Problem

Consider a project that needs a fixed investment I = $100 and yields a gross return y > I with certainty. A risk-neutral borrower wants to invest in this project, but she only has private wealth w = $58 that can be used for investment. She has the option to go to a risk neutral and competitive bank in order to borrow the rest of the money that she Why Intervene in Credit Markets?

Needs to carry out her investment project, (I - w). Once the project has yielded a positive return, the borrower can either run away with the money or repay her debt. The lender can observe the result of this particular investor's project with probability s = 0.7. If the borrower refuses to repay the money and the bank observes that the project has been successful, the bank can seize w. Explain whether you would expect the bank to be repaid in this ex post moral hazard scenario and why. (For the sake of simplicity, you can assume that the cost of raising capital for the bank is zero per each dollar lent.)