On the Concavity of the Consumption Function

Zeldes (1989) Carroll (1992; 1993), and others have shown that optimal consumption behavior for consumers facing income uncertainty can be remarkably different from the certainty-equivalent case. Carroll (1992; 1993) observes that many of the differences can be attributed to the concavity of the consumption function under uncertainty, but he does not describe the conditions under which the consumption function will be concave. We show that if labor income is stochastic, the consumption function will be concave for many commonly used utility functions, and if both labor income and capital income are stochastic, the consumption function is concave for an even broader group of utility functions.