Problem

Consider an economy with risk neutral individuals. There is a borrower who wants to run a project with a required investment of $100. If the borrower puts enough effort into her project, she will succeed with probability 0.9 and get a gross revenue of y = $150. Otherwise, she fails and gets nothing. But if the borrower's effort level is low, the probability that she will obtain the gross revenue y = $150 is only 0.75. Effort is costly for the borrower, costing c = $18. The bank's gross cost of lending is $115. Assume that the lender just wants to break even, and that the borrower cannot repay more than her current income. a. Show that investment in this case is socially efficient only if the borrower puts forth an "adequate" level of effort.

a. Compute the threshold interest rate (the maximum rate) that the lender can charge to induce an adequate effort level from the borrower.

b. Will the borrower be able to obtain the required funds from the lender? (Assume that the opportunity cost for the borrower is zero.)

c. Briefly explain the main insights gained from this ex ante moral hazard exercise for the particular case of microfinance institutions.