ECOS3010: Sample Final Exam
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ECOS3010: Sample Final Exam
Section A: Question 1-4, answer True, False or Uncertain. Brieáy explain your answer.
1. In the standard OLG model of money, the optimal monetary policy is to set a constant price level.
2. In the model with international currency traders, international currency traders can free themselves from exchange rate áuctuations.
3. If a speculative attach on a countryís currency occurs and the governmentís com- mitment proves su¢ cient, the government can prevent the currency from depreciating and citizens in that country are made no worse o§.
4. The importance of capital requirements is that it ensures that depositors do not su§er losses when banks invest in risky assets.
Section B: Question 5-7.
5. Consider an economy with a growing population in which each person is endowed with y1 when young and y2 when old. Assume that y2 is su¢ ciently small that everyone wants to consume more than y2 in the second period of life.
(a) Suppose that there exists a planner. Write down the resource constraint faced by the planner.
(b) Assume that all individuals within a generation will be treated alike and graph the set of stationary feasible allocations implied by the resource constraint. Draw the indi§erence curve and point out the allocation that maximizes the utility of future generations.
(c) Turning now to monetary equilibrium, suppose that the money supply is constant. Let vt be the value of money in period t. Write down the individualís lifetime budget constraint.
(d) Find the equation that represents the equality of supply and demand in the market for money. Derive the rate of return on money vt+1/vt .
(e) Draw the budget constraint on the graph you developed in (b) and Önd the allocation in the monetary equilibrium. Does this monetary equilibrium maximize the utility of future generations? Explain.
6. Consider the standard OLG model where people live for two periods. There are Nt individuals born in period t. The growth rate of population is n. In the Örst period, there are N0 initial old. Each individual is endowed with y units of the consumption good when young and nothing when old. Suppose that there is a production technology such that k units of the consumption good can be converted in capital goods at time t, which can be used to produce xk units of the consumption good at time t + 1. Assume that capital depreciate 100% after production. Each member of the initial old begins with a stock of capital that produces xk0 units of the consumption good in the Örst period.
(a) Consider an equilibrium without Öat money. Write down an individualís lifetime budget constraint.
(b) Use a graph to depict the equilibrium allocation chosen by the individual.
(c) Now suppose that money also exists as an alternative asset. The growth rate of money supply is z . Write down the condition that ensure both money and capital are valued in equilibrium.
(d) Following part (c), if capital displays a diminishing marginal product (i.e. f\ (k) < 0), what would happen to the stock of capital if there is a permanent increase in z?
(e) Now suppose that private debt also exists as an alternative asset. There are three assets in total: money, capital and private debt. Let Rt be the nominal interest rate paid on private debt, and rt be the real interest rate in period t. What is the relationship between Rt and rt?
(f) Describe the Fisher e§ect. Under what condition(s) is the Fisher e§ect satisÖed?
(g) Empirical evidence suggests that nominal interest rates and ináation rates tend to move together, but the gap between the nominal interest rate and the ináation rate is not constant. Can you provide a theory to rationalize the above empirical evidence?
7. Consider the model of demand deposit banking where individuals live for three periods. There are N = 100 individuals born in each period. In the Örst period, there are 100 initial old and 100 initial middle-aged. Each individual is endowed with 20 units of the consumption good when young and nothing in the other two periods of life. No one consumes when young. Everyone wants to consume in one of the next two periods of life, depending on their type. With probability 0:5, an individual wants to consume in the second period of life, which we label as type 1 consumers or early consumers. With probability 0:5, an individual wants to consume in the third period of life which we label as type 2 consumers or late consumers. No one knows his type when young. In the Örst period after birth, an individual learns his type. The type of each individual is not observed by anyone else.
People have access to two assets: storage and capital. Storage pays a gross rate of return 1 over one period. Capital produces X = 1:2 goods for each good invested, but only after two periods of its creation. Capital that has not yet produced can be sold early at a price vk = 1: Since it is possible to issue fake capital or claims to capital verifying that capital is not a fake costs 9 = 0:3 goods per unit of capital. Assume that 9 > X 一 1.
(a) Show that the one-period rate of return on storage is better than the one-period rate of return on capital.
(b) Describe how the existence of banks help improve the welfare of individuals.
(c) What is the portfolio chosen by a bank? How many goods will be placed in storage? How many goods will be invested in capital?
(d) Following part (c), how many people can be paid before the bank runs out of assets? Explain why a bank run might occur if every other type 2 individuals is going to pretend to be a type 1 individual.
(e) Suppose that banks are allowed to issued banknotes (inside money) backed by their own assets ñan elastic currency regime. Can a bank avoid a bank run described in (d)?
(f) Runs on banks can be one source of bank failures. Can you provide an alternative source of bank failures?
(g) Government deposit insurance is one way for the government to prevent bank failures. List one potential problem associated with providing government deposit insurance.
2022-11-05