A credit market has two types of borrowers: s (safe) and r (risky); each has proportion 1/2. Any borrower borrows 1 unit of capital to invest in a project. A project can result in either one of the two outcomes: good or bad. Under bad outcome, the return is 0. Under good outcome, the return is xs = 160 for type s and xr = 120 for type r. The probability of good outcome is ps = 1/3 for type s and pr = 1/4 for type r.A credit contract is given by interest i (which includes both principal and interest). Under this contract, a borrower pays back i to lender if the outcome is good and pays back nothing if the outcome is bad. The opportunity cost of a borrower is B0 = 18. The opportunity cost of a lender is L0 = 21. Assume the credit market is competitive, so a lender makes zero net profit. Showing all steps of your work, answer the following questions.(a) Find the maximum acceptable rate of interest for each type.(b) Consider the full information case where a lender knows types of individual borrowers. Determine interest rates offered, which type gets loan and the aggregate income.(c) Consider the asymmetric information case where a lender does not know types of individual borrowers and only knows there is proportion 1/2 of each type. Determine interest rate offered, which type gets loan and the aggregate income. Then determine if there is a problem of underinvestment or overinvestment Share on Facebook Tweet Follow us Sample Answer Essay: Credit Market and Borrower Types Introduction In a credit market with two types of borrowers, safe (s) and risky (r), each with a proportion of 1/2, lenders face the challenge of determining appropriate interest rates to mitigate risk while maximizing returns. This essay delves into the dynamics of credit contracts in such a market, exploring scenarios where lenders have full information about borrower types and cases where information asymmetry exists. Thesis Statement By analyzing the credit market scenario provided, we can determine the maximum acceptable rate of interest for each borrower type, identify the interest rates offered in cases of full and asymmetric information, and assess whether underinvestment or overinvestment occurs in the latter scenario. Maximum Acceptable Rate of Interest To calculate the maximum acceptable rate of interest for each borrower type, we consider their expected returns under good outcomes. For type s, with a return of xs = 160 and a probability of good outcome ps = 1/3, the expected return is 160 * 1/3 = 53.33. Similarly, for type r, with xr = 120 and pr = 1/4, the expected return is 120 * 1/4 = 30. The opportunity cost for borrowers (B0 = 18) and lenders (L0 = 21) needs to be factored in to ensure a competitive market where lenders make zero net profit. By incorporating these costs into the calculation, we can determine the maximum acceptable rate of interest for each borrower type. Full Information Case In the scenario where lenders have full information about borrower types, they can tailor interest rates accordingly. For type s, an interest rate slightly above the maximum acceptable rate would be offered to ensure profitability. In contrast, for type r, a higher interest rate reflecting the increased risk would be set. Asymmetric Information Case In cases of asymmetric information, where lenders do not know individual borrower types but only the overall proportions, challenges arise. Determining the optimal interest rate becomes complex as lenders must account for both types without specific knowledge. In this scenario, a blended interest rate that incorporates the characteristics of both types would likely be offered to mitigate risk. However, this approach may lead to issues of underinvestment or overinvestment depending on the actual distribution of borrower types. Conclusion The dynamics of credit markets with multiple borrower types highlight the importance of accurate risk assessment and tailored interest rates. Understanding how information asymmetry impacts lending decisions is crucial in ensuring efficient allocation of capital and preventing market distortions. By analyzing scenarios with full and asymmetric information, we can gain insights into the complexities of credit markets and the implications for borrower-lender dynamics. Effective risk management strategies and pricing mechanisms are essential for maintaining a healthy credit market that benefits both borrowers and lenders alike. This question has been answered. Get Answer
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