Optimal pest control in agriculture

Based on economic methodology we model an ecosystem with two species in predator-prey relationship: mice feed on grain and grain feeds on a resource. With optimizing behavior of individual organismus a short-run ecosystem equilibrium is defined and characterized that depends on the farmer's use of fertilizer and on the mice population which, in turn, is affected by pesticides. Linking a sequence of short-run ecosystem equilibria yields the growth function of the mice population which is thus derived rather than assumed. In each period the farmer harvests all grain in excess of some given amount of seed. If she maximizes her present-value profits, optimal farming is shown to depend on the prices of pesticide or to apply a chattering control. Pest eradication is never optimal. On the other hand, if the farmer takes into account steady state mice populations only, it may be optimal to eradicate mice or to use no or a moderate amount of pesticide depending on prices as well as on the shape of the grain production function which is determined by micro parameters of grain reproduction.