Problem
1. Evaluate the merits of the following statement: "Relative to standard contracts where collateral is involved, under group-lending contracts banks elicit more information about the borrowers' trustworthiness."
2. Consider an economy with two types of risk-neutral borrowers. Assume that borrowers are protected by limited liability. There are one-period projects which require a $100 investment each. The bank is operating in a competitive environment, and is only trying to break even. Specifically, the bank wants to cover its gross cost, K = $145 per each $100 loan. If able to borrow, an individual of type 1 is capable of generating a gross return y1 = $230 with certainty, and if she is denied access to credit, she can work and earn $28 in the labor market. A type 2 borrower, if able to borrow, can invest her loan for a gross return of y2 = $420 with probability 0.5, or zero with probability 0.5. If denied access to credit, a type 2 potential borrower can work and earn $55 in the labor market. Assume that 40 percent of the population in this economy is of type 1, and the rest is of type 2. Then:
a. If the bank cannot distinguish between the two types, and cannot implement group lending with joint liability, which of the two types of borrowers will be credit rationed? Compute R*, the gross interest rate for this scenario.
b. Now suppose that the bank is willing to lend to anyone on the condition that all borrowers form pairs, and that each pair accepts a clause making them jointly liable for loan repayment. Specifically, the clause states that if one individual fails to repay, her partner has to pay for her; otherwise, both borrowers will be excluded from access to future loans, which is infinitely costly. Explain how you expect potential borrowers to form groups of 2-borrower pairs.
c. Compute R**, the gross interest rate in this scenario.
d. Suppose the bank charges R**, and that there is one individual of type 1 that has no choice but to form a pair with an individual of type
2. Would the type 1 individual be willing to borrow under a joint liability clause in this particular case? Briefly explain your answer.