The Demand for Specialty-Crop Insurance: Adverse Selection and Moral Hazard

In their model, QKS interpret the unobservable effort variable, θ, as a indicator of moral hazard,
whereas including a random "managerial skill" component to their multiplicative error term
represents the effect of adverse selection on output. Although QKS define x as consisting of only
risk-increasing inputs, a more general definition, such as in the production function of Just and
Pope, allows x to contain both risk-increasing and risk-decreasing inputs.

π = pf(x,z,θ) + ε - wx - rz = π + ε;

With the technology shown in (1), producer income becomes:

Where w is the vector of variable input prices, and r is the vector of rental prices on the quasi-
fixed inputs. When deciding whether or not to insure their crops in a risky environment, however,
risk averse producers consider the expected utility of profit rather than simply the amount of
profit.

To determine the amount producers are willing to pay for insurance, begin by expanding

-     - ε -

U(π) = U(π) + εU'(π) + —U"(π) + r3 ε

the general expression for the utility of income about the mean of income:

Where the higher order terms go to zero with ε. Given the expression for income in (3), the
expected utility of profit is written as:

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