EC404 MACROECONOMICS Midterm Exam 2020–2021
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EC404
Midterm Exam 2020–2021
MACROECONOMICS
1. Answer all parts of this question.
You can answer those questions just with words. You may add equations or figures if you find them helpful but it is not necessary.
We can decompose the non-farm output in the U.S. into trend and cyclical compo- nents, as discussed in Lecture 1.
(a) [5 marks] What are the properties of the trend? List at least two properties and offer economic interpretations.
(b) [5 marks] Which models we learned in the lectures can capture the properties of the trend you listed above? Pick one model and explain how it captures the properties.
(c) [5 marks] What are the properties of the cyclical components? List at least two properties.
(d) [5 marks] What is the main difference in the cyclical components before and after mid 1980? Why?
2. Answer all parts of this question.
You can answer this question just with words. You may add equations or figures if you find them helpful but it is not necessary.
Consider the two-period overlapping generation model discussed in the lecture.
(a) [10 marks] If f、(k) < n (rate of return for capital < population growth rate), is the decentralized equilibrium efficient? Why? If the decentralized equilibrium is efficient, then under which condition it is not?
(b) [10 marks] If a decentralized equilibrium is not efficient,then how can the gov- ernment use the pension system to improve the welfare of all generations?
(c) [10 marks] If the government introduces a fully funded pension system (every household pays pension contributions into her own individual account in the pen- sion fund, and the fund invests for her and pays back to her when she retires according to her accumulated contributions and investment returns), how do the households’ private savings change? How do the total savings (private savings + savings in the individual pension accounts) change?
3. Answer all parts of this question.
Consider the OLG economy discussed in the lectures. Assume no exogenous techno- logical growth or population growth (g = 0, n = 0). Households maximise
subject to
where u (C) = log (C - C ), C ≥ 0 represents the subsidence level of consumption. Assume that consumption is always higher than the subsidence level,i.e., C > C. St denotes savings, ρ > 0 the discount rate, and rt+1 the real rate of return on savings.
The production function is Cobb-Douglas: 
. Assume full depreciation:
δ = 1.
(a) [10 marks] Derive the Euler equation of the households and solve for household savings.
(b) [10 marks] How do household savings change if subsidence consumption C in- creases? How does the answer depend on the interest rate, i.e., 
? Offer economic intuitions to your answer.
(c) [10 marks] Solve for the equilibrium and find the dynamic equation that char- acterizes law of motion for capital,i.e., find the dynamic equation showing how Kt+1 is determined by Kt.
(d) [10 marks] Now assume that C = 0. Solve for the steady state level of capital K* and the corresponding interest rate r* . Use the phase diagram to show how Kt+1 depends on Kt and how K*is determined in this case.
(e) [10 marks] Suppose that the economy is at the steady state with C = 0, from period 0 to t0. Surprisingly, C increases slightly and stays at that level from period t0 onward. How does capital change, at t0 and afterward? Use the phase diagram to show how capital adjusts and converges to the new steady state level.
2024-01-31