Problem

Consider the following timing: a loan is made first; then monitoring choices are made; next, effort decisions are made and potential borrowers expend effort in their projects; finally, returns accrue to the entrepreneurs. Suppose all entrepreneurs in this economy are identical. These potential borrowers wish to invest in a project that costs I = $100. If successful, it yields a gross return y = $300. If borrowers put in an adequate level of effort, the probability of success will be 1; if they don't, the probability of success will be p = 0.75. Assume that the cost of effort is c = $40 and that the borrowers' opportunity cost is $80. The bank is perfectly competitive, and the gross cost of a loan is R = $150.

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 self-selected groups of 2 borrowers, and that the bank imposes joint liability. A borrower can monitor her partner, which induces return-maximizing effort but costs the monitor k = $20. Assuming that there is simultaneous monitoring and that borrowers are protected by limited liability, compute the interest rate that the bank will charge. Will both entrepreneurs be able to access loans? Briefly explain your answer.

c. Does it make sense to assume symmetry, i.e., that borrowers monitor each other simultaneously?