Consider an economy with risk-neutral individuals. There is a borrower that wants to run a project with required investment of \($100\). If the borrower puts enough effort into her project, she will succeed with 90 percent probability, and get a gross revenue of y = \($150\), otherwise, she fails and gets nothing. But if the borrower misbehaves (or does not put in adequate levels of effort), she can only get the gross revenue y with probability, 75 percent. However, effort costs the borrower 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 is socially efficient only if the borrower puts in enough effort.

b. Compute the threshold interest rate (the maximum rate) that the lender should charge in order to elicit an adequate effort level from the borrower.

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