Part 1: The Lender's Risk Hypothesis

Imagine a village in a developing country where there are competitive moneylenders. There is an exogenous probability (1-p) of default for every dollar lent out and probability, p, of getting paid back with interest. Competition drives the interest rate down to a point where each moneylender earns zero expected profit on average (that is zero profit above the opportunity cost of lending the funds). Consider a typical moneylender. Let L be the total amount of funds he lends out, let r be the opportunity cost of funds for every moneylender, and let i be the interest rate charged in competitive equilibrium in the informal sector.

The expected profit of the moneylender is:

p(1+i)L -(1+r)L = 0

1. Solve for i in the above profit equation. That is, rearrange the equation so that you have: i = {something in terms of p and r}

Assume that r = 20%

2. What is the interest rate when p = 1? (i.e. when nobody defaults)

3. What is the interest rate when p = 0.5? (i.e. when there is a 50-50 chance of default)

4. Do you think it is unreasonable for a moneylender to charge interest rates above 100%? Explain.