Consider a two-period economy with a real interest rater and that there are two kinds of consumers (A and B). There are N consumers of each type and we can assume that N is large enough, so that the consumers are all price takers (cannot influence the price).
Type A consumer's utility is: UA(C₁, C₂) = log(c₁) + log(c₂)
Type B consumer's utility is: UB (C₁, C₂) = log(c₁) + Blog(c₂)
where 0 < β < 1.
For both types, the endowments in the two periods are (1, 1).
Part a. State the lifetime budget constraint (of either type).
Part b. Find the optimal first-period consumption c4 for Type A.
Part c. Find the optimal first-period consumption c3 for Type B.
Part d. Show that the equilibrium interest rate r* (that clears the market) is greater than/less than/equal to 0.
