ECON20532 Macroeconomic Analysis IV Semester 2 2022/23
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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 iat money stock of Mo = L1, 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 inlation. Assume that there is no debt coming into the irst period (bo = 0).
(a) use the government budget constraint to ind the rate of iat money creation that is required to inance the excess of government expenditures over taxes. (20%)
(b) Find the iat money stock and the price level in periods 1 and 2. use these results to verify that the gross rate of inlation 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 of the debt as well as to pay for the second period,s excess of government expenditures over taxes. Find the iat money stock in period 2 and compare it with your answers in part a. Explain the diference. (35%)
(d) using results from point c., ind the price level in period 2 and the rate of inlation 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 iat money supply of z 持 1. The tax and the expansion of the iat money stock are used to inance government purchases of g goods per old person in every period. There are N people in every generation (constant population).
(a) Find the individual,s 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 inance 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 十 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 十 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 十 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 proits). 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%)
2023-08-28