Consider an overlapping generation's economy with two assets capital and money. Suppose the number of young people born in period t is determined by Nt = 1.5Nt-1. Capital pays the gross rate of return X = 1.25. For what values of z (the gross rate of money stock growth) will fiat money be valued?
Suppose people in our overlapping generation's 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?
Suppose capital is risky and pays gross real rate 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 risk premium of capital?
Consider the model of three-period-lived individuals explained in class. Suppose the twoperiod 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:
1. net nominal rate of interest
2. net real rate of interest
3. net rate of inflation
4. net real rate of return on money
Consider the model of demand deposits described in class. Suppose N = 900. y = 10, Vk -0 = 0.9, and X = 1.2. Let each person have a two-thirds chance of being a type 1 and a one-third chance of being a type 2. Vk is price of capital when sold before capital produces the return of consumption good, and 0 is the verification costs of capital. X is the two-period rate of return on capital.
1. What bank portfolio can guarantee the rate of return 1 to all type 1 people and the rate of return 1.2 to all type 2 people? How many goods are placed in storage? In capital?
2. Now suppose the type 2 people pretend to be type 1 people and withdraw early. How many people can be paid before the bank nuts out of assets?
3. Suppose that in the period after you made your deposit at the bank, you turn out to be a type 2 person and you learn that all of the other type 2 people are about to pretend to be type 1 people so that they can withdraw early. Is it in your self-interest to also try to withdraw early?
4. Are type 2 people better off than they would be if no type 2 person tried to withdraw early? Reconcile your answer with your answer to part 4.