Calculate the interest rates charged to high types

Assignment Help Microeconomics

Reference no: EM131916111

Problem

Consider an economy with three types of risk-neutral entrepreneurs. If a type 1 entrepreneur invests $200 she gets a gross return of $400 with certainty. If a type 2 entrepreneur invests $100 she gets $200 with certainty. And finally, if a type 3 entrepreneur invests $100 she gets $300 with probability 0.75 and 0 with probability 0.25. A risk neutral, competitive lender is considering extending loans to these entrepreneurs. This bank can determine if potential borrowers are of type 1 (henceforth, high-type borrowers), but it can't distinguish between entrepreneurs of type 2 and 3 (henceforth, low-type borrowers), but it does know that half of the low-type borrowers are of type 2, and the other half are of type 3. All borrowers, on the other hand, can recognize each others' types. Under these conditions, the bank decides to extend individual loans to high-type borrowers and group loans with joint liability to low-type borrowers. As a result, a low-type borrower may have to repay for a defaulting peer. The cost of lending to high-types is $20, while the cost of lending to low-types is $30 (because the bank has to put in additional time and effort to ensure that groups are formed and to enforce debt repayments). Assume that the borrowers are protected by limited liability.

a. If the bank only aims to break even, calculate the interest rates charged to high types and to low types. Compare the two rates.

b. Now suppose that the bank holds a pool of loan contracts. It lends to three high-type borrowers and to four low-type pairs with the compositions: (2,2), (3,3), (2,3) and (3,2). Assume that one borrower in group two succeeds, while type 3 agents fail in pairs three and four. Compute the repayment rates that the bank will receive separately for the high and low types loans. Compare the two rates, and explain your answer.

Reference no: EM131916111

Questions Cloud

How much money can you expect to earn in this period of time : How much will he have to invest today so that the investment will be worth $29,000 in six years?

How much should laura include in her 2016 taxable income : How much should Laura include in her 2016 taxable income as alimony? Calculate Melissa's tax liability.

What is the minimum gross repayment r : What is the minimum gross repayment R* for each I loan at which the banks would be willing to lend?

What is the lower boundary for this stock : General Motors (GM) just paid a dividend of $5.00 per share, which is expected to increase by 4.0 percent per year.

Calculate the interest rates charged to high types : If the bank only aims to break even, calculate the interest rates charged to high types and to low types. Compare the two rates.

Draw a cash flow diagram to show all the detailed cash flow : An 1C (integrated-circuit) fabrication company is considering to build a new production plant to expand their business.

What kinds of additional information would you need : What kinds of additional information would you need to have in order to draw sharper comparisons?

What is the value of your futures position on monday : In order to hedge yourself, which position in Eurodollar futures will you take (i.e. buy or sell, contract maturity, and the number of contracts)?

What is the npv of the given project : Its pretax cost of equity is 14 percent, and its pretax cost of debt is 8 percent. The tax rate is 40 percent. What is the NPV of this project?

User Account

All Pages