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Final Examination – Econ UN3213. Mathematics & Economics

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Department of Economics Columbia University
Instructor: Stephanie Schmitt-Groh´e
Final Examination
Econ UN3213, Section 1
Intermediate Macroeconomics
Write your answer for each question on a different piece of paper. Be sure to write the questionnumber on top of each sheet. The exam has 180 points and you have 180 minutes to complete it.Show your work.
1. (60 points) [TFU] Indicate whether the following statements are true, false, or uncertain andexplain why.
(a) (10 points) In the long run, a country can control high inflation with high interest rates.
(b) (10 points) If Ricardian Equivalence holds, then fiscal deficits do not crowd out investmentin a closed economy with identical agents.
(c) (10 points) Suppose a country’s net foreign asset position is large and positive and isequal to its gross foreign asset position. This implies that the country has binding capitalinflow controls in place.
(d) (10 points) Current account deficits are an indication of a weak economy.
(e) (10 points) Free trade in goods and services is desirable but free trade in financial assetsis not.
(f) (10 points) In response to a positive supply shock, the central bank should raise interestrates to stabilize inflation.
2. (40 points) [Uncertainty-Shocks] Suppose output in period 2 is produced with the productionfunction A2I
α
1
, where A2 denotes the level of technology in period 2, I1 denotes the capitalstock in period 2, and α ∈ (0, 1) is a parameter. Suppose that in the good state of the worldtechnology in period 2 is equal to Ag
2 ≡ A + σ and in the bad state of the world it is equal
to Ab
2 ≡ A − σ, where A is a positive constant and σ satisfies 0 < σ < A. Assume that thegood and bad state occur with equal probability. Find the variance of A2. Assume that firmsborrow I1 in period 1 at the interest rate r and that the depreciation rate is 100 percent. Inperiod 1, firms pick I1 so as to maximize expected period-2 profits, that is, firms choose I1before they know the realization of A2.
(a) Find the investment demand schedule, I(r).
(b) Discuss how an increase in uncertainty about the level technology A2, that is, an increasein σ, affects the investment demand schedule.
1
(c) Discuss how an increase in uncertainty affects the equilibrium interest rate in a closedeconomy.
(d) Provide intuition for your findings.
3. (20 points) [Protectionism] Suppose that a protectionist initiative in Congress succeeds inpassing a bill closing the U.S. to trade in goods, services, and financial assets. What wouldbe the effect of this policy change on the interest rate, savings and investment in the UnitedStates and in the rest of the world.
4. (40 points) [Finite Lives and Fiscal Policy] Consider a two-period small open endowmenteconomy with free capital mobility. Households live for one period. The endowment is 10in both periods. The utility function of households living in period 1 is ln C1 and that ofhouseholds living in period 2 is ln C2. The government lives for 2 periods and has accessto the world financial market, where the interest rate is 10 percent r
∗ = 0.1. Government
spending is 2 in both periods (G1 = G2 = 2). The government levies lump-sum taxes inperiods 1 and 2, denoted T1 and T2, respectively. Finally, assume that households and thegovernment start their lives with no debts or assets.
(a) Suppose that T2 = 1. Calculate T1.
(b) Find the primary fiscal surplus in period 1.
(c) Calculate consumption in periods 1 and 2.
(d) Calculate the trade balance and the current account in period 1 (T B1 and CA1).5. (20 points) [Global Saving Glut] Some observers argue that the shrinking of the U.S. currentaccount deficit during the Great Recession of 2008 from 6 percent of GDP to 3 percent ofGDP was the result of a reverse Global Saving Glut. Critically evaluate this argument.2

Math Problem Sample Content Preview:
Your name
Subject and Section
Professor’s Name
May 9, 2020
Final Examination – Econ UN3213
1
1 True. In the long run, a country will be able to control its high inflation with high interest rates through the country’s monetary policies. Increasing the interest rates will help reduce the aggregate demand in the economy. The economy will have a slow growth and will lead to lower inflation. Higher interest rate reduce will make the consumers reduce their spending because first, high interest rate will increase the cost of borrowing which discourages the consumer from borrowing and spending. Second, higher interest rate will attract saving money. Third, it will reduce the disposable income of those with mortgages and lastly, higher interest rates will increase the value of the exchange rate leading to lower exports and imports.
2 True. because if the Ricardian theorem holds, even the upward pressures on the rates of interest in a closed economy would not crowd out investments.
3 True. Having a large and positive net foreign asset position, which is also equal to its gross foreign asset position means that the country is a lender in the international marketplace. Accordingly, the high price of domestic assets of the lender also means that it can also restrict the capability of foreigners to purchase assets within the country.
4 True. Current account deficits means that the value of imports of goods, services, and investment incomes is greater than the value of exports. This implies that the economy is relying too much on consumer spending leading to unbalances between different economies. Current account deficits indicates that the economy is uncompetitive and the exchange rate is relatively overvalued.
5 True. free trade in goods and services is desirable while free trade of financials services are not. The reason for this is because the first (current account liberalization) have a lot of benefits such as higher rate of return for the people’s money, free trade of financial services could impose a lot of risk especially in light of the enormous development gap between the US and other countries.
6 Uncertain. One of the ways for the Fed to respond to a positive supply shock is not by increasing, but rather decreasing interest rates. This would help the whole economy to invigorate the aggregate demand. However, this also posits the problem that decreasing interest rates could cause higher inflation. Even though this can help respond to the positive supply shock, this can worsen the economy.
2
7 Investment Demand Schedule
* MPK = MCK
* yi = MCK , y = A2I1α
* yi = (1 + r + δ)
* α A2I1α-1 = (1 + r + δ)
*
* Investment Demand schedule =
8 An increase in uncertainty about the level of technology (A2) can hamper investment demand due to the perceived increase in the cost of capital
9 An increase in uncertainty will result in lover equilibrium interest rate (r*) in response to the perceived decrease investment demand. This will redirect funds from saving to investment
10 Shocks are interchangeable with fluctuations and there are panic related shocks caused by uncertainty. How...
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