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 projectgives 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 wantsto break even (make zero profits). There is limited liability for borrowers.

Another problem on adverse selection in credit markets. Suppose all the assumptions are the same as problem (1), with one difference: now 70% of the borrowers are "safe" (meaning they invest in safe projects) and 30% of the borrowers are "risky" (meaning they invest in risky projects).Suppose the lender (bank) cannot recognize which loans are safe. What is the minimum interest rate the bank should charge if the bank wants to break even?