ECON20532/30532 Macroeconomic Analysis IV
Semester 2 2024/24
INSTRUCTIONS SPECIFIC TO THIS EXAM:
. Answer both questions. Each question carries the same overall weight.
. You should type in your answers, but can include pictures of hand written equations if necessary.
. Candidates are expected to demonstrate to the examiners a competent knowledge of all computations.
. Candidates are also advised that the examiners attach considerable importance to the clarity with which answers are expressed.
. Electronic calculators may be used in accordance with the University regulations.
Exam Questions
1. Consider an overlapping generations economy in which capital pays a 10% net rate of re- turn. The population of a generation grows by 10% each period. In the initial period (pe- riod 1), there are 100 young people and a pre-existing fiat money stock of M0 = $900; 000. Because of a political impasse, government expenditures exceed (non-seigniorage) tax rev- enues by 50 goods per young person in every period. Each young person wishes to hold real money balances, denoted q1, worth 200 goods regardless of the rate of inflation. 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% of total question mark)
(b) Find the fiat money stock and the price level in periods 1 and 2. Use these results to verify that the increase in money supply can finance the government deficit. Verify also that the gross rate of inflation is indeed equal to z=n, where z is the growth rate of money and n the growth rate of population. (30% of total question mark)
(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 period's 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% of total question mark)
(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% of total question mark)
2. Consider an economy in which there are 1; 000 workers. Each worker is endowed with 200 units of the consumption good when young and nothing when old. Half of the workers consume 60% of their endowment when young, the other half only consume 40% of their endowment when young. Let the (gross) return offiered by banks on deposits be 1.03, but workers need to pay a fixed fee of 3 goods in order to use a bank. Let the stock of fiat money be constant over time, with M = 50; 000.
(a) What is the aggregate level of savings in the economy? (20% of total question mark)
(b) Write down the money market-clearing condition and compute the price level in this economy. (30% of total question mark)
(c) What is the total nominal stock of money (outside plus inside) and what is the aggregate (real) value of fiat money balances in the economy? Why? (30% of total question mark)
(d) What would happen to the price level if the rate of return on banks deposit was to increase to 1.05 and banks were to increase the fee from 3 to 5 goods? (20% of total question mark)