Crop Insurance in Incomplete Markets

Abstract

When there are multiple risks threatening the loss of an asset, insurance schemes contingent on one risk alone are incomplete. Such is the case with crop insurance schemes when price variability is uninsured. This paper considers the effect of price risk on crop insurance decisions when price risk is due to supply-and-demand shocks. If demand shocks satisfy the principle of increasing uncertainty, increasing demand uncertainty reduces optimal crop insurance whenever risk aversion is constant or decreasing. In fact, the insurance is so limited for decreasing risk-averse individuals that they strictly prefer those states of the world in which no indemnity is forthcoming to those in which they receive indemnities. Special cases arise when either output risk or demand uncertainty is the sole cause of price risk. In the first case, the optimal insurance is complete even though price variability affects the demand for crop insurance through the correlation between price and output. In the second case, the principle of increasing uncertainty is trivially satisfied and price risk affects optimal insurance levels even though it is independent of output risk.