exige pas la possibilitt de rkpttition, ainsi qu’avec les rtsultats d’une prise de decision simulCe. Trois usages sont examints: la prediction du revenu de la ferrne, du changement du revenu de la ferme, et des superficies de culture. La prise en considtration des activites de I’automne prtckdent dans le processus de planification a amtliort la prtdiction du revenu et des superficies, mais non pas la prediction d’un changement de revenu resultant d’un investissement en machines. L’incorporation explicite de I’aversion pour le risque n’a pas amkliort I’habilitt du modtle dans aucun de ses usages.

Introduction

Linear programming models for crop planning are used in both research and extension. Often the plans generated by these models are assumed to be repeatable year after year, with the spring and fall operations in one year being determined simultaneously in the model. In reality, spring operations are influenced by the fall operations that were or were not done the previous year, and fall Operations of the current year influence the spring operations of the following year. For example, on a Corn Belt farm, the extent of

Agriculture Canada and Purdue University, respectively. Indiana Agricultural Experiment Station Journal, Paper No. 7561. The helpful comments of Earl Kehrberg, Bill McBride, Peter Nuthall. George Patrick and Kelley White, are gratefully acknowledged.

Canadian Journal of Agricultural Economics 27(3), 1979

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falI wheat planting and land preparation determines the extent of spring land preparation and corn and soybean planting. An analysis of how this problem influences the usefulness of the model is available to model builders and users.

The farm planning literature has numerous suggestions that the usefulness of crop planning models would be improved if risk aversion was modeled explicitly. Several techniques for implementing explicit risk features in planning models have been developed. However, evidence of how any of these techniques affects the usefulness of operational crop planning models is stdl scarce, and additional evidence in this area is also valuable to model builders and users.

This paper has two objectives. The first objective is to analyse how the usefulness of a particular planning model is affected by the fact that cropping activities are related between years but the model covers only one year (i.e., the planning model generates a plan that is assumed to be repeatable). The second objective is to a n a l p how the usefulness is affected by the explicit incorporation of risk aversion in the model. The procedure is to compare results from the planning model with results from a model variant that does not assume repeatability. These comparisons are made under various conditions, such as risk neutrality and under two levels of risk aversion, and in Crow and 6-row machinery situations. The Model and Its Uses The particular planning model studied is the Purdue Top Farmer Cropping Budget (for details see (71). This model is also known as Model B.

Model B has 112 constraints and 178 activities. Within the model the crop year is divided into fifteen periods of unequal length. Time periods are short (1 week) during spring planting to facilitate the depiction of timeliness effects on yield, and they are longer (2-5 weeks) during the rest of the year. Main activities are land preparation, planting, cultivating, and harvesting of corn, soybeans, wheat, and double crop soybeans. In addition, there are activities for buying and selling resources. Most constraints are based on time availability. The model maximizes farm income (farm revenue less operating costs). This model has achieved wide use in the U.S. Corn Belt [7] and modified verions have found use in other areas, such as Ontario 191.

The d y s k is based on three important uses of crop planning models: decision guidance within the year, budgeting for investment decisions, and studies for the purpose of policy decisions (for example in the area of supply response). Model B has achieved its widest application in the first two areas. When the model is used for guidance within the year. interest is focussed on the income effect of actions taken during the year while attempting to follow a plan made at the beginning of the year. The plan gives acreage distribution between crops and timing of operations based completely on expectations, whereas actions taken during the year are based on both expectations and certainty information. Although using the model for decision guidance within the year is rarely encouraged, farmers and others sometimes believe that the model can be helpful in that area. When the model is used for investment budgeting, emphasis is on the ability of the model to predict correctly what the change in farm income wil l be if a proposed investment is made. When a crop planning model is used for policy guidance, its ability to predict crop acreages correctly may be of more interest than its ability to predict farm income and farm income changes.

Considering these three uses of a crop planning model, Model B is evaluated in terms of its ability to predict correctly farm income, farm income change from investment, and crop acreages.

