Exercise 1 (Adverse Selection) Suppose that there are two different borrowers: William and Johnson. Williams's returns will be 500 with probability 0.9 and zero otherwise. Johnson's project delivers $800 with probability 0.5 and zero otherwise. At the end of the period both have some assets worth $250 (which can be used as collateral). The project requires an investment of $200 up front and this amount is borrowed from the bank. The bank can't distinguish between the types of borrower. Assume that the interest rate is 5% and everybody is risk neutral