ECON20532/30532 Macroeconomic Analysis IV
Resit paper 2023/24
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 a random-relocation economy where each young person receives 100 units of the consumption good. There are 500 young people in the economy at time 1, and the population grows at 2% per year. The total stock of money at time 1 is equal to $40,000, and it grows by 1% every year. Suppose a personís preferences are such that they only want to consume when old, and they dislike risk. We also assume that the probability that a person is relocated is 40% (known to everybody) and if relocated they need to move at the end of the first period, before capital matures. Endowment goods can be transformed into capital, which gives a gross rate of return of 1.02 after one period. Capital cannot be sold or transformed back into consumption goods before maturity. Individual agents don't have the technology to convert goods into capital, but there exists a (perfectly competitive) banking sector that accepts deposits and can invest in capital.
(a) Write down the money-market clearing condition for this economy. Where is the demand for money coming from? How does the value of money change over time? (30% of total question mark)
(b) What is the state contingent rate of return o§ered by banks on deposits? (20%)
(c) Compute the equilibrium value of money at time 1 for this economy. (30% of total question mark)
(d) Assume now that both population and the stock of money remain constant over time. What would change in your answers to points (a), (b) and (c)? (20% of total mark)
2. Consider an overlapping generations economy with 100 young people born in every period. Government debt and capital both pay real net rates of return equal to 5 percent. The fiat money stock is fixed. Each young person wishes to save 50 goods in each period and, for equal rate of return, prefers government debt over capital. In period 0, the government issues a total amount of real government debt equal to 2; 000 goods. The government attempts to roll over this initial debt in subsequent periods.
(a) What are the real holdings of capital and bonds of each young person in period 0 and in period 1? (30% of total question mark)
(b) In what period does it become impossible for the government to continue to roll over its debt? (30% of total question mark)
(c) Now suppose that the number of young people born in each period grows at the net rate of 10 percent. There are 100 young people born in period 0. Reconsider your answer to part (b) and explain how things would di§er now. (20% of total question mark)
(d) What if instead population grows that the rate of 2% per year? Will the government be able to roll over its debt forever, and if not when will it stop being able to do so? (20% of total question mark)