This problem illustrates the rationale behind credit rationing. Suppose there are two types of borrowers. Half the potential borrowers are

“good,” who want to borrow $100,000 on projects that will pay back

$130,000 in a year. The other half are “bad” borrowers, who want to borrow $100,000 on projects that will pay back $120,000 if they succeed and only $80,000 if they fail (there is half a chance they will succeed). Assume borrowers lose nothing if the project fails. What is the lowest interest rate banks must charge to be sure they only get good borrowers? What will happen to the bank’s returns if they lower the interest rate? (Assume they cannot tell who is bad and who is good when making a loan.) Suppose the Fed lowers the discount rate: Will this encourage banks to lend at lower interest rates?