For simplicity, we will assume that the GMV eliminates pest pressure altogether, so with these technologies, ym = ym^g- yf • The damage is assumed to be a random variable D = aNh(x0)where aN is a random variable with mean ¡xN and variance aN2 multiplied by the damage reduction as a function of pesticide use presented by h(x0). The farmer determines the pesticide use before the true state of nature is revealed. We also assume that the farmer is risk averse, and his decisions are approximated well by following maximization of a linear combination of the mean and variance of profit.1
The decision problem with the traditional technology becomes
where 7teqa is certainty equivalence of the expected utility of the farmer and (p is a risk-aversion coefficient. The first order of (9) with respect to pesticide use is s
This condition states that optimal pesticide use occurs where the marginal benefits of pesticides in increasing mean profits and reducing variance are equal to its price. Compared to the condition under certainty (3), here there are extra marginal benefits of pesticides—the marginal benefits through risk cost reduction. The extra benefit increases pesticide use relative to the case with full certainty.
1 The mean variance rule corresponds to situations where it is normally distributed, and the farmer has an expected utility maximizer with a negative utility function.
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