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 xt, for t=1,2. intertemporal utility functions for the two consumers are:

ui(x1,x2)=ln(x1)+ln(x2), i=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 consume in each period? how well off is each consumer?

b) now suppose there are competitive "spot" and "futures" markets for this good. let p1 be the (spot) price per unit in period 1, and p2 be the (futures) price prevailing in period 1 for delivery of one unit of the good in period 2. what will be the equilibrium relative prices p2/p1?

ui(x1,x2)=ln(x1)+ln(x2), i=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 consume in each period? how well off is each consumer?

b) now suppose there are competitive "spot" and "futures" markets for this good. let p1 be the (spot) price per unit in period 1, and p2 be the (futures) price prevailing in period 1 for delivery of one unit of the good in period 2. what will be the equilibrium relative prices p2/p1?