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

E[U(π )] = u(∏) + (i∕2)^h∫ εφ(α)dαU "(π) + E[r3ε],
El

Where φ is the density function of a the random error term. In order to determine the “price of
risk”, Stiglitz and Newbery (1984) compare the mean level of income to its certainty equivalent,
or the certain level of income that generates a utility level equal to the expected utility of a
random income:^E[U(n)] = ^U(n) . Using this result, the price of risk is then the difference
between the mean and certainty equivalent levels of income: p = ^{π - π}∙ Expanding the utility of
the certainty equivalent income gives an expression in terms of the mean income and the price of

U(π) = U(π - ρ) = U(π) - ρU'(π) + r2(ρ),

risk:

where again the higher order remainder terms go to zero with the price of risk. Setting (5) equal

' var( ε)U "( ∏) )
< U '(∏) ;

to (4) and solving for the price of risk gives:

Several conclusions follow from this result. Most important, under the assumption of
decreasing absolute risk aversion (DARA), an increase in the variance of output, and, hence
income, causes the price of risk to rise. Therefore, production inputs that cause the variance of
output to rise are likely to cause the willingness to pay for insurance to rise, while risk-reducing
inputs reduce the willingness to pay for insurance. Ramaswami (1993) provides a similar result in

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