Myopic separability

• Investigate certainty multiperiod, multigood (static) demand problem.
• Consider when demand is myopic.
• Derive restrictions on preferences for demands to be myopic.
• Provide equilibrium implications of myopic versus additive separability.

In the classic certainty multiperiod, multigood demand problem, suppose preferences for current and past period consumption are separable from consumption in future periods. Then optimal demands can be determined from the standard two stage budgeting process, where optimal current period demands depend only on current and past prices and current period expenditure. Unfortunately this simplification does not significantly reduce the informational requirements for the decision maker since in general the expenditure is a function of future prices. Recent behavioral evidence strongly suggests that frequently individuals significantly simplify intertemporal choice problems. We derive necessary and sufficient conditions such that the current period's expenditure and hence optimal current demands are independent of future prices. Since this preference property is a special case of separability, it is referred to as myopic separability. One well known special case of myopic separability is log additive (or equivalently Cobb–Douglas) utility. However, this form of utility is overly restrictive, especially given the general aversion of Fisher, 1930 and Hicks, 1965 and Lucas (1978) to requiring preferences to be additively separable. Myopic separability requires neither additive separability nor logarithmic period utility. As an application, we derive simple restrictions on equilibrium interest rates which are necessary and sufficient for utility to take the myopic separable form. These conditions are arguably less restrictive than those implied by additively separable preferences.