Intertemporal Substitution and Gambling for Long-Lived Agents

We examine the ability of expected utility function ofthe Friedman-Savage type to account for gambling when consumers also have opportunities for intertemporal substitutions. When the time horizon is infinite, we demonstrate that even in intra-period utility functions have the Friedman-savage shape, borrowing and lending without gambling is weakly preferable to gambling provided the rate of interest and time preference are equal. This is true even if any actuarially fair gamble is available; if all gambles are unfair, the preference is strict. When the rates of interest and time preference differ and borrowing, lending and gambling are permitted, a demand for gambles arise. However, it is never optimal to gamble in more than one period. This is apparently at odds with observed behaviour of gamblers and cast considerable doubts on the explanatory power of the Friedman-Savage approach.