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Sequential, Adaptive Decision Making

FARM DECISION MAKING

In order to evaluate the usefulness of Model B for within year decision guidance, observations on real farm decision making are desirable. A cheaper alternative was to model within year farm decision making, and the most practical way to develop such a model was to use the existing planning model, Model B, and develop it into a model of decision making. The reasoning underlying this development was that a farm decision maker uses a plan for guidance during the year but does not normally implement it without changes. The reasons for such changes may be that the plan is infeasible or that a more attractive alternative appears during the year. For example, bad weather in the spring may make it impossible to plant crops as planned, or the weather outcome may change price and yield expectations in such a way that the expected gross margin relations between crops are changed.

A theory of decision making under these conditions has been suggested by Hart [4] and further developed by Modigliani and Cohen [8] and by Rigby [lo]. The basic idea is that the decision maker makes an early plan, based on expectations, then makes a decision and takes action on the basis of the outcome in the first "period" in question, then makes a new plan incorporating the actions already taken and any revisions in expectations. The sequential, adaptive framework is often used in f i i growth models

For the purposes of this analysis, the Hart framework is interpreted in the following way. During the course of the year a farmer makes a sequence of decisions. His earliest decisions concern spring land preparation and planting and his last decisions concern harvesting and fall land preparation. Although the work performed until the day when a decisioq is made is known with certainty, the return outcome is unknown. Knowledge of the return outcome is gradually improved during the year, as information is obtained about weather, price, timeliness of cropping operations, and the biological growth of the crop. However, once a decision has been made and action taken, the action is usually irreversible in practice (e.g., herbicide application for corn cannot be undone). Therefore, during the course of the year decision making is more and more constrained by actions taken earlier in the year.

(e.g., 131).

A SEQUENTIAL, ADAPTIVE MODEL

A model that could simulate sequential, adaptive decision making was obtained by incorporating this framework in Model B. The modified version is called the sequential, adaptive (SA - ) model. Actual weather outcome is represented by a number of good field days in a model period. Return outcomes are represented by enterprise gross margin, i.e., total enterprise revenue less enterprise operating costs (direct costs).

A sequential, adaptive simulation of decision making is achieved by solving the SA-model the same number of times as there are periods in the model year (fifteen times). Between each solution, gross margin expectations are revised by a constant fraction of the original difference between expectation and actual outcome so that, at the end of the year, gross margin expectation coincides with outcome. Also, the actual number of good field days is substituted for the good field day expectations in the

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current period. In this way the decision making procedure during the year is broken into fifteen steps.

Future period activities of the solution constitute a plan, based on expectations. Past period activities represent the irrevocable actions taken in past periods. Current period activities of the solution represent current actions. These activity levels are held constant when solving the model for later periods.1 The procedure simulates planning and revising of plans in a situation where gross margin expectations are revised and weather outcomes become known.

BETWEEN-YEAR LINKAGES

A problem arises because decisions made in the current year are predicated upon decisions made in the previous year. This is the case for wheat harvesting in the summer, since the acreage of wheat is determined already at planting time the previous fall. Similarly, decisions about land preparation for corn and soybeans in the spring are influenced by the decisions made about fall land preparation the previous year. Therefore, the SA-model requires that the acreage of wheat planted and acreages prepared for corn and soybeans in the previous year be specified exogenously before decision making in a year is simulated. These acreage specifications are called between- year linkages.

The SA-model chooses between planting and not planting wheat and between preparing and not preparing land in the fall of the current year. The choice is made on the basis of resource requirements as well as contribution to the objective function of these operations. This, in effect, requires that wheat planting and fall land preparation are assigned objective function coefficients that can be added to the gross margins of the other activities. These coefficients should reflect the anticipated value next year of planting wheat or preparing land in the current fall. They need to be specified exogenously. The specification of anticipated values is based on the imputed values of land preparation and wheat planting in a number of runs with Model B for different numbers of good field days.

