## Permanent income hypothesis: a theoretical formulationThis paper defends the view that in dealing with a consumer's reponse to short-term changes, it is reasonable to assume that the marginal utility of money is constant. A theoretical defense of this view is made in terms of the consumer's intertemporal maximization problem. It is assumed that the consumer may hold money, but may not borrow. The consumer's utility function is assumed to be additively separable with respect to time. Prices, the consumer's income, and his utility function for each period are assumed to fluctuate according to a stationary stochastic process. It is proved that if the time horizon of the consumer's problem is sufficiently distant, if his discount rate for future utility is sufficiently small, and if he has a sufficient quantity of money, then the marginal utility of money is nearly independent of current prices and income and is nearly constant over time. The proof of these facts is based on economic common sense and the strong law of large numbers for stationary processes. (Author). |

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arguments assumed completes the proof conditional expectation consumer consumer's willingness continuous function converges almost surely converges to infinity defined definition discount rate Doob dynamic programming equality ergodic theorem feasible policy fluctuations form a stationary Friedman Holdings of liquid implies induction initial stock integer large numbers law of large Lemma Lemma Let lim inf lim sup limit policy liquid assets main theorem marginal utility measurable function measurable with respect money in period monotone convergence theorem n n n N-oo N-period policy N—oo n=0 almost surely non-decreasing function non-negative O.oo oo almost surely paper period zero permanent income hypothesis probability zero problem with discount quantity of money random variables rational numbers satisfies the following satisfy conditions Schechtman stationary and metrically stationary process stock of money strictly concave strictly decreasing strong law sufficient to prove Suppose units of utility utility function utility of expenditure utility of money vector Yaari