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. LetLbe the total amount of funds he lends out, letrbe the opportunity cost of funds for every moneylender, and letibe 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.