In summary, the SA-model needs an inventory of prepared land and planted wheat and it needs an anticipated valuation of these acreages in the coming year. The SA-model is, therefore, simply a version of Model B which accepts initial stocks of prepared land and planted wheat and depicts an unlimited demand for prepared acreage and planted wheat acreage at specified fixed prices. The SA-model also includes facilities for easy fixing of past actions in a sequential way. This makes it possible to use the SA-model for simulation of decision making during the year as actual weather outcomes become known and gross margin expectations approach their actual values.

Although the model has not been formally validated, it does incorporate actual outcomes in a sequential way. This supports the belief that results from the SA-model are closer to reality than are the plans from Model B. RISK AVERSION

Risk aversion can be handled 4 Model B by the proper use of safety margins and “discounts” in the input data, but the model has no explicit risk aversion feature. In this study, a simple technique based on the work of Hazell [S] is introduced in Model B

1 Due to the representation of timeliness considerations in the model either single activity levels or sums of activity levels are held constant in order to capture the irrevocability of past decisions and actions.

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and, consequently, also in the SA-model. This technique measures objective function risk as total negative deviation from a five-year moving average of historical gross margin outcomes. Three levels of risk aversion are considered: risk neutrality, low aversion, and high aversion. The risk neutral case is identical to Model B or the SA-model without the explicit risk aversion feature. The low risk aversion case corresponds to the attitude among a group of Corn Belt crop fanners in a pilot study (21. High risk aversion is expressed by a risk aversion coefficient 10 times as large.

DATA

The data used in this study are largely the base plan data in the 1975 Model B version [6]. In addition to these base data, two sets are needed on historical enterprise gross margin outcomes and number of good field days. Historical gross margin outcomes for corn, soybeans, wheat, and double crop soybeans were synthesized for a hypothetical farm in central Indiana for 24 years from observations on prices, yields, and costs [ 11. The number of good field days in each one of the fifteen model periods in each of the years 1951-1974 in west central Indiana were compiled from historical records. These records were based on reports made by observers in the field to the agricultural statistician at Purdue University.

The series of enterprise gross margin outcomes was used both for derivation of risk and as actual gross margin outcomes in simulated decision making. The good field days data were used in simulated decision making during individual years under weather conditions such as those that occured in 1951-1974.

Experiments and Results EXPERIMENTS The evaluation of the usefulness of Model B involved several experiments. These experiments required the generation of five types of farm resource allocation as output from Model B and the SA-model. Most SA-model output was generated for a sequence of 24 years (1951-1974) but for cost reasons some output was generated only for 12 years (1951-1962). The years differed in terms of number of good field days and outcomes of gross margins. Gross margins were inflated so as to be expressed in real 1975 dollar values.

In the remainder of the paper, “plan” refers to model output based entirely on expectations, and “allocation” refers to model output based partly or entirely on actual weather and gross margin outcomes. The five types of model output were: 1) Plans derived from Model B under three levels of risk aversion. These are the plans, based entirely on expectations, that would be obtained from Model B with or without the risk aversion feature. 2) Plans in the fxst period of all years derived with the SA-model under three levels of risk aversion. These plans are based on expectations just like the plans from Model B, but they also consider the fall operations of the previous year (land preparation and wheat planting). 3) Year-end allocations for all years after 15 periods of simulated sequential, adaptive decision making under three levels of risk aversion. These allocations from the SA-model are a substitute for observations on actual farmer decision making under controlled conditions, which would have been the ideal standard against which to compare the plans from Model B.

4) Year-end allocations for all years derived from the SA-model, given perfect information on the number of good field days and gross margins. These allocations are, of course, identical to the plans in the f i s t period, given perfect information, since then there is no difference between outcome and expectations. 5 ) Year-end allocations for all years from the SA-model under three levels of risk aversion with total acreage of each crop restricted to that of the Model B plan. These allocations indicate the farm income that would have been obtained if the original acreage plan had been implemented and sequential, adaptive decisions that had not been made during the year.

