Question

Imagine that there are two types - high and low - of potential borrowers. Both exist in equal proportion in the population. The high type has access to a technology that generates a gross return of 2 with probability 0.8 and a gross return of 0 with probability equal to 0.2. The low type can generate a gross return of 5 with probability 0.1 and a gross return of 0 with probability equal to 0.9. Assume that commercial banks can secure a gross return of 1 by making a deposit at the FED. If a commercial bank operating in a competitive market could distinguish between the two types then it should charge a gross interest rate of

Group of answer choices
a. None of the above
b. 1 to both types
c. 5 to the low type
d. 5/4 to the high type

Answer 1

The optimal interest rates would reflect the expected rate of return and associated risk of each type of borrower, ensuring a higher return than what the FED provides and suitable compensation for default risk.

Step-by-step explanation:

The question revolves around the idea of lending by commercial banks to two different types of borrowers in a competitive market, and the interest rates that should be charged to each if the banks could differentiate between the two types. Given the default risk of the borrowers and the certainty of a return from the Federal Reserve (FED), a bank would prefer to charge an interest rate that reflects the expected rate of return and the risk associated with each type of borrower.

The high type borrower has an expected return of 1.6 (0.8*2) with a lower risk, while the low type borrower has an expected return of 0.5 (0.1*5) with a higher risk. If the bank could distinguish between them, charging a rate that ensures a return higher than what the Federal Reserve offers (which is 1) while compensating for the risk involved would be the optimal strategy.