Consider an endowment economy populated by Ben and Jerry. They live at t = 0,1 and their lifetime endowments are measured by the quantities of goods given at period 0 (e0) and at period 1(e1). Ben's lifetime endowment is represented as vector of (eBen,0, eBen,1)=(2, 1) whereas Jerry's endowment as (eJerry,0, eJerry,1)=(1, 2). Note that those endowments cannot be stored. As for preferences, Ben holds a utility function UB(c0, c1) logc0 + 1 2 logc1, but Jerry holds a utility function UJ (c0, c1) min [c0, 1 /2 c1]. Now, answer the following questions based on the descriptions so far.

(a) Assume that the two does not know the presence of each other. At this autarky state, what are their intertemporal MRSs? Are they different?

(b) Now Ben and Jerry hear a news that a bank has just opened in a town and from the bank they can make either deposits or get loans. At a given interest rate r, how much will Ben and Jerry make deposits or get loans?

(c) Suppose that the bank is a non-profit organization and it just only determines the interest rate r, where deposits and loan demands are equalized. Find r. At r, what are the levels of their intertemporal MRSs?

(d) Compared with the autarky, will they be happier or not after the introduction of the loan market. Show this claim by drawing an Edgeworth box.