Several runs were also made with two different machinery complements, so that the investment budgeting usefulness of the models could be examined. The machinery complements were basically Crow and 6-row equipment and capacities and f i e d costs were changed accordingly.

These experimental results are analyzed with respect to the following hypotheses. A plan from Model B is not as good a predictor of acreage, income, and income change as is the plan from a model that incorporates the operations performed the previous fall. A plan derived under risk neutrality is not as good a predictor of acreage, income, and income change as is a plan derived under risk aversion. Correct information on number of good field days and gross margins has a positive value.

RESULTS

The results of these experiments in terms of acreage and farm income (total gross margin less futed costs) are given in Tables 1 to 5 . The figures are %year or 12-year means. Table 1 gives plans from Model B under three levels of risk aversion. Table 2 represents the set of plans obtained in the f i s t period with the SA-model, based on expectations for the current year, and incorporating knowledge of the operations performed the previous fall. Table 3 summarizes the set of year-end allocations obtained through simulated sequential, adaptive decision making. Table 4 illustrates the set of year-end allocations from the SA-model which would have been obtained under perfect information on gross margins and number of good field days. These results are presented only for risk neutrality, since a combination of perfect information and risk averse decision making is difficult to justify. Table 5 summarizes the allocations obtained with the SA-model with perfect and imperfect information, under the condition that acreages are restricted to their levels in the plan derived with Model B.

Interestingly. in Table 2, farm income increases as risk aversion increases. This is due to the way in which farm'income is calculated from the objective function value of a model solution. Farm income differs from the objective function value by the risk discount (risk aversion coefficient times total risk in the solution) and by the anticipated total values of fall operations (wheat planting and fall land preparation). Farm income is obtained from the objective function value by adding the risk discount and subtracting the anticipated values of fall operations. The effect is that, under certain conditions, the calculated farm income may increase when the objective function value decreases.

For example, for 6-row machinery in Table 2, farm income shows an increase of about $9,000 as risk aversion increases from neutral to high. This is the net effect of a decrease in objective function value of $6,000, an increase in the risk discount from $0 to $24,000, and an increase in anticipated value of wheat planting and fall land preparation of $9,000.

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TABLE 1

Plans from Model B

Machinery Risk Double Crop Fann S i z e A t t i t u d e Corn Soybeans Wheat Soybeans I n come

Crops

&row N e u t r a l 366 202 33 33 181,173 LOW 314 286 0 0 181 , 155

High 241 359 0 0 179,389

&row N e u t r a l 365 202 33 33 180,533

Low 316 284 0 0 180,519

U g h 229 371 0 0 178 , 710

TABLE 2

Summary of First-Period Plans from the SA-model.a

Machinery Risk Double Crop Farm S i z e A t t i t u d e Corn Soybeans Wheat Soybeans Income

Crops

$ -------acres-----------

6-row Neutra l 307 (2)

(3)

(2)

(1)

(2)

. (2)

Low 305

High 265

N e u t r a l 313

Low 313

U g h 261

169 , 901 (633)

170,974 (1,314)

179,088 (2,005)

169,726 (426)

170,447 (1,063)

178,125 (2,662)

a Figures for Crow machinery are 24-year means and for 4-row, 12-year means. Figures in parentheses are standard deviations.

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TABLE 3 Summary of Allocations from Simulated Sequential, Adaptive Decision Making . (SA-Model).”

Machinery Risk Double Crop Farm S i z e A t t i t u d e Corn Soybean Wheat Soybeans Income

Crop

-----acres------------- $

118 160,613 6-row N e u t r a l 308 173 118 (7) (8) (7) (7) (45,448)

Low 309 185 106 106 160,967 (8) (11) (12) (12) (44,515)

High 275 321 4 4 158,107 (19) (25) (20) ( 2 0 ) (39,339)

&row N e u t r a l 311 174 114 114 157,534 (6) (8) ( 4 ) (4) (35,111)

157,611 Low 312 184 104 104 (7) (10) (9) (9) (34,668)

8 8 150,507 High 274 318 (12) ( 2 6 ) (28) (28) (28,291)

a Figures for 6-row machinery are 24-year means and for Crow, 12-year means. Figures in parentheses are standard deviations.

