Suppose the wealth distribution in Ping is as follows: Assume that all people are equally productive and that if they undertake an investment project that requires $1000, they produce the same gross return y = $2000 with probability 100%. Assume that the bank's cost of capital is $500. Assume that all borrowers in this economy are protected by limited liability. (a) Show that it would be socially efficient to lend $1000 to everybody in Ping. (b) Now assume that the bank cannot observe whether the project was a success. Solve for the condition on the gross interest rate the bank will have to observe in order to induce repayment. Assume borrowers will lose all their collateral when they default on their loan. Who will the bank agree to lend to? (c) Now suppose that the bank offers a group contract. It will lend to a groups of 2 and it imposes a "joint responsibility" clause, that is, if one individual runs away, her partner has to pay for her. By incurring an effort cost of $50 a borrower can monitor her partner. Will this improve the situation? What might improve the situation