Problem

Consider again an economy like the one described in exercise 6 in terms of the timing of events, but now suppose that at date 1, the borrower can turn out to be type 1, type 2, or type 3 with equal probability (of π = 1/3). Type 1 can get a gross return of $300 with certainty, type 2 can get a gross return of $360 with probability p2 = 0.75, and type 3 can get a gross return of $400 with probability p3 = 0.5. Assume that the bank operates under the conditions described in exercise 5, and that the opportunity cost for all borrowers is zero. Compute the interest charged by the bank if group lending is implemented at date 0, and explain clearly whether all potential entrepreneurs will be able to borrow.