Consider the following timing. First a loan is made. Then monitoring choices are made. Next, effort decisions are made and effort is applied. Finally, returns are received. Suppose that the economy is made up of identical borrowers. These borrowers want to invest in a project that costs I = \($100.\) If successful, the project yields a gross return y = \($300,\) but borrowers have to put in an “adequate” amount of effort.

When borrowers do not put in any effort, the project succeeds with probability p = 0.75. The cost of effort is \($40.\) The borrowers’ opportunity cost is \($80.\) The gross cost of a loan is R = \($150.\) The bank is perfectly competitive.

a. Can a potential borrower obtain a loan when group-lending contracts are not allowed in this economy? Briefly explain your answer.

b. Now suppose that the bank can lend to a group of two agents, and that it imposes a “joint responsibility” clause. By incurring a cost k = \($20,\) a borrower can monitor her partner and induce an appropriate effort level. Her partner can in turn do the same. Compute the interest rate that the bank will charge in this case. Will both borrowers can obtain a loan in this case? Briefly explain your answer.