On Risk Aversion with Many Commodities and Nonlinear Budget Constraints

In this paper, the theory of behavior under income uncertainty with many commodities is extended to allow for nonlinear budget constraints, where random variations in income induce simultaneous randomness in shadow prices. It is shown that (1) any change in the marginal (indirect) utility of income can be decomposed into a linear and a nonlinear component; (2) risk attitudes are biased in a predictable fashion, depending on the properties of the constraint function and the indifference map; and (3) standard measures of income risk aversion vary endogenously with income, even when the underlying utility functions indicate otherwise with linear budget constraints.