Consider an overlapping generations model with 200 lenders and 100 borrowers born in every period. Everyone lives for only two periods. Each lender is endowed with 20 goods when young and nothing when old. Each borrower is endowed with nothing when young and 40 goods when old. The lenders want to save 10 goods each, regardless of the rate of return on their savings. Each borrower wants to borrow 10/r goods each, where r is the gross real interest rate on private IOUs. The lending market is free and competitive.

a. In a non monetary equilibrium, what will the market-clearing value of r be?

b. Now turn to a monetary equilibrium. Suppose z = 0.5. What will the real fiat money holdings of a typical lender be?