The Marginal Utility of Income Does not Increase: Borrowing, Lending, and Friedman-Savage Gambles

There has been a great deal of discussion about whether the marginal utility of income rises with income. Most notably, Milton Friedman and Leonard J. Savage argued in their classic paper that the willingness to gamble implies that the marginal utility of income is rising over a range. The discussions of rising marginal utility and of Friedman-Savage gambles have proceeded independently of the literature on time preference, although the issues are in fact related logically. Drawing on this logical relationship we shall show 1) that at least when intertemporal utility is separable, the stable levels of consumption that are usually observed imply that the marginal utility of income decreases as income rises. 2) Even if the marginal utility of income does increase, Friedman-Savage gambles normally will not maximize utility; saving and dissaving can attain the levels of consumption which generate the most utility per dollar of income at a lower cost than gambles unless imperfections in the capital market are severe. 3) Even when the utility function is not temporally separable, repeated gambling cannot be a rational way of dealing with a rising marginal utility of income. We therefore conclude that observed gambling is seldom if ever explained by the logic set out in Friedman and Savage's seminal paper. In view particularly of the stability of consumption levels and the lack of FriedmanSavage gambles, we conclude that marginal utility of income does not rise with income. I. A Conceptual Framework