On risk aversion with many commodities and non-linear budget constraints

In this paper the theory of behaviour under income uncertainty with many co mmodities is extended to allow for non-linear budget constraints, where ran dom variations in income induce simultaneous randomness in shadow prices. I t is shown that (i) any change in the marginal (indirect) utility of income can be decomposed into a linear and a non-linear component; (ii) risk atti tudes are biased in a predictable fashion, depending on the properties of t he constraint function and the indifference map; and (iii) standard measure s of income risk aversion vary endogenously with income, even when the unde rlying utility functions indicate otherwise with linear budget constraints. JEL Classification: D81.