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income with a high probability, X m units of land are planted in a low risk crop or crop combination in the first semester (or in the crop season if there is only one). The remainder of the available land (X-XM ) can then be put into a higher risk, but higher mean earning, crop in order to maximize profit (or other goals can be pursued, such as maximizing return to capital). Assuming constant net returns per unit of land, profit is a linear function of land. In Figure 1, the two-stage combination of stabilizing an income floor and maximizing profit, for example on X land units, is~given by QAB with profits given by 11r. If one were to maximize profits on the entire X units of land, the expected value of profits would be ]'mx. The difference in expected earnings between the two activities is equal to H~mX rs which is the expected annual or semestral cost of the security given by the lower risk option.
Minimizing expected losses
A second possible income goal of farmers, and also a conservative response to the risks in agriculture, is to minimize the expected value of loss in bad years. Losses occur when the farmer fails to earn the opportunity cost of his owned capital, and the monetary costs of the loss consist of three components. These three components are the alternative earnings foregone by not investing in another activity, the amount of money actually lost, i.e., negative profits, and the penalty interest incurred on the borrowed funds in the investment.
Foregone alternative earnings.--The activity in which a farmer
sustains a loss is usually only one of many available investment opportunities. For simplicity the alternative investment of importance will b e that which yields the highest risk-free return. Admittedly no