Diminishing Marginal Utility of Wealth and Calibration of Risk in Agriculture

Abstract

Expected utility theory (EUT) has dominated the agricultural economics literature on behavior under risk, particularly since the late 1970s. In EUT, risk preferences are completely defined by the curvature of the utility function. An expected utility maximizer with a concave utility curve would avoid choices that represent a greater wealth risk. Estimates of risk aversion coefficients, based on assumed utility functional forms, have been valued in predicting producers' responses to proposed policy (see Saha, Shumway, and Talpaz for a review). Yet, these estimates are biased if there are omitted variables (such as knowledge, understanding, and managerial expertise) that are related to the probability distribution of profit. If the production function is jointly estimated with the utility function, then the riskincreasing or risk-reducing properties of production inputs may also wrongly be ascribed to the concavity of the utility function. Since Allais, substantial evidence has been accumulated to suggest systematic flaws in EUT, mostly in experimental settings with small stakes. Applied economists have regarded these violations as exceptions due to the special circumstances surrounding their observation. Recently, Rabin showed that attributing all risk behavior in small gambles solely to diminishing marginal utility of wealth leads to improbable levels of risk aversion. His calibration theorem, based on dichotomous choices, suggests that a person who turns down a lottery with a 0.5 probability of winning $125 and 0.5 probability of losing $100, will always turn down any bet with a 0.5 chance of losing $600, no matter how large of a gain may be had with the remaining 0.5 probability. We generalize Rabin's work to continuous payoff distributions and continuous choice problems to show that his criticism extends to realistic risky situations. The concavity problem is not limited to small money risks. Rather, when risky choices have similar average payouts, utility functions must display ridiculous levels of concavity to predict individual choices. Below, we present our general calibration problem and apply the results to an empirical risk study in agricultural economics to illustrate the unintended consequences of using EUT to explain risk response.