TABLE 4

Summary of Perfect Information Allocations from the SA-Model.a

Crop Machinery Risk Double Crop Farm S i z e A t t i t u d e Corn Soybean Wheat Soybeans Income

&row N e u t r a l 340 1 4 1 118 94 170,590 (96) (96) (7) (47) (44,710)

&row N e u t r a l 356 130 114 95 169,666 (85) (87) (4) (43) (36,368)

a Figures for 6-row machinery are 24-year means and for d-row, 12-year means. Figures in parentheses are standard deviations.

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TABLE 5

Summary of Allocations from the SA-model, Restricted to Model B Plan Acreages.a

Information Risk Double Crop Farm Mode A t t i t u d e Corn Soybeans Wheat_ Soybeans Income

Crops

---------------ac=e3------------- $

P e r f e c t Neu t ra l 366 201 33 28 158,099 (29,197)

Adaptive Neut ra l 365 202 33 33 154,543 Decision (30,699) Making

Low 314 286 0 0 154,458 (26,118)

Bigh 241 359 0 0 146,944 (26,594)

a All allocations are 12-year means for 6-row machinery. Figures in parentheses are standard deviations.

Discussion

ACREAGE PREDICTION

Crop acreages are compared between Model B plans and SA-model allocations after simulated decision making. Crop acreages are also compared between SA-model plans after the f i s t period, where previous fall operations are considered, and SA-model allocations after simulated decision making.

Crop acreage difference is measured as absolute acreage difference summed over all crops. For example, in the case of risk neutrality and Grow machinery, the difference between the Model B plan (Table 1) and the allocation after simulated decision making (Table 3) is 1366-3081 + 1202-1731 + 133-1181 + 133-1181 acres = 257 acres. This measure aggregates the magnitudes of individual crop acreages in the tables. Since double crop soybeans are planted after wheat, it may appear that this acreage is double counted. However, the double crop soybean acreage does not have to equal the wheat acreage and it is therefore preferred to count the acreages of both crops.

The difference, given Grow machinery, between Model B plan and allocation after simulated decision making were 257 acres, 318 acres, and 80 acres, respectively, for risk neutrality and low and high risk aversion. In the case of Qrow machinery, the corresponding differences were 244 acres, 312 acres, and 114 acres. The differences between plans in the f i s t period with the SA-model, which considered previous fall operations, and the year-end allocations, derived through simulated decision making with the Same model, were not nearly as large. This is evident from a comparison of Table 2 with Table 3. The aggregate absolute acreage difference ranges only between 2 and 25 acres.

The crucial factor behind this difference was fall land preparation for spring planting of corn and soybeans. The conclusion is that a plan from Model B is not as good a

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predictor of acreage decisions as would be a model which incorporates the actions taken in the previous year. This further suggests that Model B is of questionable use for decision guidance during the year.

PREDICTION OF FARM INCOME

The farm incomes in the Model B plan (Table 1) and in the first period plan from the SA-model (Table 2) are compared with the farm income in the year-end allocation from simulated decision making with the SA-model (Table 3). In all machinery and risk attitude situations, planned farm income is higher than outcome. Although planned income is actually within half a standard deviation from the outcome, the consistent over-prediction suggests that expectations of activity gross margins or number of good field days are overly optimistic.

An indication of the magnitude of the error in income prediction due to optimistic gross margin expectations is obtained by comparing the income predicted by Model B (Table 1) with farm income after simulated decision making, restricted to the same crop acreages as with Model B (Table 5). Planned income is about one standard deviation above income, which confirms that expectations are overly optimistic. This difference may appear small in statistical significance terms, but the absolute amount is large enough to be important.

