Consider a simple economy with two consumers, a single consumption good x and two time periods. Consumption of the good in period i is denoted b xt for t = 1, 2. Intertemporal utility functions for the two consumers are:

 t = 1,2,....

Endowments are e1 = (10, 0) and e2 = (20, 5). The good is perfectly storable, so what is not consumed in the first period can be saved and consumed in the second period.

(a) Suppose the two consumers cannot trade with one another. How much does each consumer in each period? How well off is each consumer?

(b) Now suppose that there are competitive ’spot’ and’futures’ market for this good. Let p1 be the (spot) price per unit in period 1, and let p2 be the (futures) price prevailing in period 1 for delivery of 1 unit of the good in period 2. What will be the equilibrium relative price, p2/p1?
 

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u²(x₁, x2) = ln(x₁) + In(x2)- u²(x₁, x2) = ln(x₁) + In(x2)-