1. Explain the analogy between the intertemporal optimumof the consumer (choice

Question

1. Explain the analogy between the intertemporal optimumof the consumer (choice between current consumption C and future consumption C) and the optimum of the consumer at a moment of time (choice between consumption of commodity Xand commodity Y) 2. Which is correct, and explain: The annual rate of interest is the ratio h/ P, the price of a current consumption a· claim divided by the price of a consumption claim dated one year in the future. 492 15. THE ECONOMICS OF TIME b. The annual rate of interest isthe premium on the value of current relativeto l-year future claims, as given by the expression (Po/ P)1

Explanation / Answer

The intertemporal choice consists of choosing among the bundles such that the consumer maximizes his consumption of today and tomorrow. In the optimization exercise, we have two consumption good with their prices and income. The consumer chooses his bundle such that the Marginal utility from spending the last dollar gives the same utility irrespective of on the good it is spent on. i.e. MUx/Px = MUy/Py where x and y are the two goods and Px and Py are their respective prices. We can consider the consumption between two periods as a basket of a set of goods such that the Prices are the wages in the current period(w0) and the discounted wage in the future (w0/(1+r). The optimization occurs at the point where the last dollar spent provides same marginal utility in the current period and in the future.

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