Comparing planned incomes in Table 1 and Table 2 with outcomes in Table 3 again indicates that a planning model that is capable of incorporating knowledge of the actions the previous fall is a better predictor of income. However, both types of planning models are unsatisfactory income predictors because of the considerable over- prediction of income in most years. This is obviously due to problems in formulating correct expectations for enterprise gross margins and number of good field days.

PREDICTION OF INCOME CHANGE

One of the important farmer uses of the planning model is to budget a change in income from making an investment. For example, a farmer would be interested in finding the increase in income if he changed to larger machinery. This focuses interest upon the error in predicting income change.

The error in predicting income increase from changing from 4-row machinery to 6-row machinery can be obtained from Tables 1,2, and 3. In the case of risk neutrality, Model B (Table 1) predicts an income of $180,533 for Crow machinery and $181,173 for Grow machinery, which amounts to an increase of $640. The income increase indicated by simulated decision making is $160,613-$157,534 = $3,079 (Table 3). Thus, Model B underestimates the income gain from changing to 6-row machinery by $2,439. In the case of low risk aversion, the amount of underestimation is $2,720, and in the case of high risk aversion it is $6,921. Hence, the prediction error shows a tendency to increase as risk aversion increases in Model B. The large size of the prediction error under risk aversion is of course due to the low Crow machinery income of $150,507, which in turn is due to a larger acreage of soybeans. Soybeans were modelled with lower enterprise gross margin than corn, and farmers often plant soybeans later in the season than corn as a result of not having enough capacity to plant corn.

The f i s t period plan from the SA-model, which considers previous fall operations, also under-estimates tKe gain from changing to larger machinery (Table 2 and Table 3). For example, in the risk neutral case the predicted income increase is $175 (Table 2).

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The tendency is again toward a larger error for larger risk aversion. The magnitude of the prediction errors are about the same from the two planning models (Model B and the fust period of the SA-model), and no f m conclusion can be drawn about the superiority of either.

A farmer might exhibit lower risk aversion in actions during the year than in budgeting for investment. The implications of such behaviour on the suitability of the planning models studied is brought out by computing prediction errors across risk aversion levels in Tables 1, 2, and 3. For example, the $640 increase in Table 1 is compared with an increase of $160,%7-$157,611 = $3,356 in Table 3. Such comparisons show that the prediction error is somewhat larger when fall prepared acreages are considered, but the difference is quite small. Thus, a superiority of the planning model that considers fall prepared land cannot be established in income change prediction.

INFLUENCE OF RISK AVERSION

Increased risk aversion changes the crop mix substantially throughout these experiments. Generally, corn and wheat acreages decrease and soybean acreage increases. However, the shifts in crop mix do not greatly influence farm income. Planned and simulated incomes are remarkably stable. It is noteworthy that the ability of either planning model to predict an income change due to machinery size change is smaller in the highly risk averse case than in the risk neutral case.

A comparison of Model B plans with allocations from simulated decision making (Table 1 and Table 3) shows that the error in income prediction is quite stable as risk attitude goes from neutral to risk averse. A similar comparison for the plans from the model that considers between-year linkages shows that income prediction error increases with risk aversion (Table 2 and Table 3). For example, in the w e of 6-row machinery and risk neutrality, planned income is $169,901 and the outcome is $160,613, i.e., an error of about $9,300. For high risk aversion, the error is about $21,000. The 4row situation shows a similar pattern. The error in acreage prediction is not reduced, either, as risk aversion increases. Variability of planned incomes, measured as standard deviation, increases with risk aversion (Table 2), but variability of income outcome decreases with increasing risk aversion in simulated decision making (Table 3).

