ECON20532 Macroeconomic Analysis IV Semester 2
2022/23
Exam Questions
1. Consider an overlapping generations economy in which capital pays a 25% net rate of
return. The population of a generation grows by 10% each period. In the initial pe-
riod (period 1), there are 100 young people and a pre-existing fiat money stock of M0 =
$1; 000; 000. Because of a political impasse, government expenditures exceed (non-seigniorage) tax revenues by 40 goods per young person in every period. Each young person wishes
to hold real money balances worth 200 goods regardless of the rate of ináation. Assume that there is no debt coming into the first period (b0 = 0).
(a) Use the government budget constraint to find the rate of fiat money creation that is required to finance the excess of government expenditures over taxes. (20%)
(b) Find the fiat money stock and the price level in periods 1 and 2. Use these results to verify that the gross rate of ináation is indeed equal to z=n, where z is the growth rate of money and n the growth rate of population. (30%)
(c) Suppose instead now that in the initial period (period 1), the monetary authority hesitates to print new money, forcing the government to issue debt at the market rate of interest. In the second period, the monetary authority relents, printing enough new money to pay off the debt as well as to pay for the second periodís excess of government expenditures over taxes. Find the fiat money stock in period 2 and compare it with your answers in part a. Explain the difference. (35%)
(d) Using results from point c., find the price level in period 2 and the rate of ináation between period 1 and period 2. (15%)
2. Consider the following economy. Individuals are endowed with y units of the consumption good when young and nothing when old, but would like to consume in both periods. People face a lump-sum tax of τ goods when young and a rate of expansion of the fiat money supply of z > 1. The tax and the expansion of the fiat money stock are used to finance government purchases of g goods per old person in every period. There are N people in every generation (constant population).
(a) Find the individualís budget constraints when young and when old. Combine them
to derive the individual's lifetime budget constraint. Explain the results. (25%)
(b) Find the government's budget constraint. Explain each component. (25%)
(c) Find the feasible set. Explain what is the role of z , τ and g in it, and why. (25%)
(d) Now consider instead the case where the lump-sum tax of τ goods is levied on the old
and used to finance a transfer of g goods to the young. Derive the new government budget constraint and feasible set. Explain the results. (25%).
3. Consider a three-period overlapping generations economy with N young people born each period. Each young person receives y goods, but nothing when middle-aged or when old. People can access a storage technology that yields one good next period for every good put in storage in the current period. Alternatively, there is a capital good, with one unit of the consumption good acquiring one unit of capital. For each unit of capital acquired in date t, 1:2 units of the consumption good will be received at date t + 2. If the person liquidates the capital after one period, though, then only :8 units of the consumption good can be obtained at date t + 1. Assume that there is a 50% probability that a person will want to consume only when middle-aged and a 50% probability that a person will want to consume only when old. Whether someone is an "early" or "late" consumer will be revealed only at time t + 1.
(a) Derive the equilibrium in this economy without an intermediary bank. How much would people invest in the storage technology if they are risk-neutral? How would your answer change if you assume instead that agents are risk averse, so they prefer less variance for the same expected return? (25%)
(b) Derive the equilibrium with a bank, assuming the bank operates under perfect com- petition (no profits). Assume also that the bank does not expect a bank run to occur. What is the advantage of pooling risk? (25%)
(c) What is the outcome in case of an (unexpected) bank run, assuming that the bank equally splits the value of its portfolio among all depositors? (25%)
(d) Compare and rank outcomes from points a., b. and c., both in terms of ex-ante expected consumption (before agents are revealed whether they are early or late consumers) and ex-post actual consumption for early and late consumers. (25%)