Problem
1. If banks lack local knowledge and loan repayment enforcement is limited, why can't they overcome all sorts of problems by simply hiring local, knowledgeable individuals as their agents?
2. Comment on the merits of the following statement: "A borrower is always better off if she is able to hide her earnings from the bank."
3. Suppose that there are two types of potential borrowers, each one making up half of the population. When they receive a loan of $100, risky borrowers will get a return of $150 with probability 0.5, and a return of zero with probability 0.5. Safe borrowers are not completely safe: they get $150 with probability 0.9, but still get zero with probability 0.1. Suppose that both types have zero wealth, and have an outside option in the labor market worth $10. Both borrowers are risk neutral.
a. Suppose there is a bank that can differentiate between the borrowers' types. For simplicity, assume that the bank's gross cost of capital is k = 1-in other words, the bank's cost of lending $100 is $100. Assuming the bank faces perfect competition, which of the two borrower types will it lend to?
b. Now suppose the bank cannot differentiate between types. Which of the borrower types will it lend to?
c. Suppose that there is another lending option in this community: a moneylender. This moneylender offers loans with a new feature: if you do not pay back your debt to the moneylender, he will smash your kneecaps. The value to the borrower of smashed kneecaps is -$200. The value to the moneylender is zero. In all other ways, the moneylender is identical to the bank. Would the moneylender be willing to lend in the first place, and would anyone enter into such a dangerous contract with the moneylender? Briefly explain your answers.
d. Assuming that neither banks nor moneylenders can distinguish between borrowers' types, are borrowers better off or worse off when kneecapping contracts are available? Explain why and what kind of problem, if any, smashing kneecaps solves.
e. Briefly explain how things might change if borrowers had some positive wealth.
f. This is a typical adverse selection exercise. Briefly explain how the reasoning would differ or stay the same if this had been an exercise focusing on moral hazard.