VALUE OF PERFECT INFORMATION

A net revenue comparison between Table 3 and Table 4 indicates that perfect information is worth $10,000 - $12,000 to a risk neutral decision maker in the situation studied. This amounts to about a 7 percent increase in income if a planning environment without the risk elements modelled here could be achieved. The value of perfect information is higher in the case of small (4-row) machinery. This seems to corroborate the often heard suggestion that an oversized machinery complement is a hedge against risk. LARGE VERSUS SMALL MACHINERY

The additional annual fixed cost for the &row machinery complement, compared to a 4-row complement. is about $600 in the situation studied. The income differences between &row and Crow machinery are $3,100 and higher (Table 3). This indicates that the gain from changing to larger machinery is at least $2,500 per year in the simulated situation. The gain is due to improved timeliness of field operations.

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Conclusion

This study has examined the usefulness of a particular crop planning model of a common type employed in the United States and Canada. Three important uses were investigated: prediction of farm income, farm income change, and acreages. A model capable of generating a plan in the first period of a year, incorporating the operations performed the previous fall, was developed. Such a plan did not require the repeatability assumption. The plans from Model B and the model incorporating previous fall operations were compared with acreage allocations in simulated decision making in 12 or 24 years. The incorporation of previous fall operations improved the prediction of income and acreages, but the prediction of income change from investment was not improved. The explicit introduction of risk aversion did not improve the abilities of either model to accomplish any of the purposes considered.

Great caution is necessary when using crop planning models of the Model B type so that the resulting plans are not used for decision guidance in crop planning. The emphasis is already on their use for income change budgeting, but the importance of not using the models for anything else cannot be overstated. If there is a need for decision guidance and acreage prediction, it is necessary to pay heed to the importance of between-year linkages. A model must then be created which uses information on land commitments made prior to the time of planning and which also carries out forward planning based on anticipations about pay-offs in the following year from operations performed in the current year.

REFERENCES

1 Brink, Lars. “Plans, Decisions, and Results: An Evaluation of a Procedure for Farm Planning Under Risk”, Ph.D. thesis, Department of Agricultural Economics, Purdue University, December, 1976.

2 Brink, Lars and Bruce McCarl. “The Tradeoff Between Expected Return and Risk Among Corn Belt Crop Farmers”. American Journal of Agricultural Economics, Vol. 60, No. 2, May, 1978, pp. 259-263.

3 Chien, Ying, I., and Garnett L. Bradford. “A Sequential Model of the Farm Firm Growth Process”. American Journal of Agricultural Economics. Vol. 58, No. 3, August, 1976, pp.

4 Hart, Albert Gailord. Anticipations, Uncertainty. and Dynamic Planning. New York: Reprints of Economic Classis, August M. Kelley, Publisher, 1965.

5 Hazel], P.B.R. “A Linear Alternative to Quadratic and Semivariance Programming for Farm Planning Under Uncertainty”. American Journal of Agricultural Economics, Vol. 53, No. 1, February, 1971, pp. 53-62.

6 McCarl, Bruce and Jeurene Falck. “Documentation Model B-9”. Department of Agricultural Economics, Purdue University, Station Bulletin No. 98. September, 1975.

7 McCarl, B.A., W.V. Candler, D.H. Dostcr, and P.R. Robbins. “Experiences with Farmer Oriented Linear Programming for Crop Planning’’. Canadian Journal of Agricultural Economics, Vol. 25, No. 1, February, 1977, pp. 17-30.

456-465.

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8 Modigliani, Franco and K h a n I. Cohen. The Role of Anticipations and Plans in Economic Behaviour and Their Use in Economic Analysis and Forecasting. Urbana. Illinois: University of Illinois, Bureau of Economic and Business Research, Studies in Business Expectations and Planning, No. 4, 1961.

9 Pfeiffer, W.C. The Ontario Automatic Cropping Budget System for Cash Grain Farms. AEEE/76/3, School of Agricultural Economics and Extension Education, University of Guelph, Guelph, Ontario, 1976.

10 Rigby, Fred D. “Heuristic Analysis of Decision Situations”, in Shelly, Maynard, W., 11, and Bryan, Glenn L. (eds.) Human Judgements and Optimality. New York: John Wiley & Sons, Inc., 1964.