In a credit market any borrower needs to borrow one unit of capital to invest in its project. Any project results in one of the two outcomes: success (return $5000), or failure (return $0). There are two types of borrowers: type s (safe) and type r (risky). The probability of success is 1/4 for type s and 1/8 for type r.Loans are given to groups of two borrowers through the joint liability contract (1260, 960), where 1260 is the individual liability component and 960 is the joint liability component. Denote by yab the average net income of a borrower whose own type is a and whose group partner is of type b.(a) Showing all steps of your work, determine ysr, yrs, yss, yrr.(b) Suppose there are four borrowers: two of type s, two of type r. Show that same types forming groups is a stable formation. Share on Facebook Tweet Follow us Sample Answer Essay: Understanding Joint Liability Contracts in a Credit Market In a credit market, borrowers often seek capital to invest in projects with uncertain outcomes. When borrowers are categorized into safe (type s) and risky (type r) groups, the joint liability contract becomes a crucial mechanism to ensure repayment and risk-sharing. In this analysis, we will delve into the dynamics of joint liability contracts by evaluating the average net income of borrowers based on their types and partnerships. Part (a): Calculating Average Net Income for Different Borrower Combinations 1. Average Net Income for Type s and Type r Borrowers- Let’s start by calculating the average net income for different combinations of borrowers: – For Type s and Type r partnership (ysr): – Type s borrower: Success with probability 1/4, returns $5000. – Type r borrower: Success with probability 1/8, returns $5000. – Therefore, – ysr = 1/4 * $5000 + 1/8 * $5000 = $1250 + $625 = $1875. – For Type r and Type s partnership (yrs): – The calculation remains the same as ysr due to the symmetry of outcomes. – yrs = ysr = $1875. – For Type s and Type s partnership (yss): – Both Type s borrowers have a success probability of 1/4. – Thus, – yss = 1/4 * $5000 + 1/4 * $5000 = $1250 + $1250 = $2500. – For Type r and Type r partnership (yrr): – Both Type r borrowers have a success probability of 1/8. – Hence, – yrr = 1/8 * $5000 + 1/8 * $5000 = $625 + $625 = $1250. Part (b): Stability of Same-Type Borrower Groups 2. Stability in Same-Types Forming Groups- Let’s consider a scenario with two Type s and two Type r borrowers:- If both Type s borrowers form a group (yss), the average net income is $2500. – If both Type r borrowers form a group (yrr), the average net income is $1250. – As yss > yrr, same-type groups are stable formations due to higher expected returns. Conclusion In conclusion, the joint liability contract plays a pivotal role in credit markets by influencing borrower partnerships and risk-sharing. By analyzing the average net income of different borrower combinations, we can understand the dynamics of risk allocation and stability within the credit market ecosystem. Through this evaluation, we have demonstrated how same-type borrower groups can lead to more favorable outcomes, showcasing the significance of strategic partnerships in mitigating risks and maximizing returns. This question has been answered. Get Answer
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