The theoretical framework adapted for this study is the mean-variance (E-V) efficiency criteria. The E-V approach assumes the decision-maker is risk averse and has a quadratic utility function (Boisvert and McCarl, 1990). However, several linear approximations to the E-V model have been evolved. In this analysis, linear approximation the MOTAD was employed to develop a Compromise MOTAD. This approach generally assumes that the decision-maker maximises expected utility (Anderson, et al 1977). Thus, his preferences among alternative farm plans are expressed in terms of expected income and associated variance. It is assumed that the outcome distributions are distributed normally.
MOTAD and...
Traditional risk analysis models are in effect multi-objective programming (MOP) models involving two objectives. The first objective is to maximise returns from individual enterprises. The second objective of risk programming models is to minimise the variability of income expressed as variance (Freund, 1956) or mean absolute deviation (Hazel, 1971). Since an optimal solution for two or more simultaneous objectives cannot be traced, MOP models identify the set of efficient solutions.
Generally, three different methods are used to generate efficient sets in MOP models. They include: (1) the constraint method, in which one objective is optimised while other objectives are specified...
The MOTAD and Compromise MOTAD models used for analysing risk efficient resource allocation, require enterprise budgets with additional information on the time series data in returns and cost of production for each enterprise in the model to develop a distribution of gross margins. The IFFS model is used for generating enterprise budgets. The deviations are computed by subtracting expected gross margin from the gross margin for each enterprise for each year in the series. This deviation matrix is the heart of MOTAD and Compromise MOTAD models and is used to compute risk.
Data on enterprise budgets are required to specify...
One representative farm is growing almost all the traditional and non-traditional crops that are being grown in the study area. The traditional crop rotations include wheat, rice, sugarcane, sorghum and berseem. The non-traditional crops include peas, brinjal (eggplant), gourds and carrots. The non-traditional crops are labour-intensive and are, generally, grown only on the farms that have enough family labour or on farms where sharecropping arrangements are made. The weather and rotation system permits production of two crops from the same land every year.
Livestock enterprises are an integrated part of the crop rotations in the study area. Generally, livestock is...
The farm has an area of 20.5 acres and the land is assumed to be homogeneous in fertility. Average crop yields are used for the computation of gross margins. Availability of surface irrigation water is a constraint on the farms where supplementary tube-well water is not available, but as the farm owns a tube-well, irrigation water is not specified as a binding constraint. The binding constraints include institutional credit and hired labour, the latter being critical during the peak periods, such as planting and harvesting. Labour inputs are specified on monthly basis. The availability of family labour, hired labour and...
Farmers, it is frequently argued, tend to maximise profits from their farming business. To look at the profit maximising resource allocation of the farm, a basic linear programming (LP) model was developed. The results of the LP model are presented in Table 1. Risk theory indicates that risk-neutral farmers will seek the LP profit-maximising plan. The expected income (Rs. 96,736) associated with this plan reflects the maximum attainable income given the existing resources of the farm. The profit-maximising plan is a high-risk plan as also ind1icated by the associated mean absolute deviation (MAD) of Rs. 32,946.
The profit-maximising farm plan...
In agricultural planning problems the farmers face multiple objectives, often conflicting in nature. In situations where multiple objectives are involved, the farmer is interested not in optimising a single objective but finding a compromise among several objectives. In this analysis two conflicting objectives, profit maximisation and risk minimisation, are involved. A Compromise MOTAD model was developed to identify the compromise set of risk efficient plans for these two conflicting objectives.
The MOTAD model is employed to generate risk efficient farm plans. Expected income is parameterised in arbitrary increments of Rs 5,000 to trace the efficiency frontier (Figure 16). Each point...
The information generated can also be utilised to estimate the risk aversion behaviour of the farmers.
It is intuitively clear that minimising the objective function of Compromise MOTAD is the same as maximising the following function: \[\text{(13)}\quad \text{Max}\,\text{Z(x)-}\frac{\text{(Max}\ \text{EGM-Min}\ \text{EGM)}}{\text{(Max}\ \text{MAD-Min}\ \text{MAD)}}\text{}\frac{{{\text{W}}_{\text{1}}}}{{{\text{W}}_{\text{2}}}}\text{}\frac{\text{1}}{\text{n}}{}_{\text{i=1}}^{\text{n}}\text{(}\overline{\text{y}}\text{+}\overset{\text{+}}{\mathop{\text{y}}}\,\text{)}\] or \[(14)\quad \text{Max}\,\text{Z(x)- }\!\!\gamma\!\!\text{ }\frac{{{\text{W}}_{\text{1}}}}{{{\text{W}}_{\text{2}}}}\text{}\frac{\text{1}}{\text{n}}{}_{\text{i=1}}^{\text{n}}\text{(}\overline{\text{y}}\text{+}\overset{\text{+}}{\mathop{\text{y}}}\,\text{)}\]
where \[\text{ }\!\!\gamma\!\!\text{ }\text{ }\!\!~\!\!\text{ =}\frac{\text{(Max}\,\text{EGM-Min}\,\text{EGM)}}{\text{(Max}\,\text{MAD-Min}\,\text{MAD)}}\] and EGM is the expected gross margin. The expression (14) maximises the utility function of the farmer. It can be noticed that for any conceivable form of the utility function, the point of maximum utility will lie in the compromise set.
The term \[\text{ }\!\!\gamma\!\!\text{ }\bullet \frac{{{\text{W}}_{\text{1}}}}{{{\text{W}}_{\text{2}}}}\] can be viewed as a measure of risk aversion because it is a multiplicative factor...
There are several mathematical programming techniques available for modeling of specific agricultural systems problems. Probably, no single model is the best at farm level, but the use of MOTAD with compromise programming seems to offer a more powerful analytical instrument for agricultural systems modeling. In addition to the information that MOTAD offers (risk-efficient set of farm plans and trade-off among objectives), Compromise MOTAD furnishes the farmer with very useful information on the compromise sets of farm plans. The compromise set is a subset of the risk efficient set of farm plans identified in MOTAD. This implies that application of Compromise...