This is a problem on adverse selection in credit markets. The assumptions are the following. Suppose 50% of the borrowers are "safe" (meaning they invest in safe projects) and 50% of the borrowers are "risky" (meaning they invest in risky projects). The safe project gives a return of 140 with probability 100%. The risky project gives a return of 300 with probability 50% and a return of zero with probability 50%. The size of the loan is 100 and the entrepreneurs (borrowers) need to borrow the whole 100. The bank wants to break even (make zero profits). There is limited liability for borrowers.

a. Perfect information.

Suppose the lender (or bank) has perfect information, which means that it can recognize which loans are safe. What is the minimum interest rate the bank should charge if the bank wants to break even?

b. Imperfect information.

Suppose the lender (bank) cannot recognize which loans are safe. The lender knows that there are two types of borrowers/projects and that 50% of the borrowers are safe and 50% of the borrowers are risky. However, the bank cannot tell if a borrower has a safe or risky project. What is the minimum interest rate the bank should charge if the bank wants to break even?

c. Imperfect information.

Suppose the lender (bank) cannot recognize which loans are safe. The lender knows that there are two types of borrowers/projects and that 50% of the borrowers are safe and 50% of the borrowers are risky. However, the bank cannot tell if a borrower has a safe or risky project. Assume that at the interest rate you found in b) there is an excess demand for loans (quantity demanded > quantity supplied). What happens if the lender charges a higher interest rate? Above what interest rate would the safe borrowers stop demanding a loan?