ECON20532 Macroeconomic Analysis IV
Mock Exam Paper
INSTRUCTIONS SPECIFIC TO THIS EXAM:
. Answer all three questions. Each question carries the same weight (1/3).
. 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.
Exam Questions
1. Consider an overlapping generations model with the following characteristics: Each gen- eration is composed of 1,000 individuals. The fiat money supply changes according to Mt = 2Mt-1 . The initial old own a total of 10,000 units of fiat money (M0 = $10, 000). Each period, the newly printed money is given to the old of that period as a lump-sum transfer (subsidy). Each person is endowed with 20 units of the consumption good when born and nothing when old. Preferences are such that individuals wish to save 10 units when young, independently of the rate of return on money.
a. What is the gross real rate of return on fiat money in this economy? Explain your derivation. (1/3 of total question mark)
b. What is the value (in goods) of the subsidy received by the old people in period 1? Explain your derivation. (1/3 of total question mark)
c. What is the loss (in goods) for the money holders due to the increase in money (ináation tax) in period 1? Explain your derivations. (1/3 of total question mark)
2. Suppose the government must borrow 1,000 goods in period 1. The government has no previous accumulated debt. Let the gross real marginal product of capital equal 1.07. Assume people always want to hold fiat money balances worth a total of 100 goods and that the Öat money stock in period 1 is £ 10,000. Suppose people expect the government to increase the fiat money stock by 100% and that the population is constant.
a. What will the nominal net interest rate be? Explain your derivation. (1/3 of total question mark)
b. What will the real value of the debt be in period 2? Explain your derivation. (1/3 of total question mark)
c. What will it be instead if the fiat money stock raises by 10% but this rise in unexpected? Explain your derivation. (1/3 of total question mark)
3. Consider a simple random-relocation model as seen in ch. 14. Each individual is endowed with 50 goods when young and nothing when old. People only want to consume when old. The money stock is constant and equal to $1million. Each island has a constant population, with 500 people born in each period. Suppose the fraction of movers (π) takes on either of two values, high (πH = 20%) or low (πL = 5%), each with a probability of 50%. That is, in the small-fraction event, with probability of 0.5, 5 percent of the population must move to the other island; in the high-fraction event, with probability of 0.5, 20 percent of the population must move.
a. Calculate the total currency needed by movers in the event that the small fraction of movers is realized. Explain your derivations. (1/3 of total question mark)
b. Calculate the total currency needed by movers in the event that the high fraction of movers is realized. Explain your derivation. (1/3 of total question mark)
c. Assume that the reserve-to-deposit ratio is equal to the (expected) fraction of movers, or γ = π . Will the bank have enough in currency to meet the needs of the movers in the high-fraction event? Explain your answer. (1/3 of total question mark)