Economics of Money and Banking Assignment -

Part A -

Question 1 - 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 charged 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?

Question 2 - Suppose capital is risky and pays gross real rates of return of 1.2, 1.1, and 0.9 with probabilities 0.1, 0.7, and 0.2, respectively. A risk-free asset pays a safe gross real rate of return of 1.04. What is the expected rate of return on capital? What is the risk premium of capital?

Question 3 - Consider our model of three-period-lived individuals of chapter 8. Suppose the two-period real rate of return on capital is X = 1.44, the rate of population growth is n = 1.1, and the rate of fiat money creation is z = 1.2. Find the following net rate for both one and two periods

a) Nominal rate of interest.

b) Real rate of interest

c) Rate of inflation.

d) Real rate of return on money.

Part B -

Question 1 - Consider a three-period OLG model. There are N_t people born in time t and gross rate of population growth is n. A member of generation t consumes c_1,t when young, c_2,t+1 when middle age and c_3,t+2 when old. An Individual is endowed with y₁ and y₂ units of the consumption goods in the first and second period of his life and nothing in the third period. There is one single physical asset: capital, k_t. A unit of capital is created from a unit of the consumption good in any period t. Two periods after its creation, a unit of capital produces X units of the consumption good and then disintegrates. Let X > n². Suppose it is impossible to observe the capital created by others. Hence, there is no credit market. Suppose sum of savings in the first period of life (in the form of fiat money) and y₂ finances the expenses for consumption good in the second period of life.

Assume that an individual faces a lump-sum taxes of τ₁ and τ₂ goods in the first and second period of his life, respectively. These taxes finances the government debt. Moreover, suppose M_t = M_t-1.

a) Write down the feasible constraint. Rewrite it for stationary case.

b) Find the individual's budget constraints when young, middle age and old. Combine them and find the individual's lifetime budget constraint.

c) Find the rate of return on money. Compare the rate of return on capital, X, and that of fiat money and discuss whether an individual will choose to provide for c_3,t+1 by holding capital

d) Discuss the substitutability of fiat money and capital

e) Suppose M_t = zM_t-1 where z > 1. Find the rate of return on money in this case. Find an assumption that you need to impose so that an individual will choose to provide for c_3,t+1 by holding capital.