Suppose people in our overlapping generations model have the opportunity either

Question

Suppose people in our overlapping generations model have the opportunity either to hold fiat money with complete safety or to lend to someone who may never repay the loan. The chance of such a default is 10 percent. Assume a stationary monetary equilibrium in which the population grows at a net rate of 8 percent and the fiat money stock is fixed. What real interest rate will be changed to the borrower if people are risk neutral? What can you say about the level of the real interest rate if people instead are risk averse?

Explanation / Answer

People will lend money if the rate of return is above the risk free rate.

In this case fiat money stock is fixed while population is growing at 8%.

So, N / P = 8 / 1 = 8%

Risk free rate is 8%

Expected return = (0.1*0) + (0.9*(1+r))

1.08 = 0 + 0.9(1+r)

1.2 = 1+r

r = 0.2 or 20%

Real interest rate should be 20%.

In case people turned out to be risk averse then they will be needed extra premium over the rate to induce them to lend.

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