You have been assigned to study credit markets in a poor agricultural region. Farmers do not have access to formal credit, but need to borrow money for seeds and fertilizer which they can only repay after the harvest. Assume they have no assets of their own. There are many sufficiently wealthy people in the nearby city who can lend money to the farmers and charge an interest rate higher than that legally set by the bank. The prevailing interest rate on deposits in the bank is 12%. You interview the farmers to learn about their needs and the interest rates they pay. There are three types of farmers: those with 1 acre of land, those with 5 acres and those with 10 acres. Seeds and fertilizer for a single acre costs $100. You also learn that they pay interest rates ranging form 28% to 76%. Parts a and b are as straightforward as they seem:

1. How much does each type of farmer need to borrow?
2. What interest rate should the moneylenders charge given what we know already?

You next interview the moneylenders in the city to learn about their costs. For each of the following parts, explicitly write down the condition that determines the interest rate the moneylenders should charge based on the additional information, denoting the loan amount X, the interest rate r, and the opportunity cost of capital i. Then calculate interest rate they would charge each type of farmer.

3. You find out that they face administrative costs ( that are per dollar (not per loan as we saw in class). Administrative costs are 5 cents per dollar.
4. In addition to administrative costs, they face default risk: 25% of the farmers will not come to the city to repay the moneylender. Denote this percent p.
5. To reduce the default rate to 5% (denote this d), the moneylenders can hire a local agent to collect his money. Such agents charge $50 (denote this m) per loan they try to collect. Assume they still pay the administrative cost per dollar.

The above costs should have explained the interest rates paid by farmers in that region. You next find out that these same moneylenders charge different interest rates to farmers in another rural area. Those farmers are similar to the ones you interviewed with similar plot sizes and needs.

The interest rates range from 33.3% to 63.3%.

6. Assuming they face the same administrative costs and using the equations you wrote down in part e, calculate the default rate (d) if the moneylenders hire a local agent in this new village and what these agents charge (m).