Consider the two period endowment economy in the Macro Review slides: a household is endowed with Q1 units of goods in p
EC442 Problem Set 1 Ling Zhu, University of Maryland Due at the beginning of the class on Wed, Feb 05, 2013
Warning: answers without derivation or explanation receive no credit. If you work in groups, you still need to hand in an independent write-up. Identical write-ups will receive no credit. Also remember to put down the names of your group-mates.
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Math Review Problem
Make sure you understand all the material in the math review slides before working on the first problem. Constrained Optimization a. Solve for {x, y} in terms of {a, b, c}: max ln(x) + a ∗ ln(y)
(1)
x + y/b = c
(2)
{x,y}
subject to
b. What happens to the solution {x, y} you find in the last question if ab = 1?
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Macro Review Problem
Consider the two period endowment economy in the Macro Review slides: a household is endowed with Q1 units of goods in period one and Q2 units of goods in period two. The goods are perishable, hence the household cannot store the endowment from period one to be consumed in period two. However, the households could save/borrow from each other by buying/issuing domestic bonds at real interest rate rd in period one. All loans are settled in period two and no new loans are issued in period two since the world ends after period two. Let household’s utility over the two periods be U (c1 , c2 ) = ln(c1 ) + βln(c2 ), where β is called the discount factor (it discounts tomorrow’s utility to today’s value). Answer the following questions: Basic Model Set-up a). set up the first period consumer budget constraint; b). set up the second period consumer budget constraint; c). derive the intertemporal consumer budget constraint; d). solve for household’s optimal choice of {c1 , c2 , b1 } in terms of the variables {rd , β, Q1 , Q2 }; 1
e). write down the market clearing conditions; f). solve for the real interest rate rd in terms of exogenous variables {β, Q1 , Q2 }; g). express the equilibrium levels of {c1 , c2 , b1 , rd } in terms of {β, Q} if Q1 = Q2 = Q Experiments h). compared to your findings in g), what happens to equilibrium levels of {c1 , c2 , b1 , rd } if Q1 = Q − ∆ where ∆ > 0 while Q2 = Q; i).compared to your findings in g), what happens to equilibrium levels of {c1 , c2 , b1 , rd } if Q2 = Q−∆ where ∆ > 0 while Q1 = Q; j).compared to your findings in g), what happens to equilibrium levels of {c1 , c2 , b1 , rd } if β goes up while Q1 = Q2 = Q; k). describe any insights or conclusions you learn from experiments h-j.
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Accounting of Current Account
Describe how each of the following transactions affects the U.S. Current Account Balance. (a) An American university buys several park benches from Spain and pays with a $120,000 check. (b) Floyd Townsend, of Tampa Florida, buys 5,000.00 dollars worth of British Airlines stock from Citibank New York, paying with U.S. dollars. (c) An American company sells a subsidiary in the United States to a Chinese company and with the proceeds buys a French company. (d) A group of American friends travels to Costa Rica and rents a vacation home for $2,500. They pay with a U.S. credit card. (e) The United States forgives debt of $500,000 to Nicaragua.
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Empirical Exercise
You need to find data online to answer the following two questions. Navigating through the websites and finding the proper dataset is part of the assignment. 4.1 Current Account Balance of U.S. Replicate Table 1.1 in the notes by Stephanie Schmitt-Grohe and Martin Uribe for years 2007, 2009 and 2011. You can find both the current account data and GDP data from http://www.bea.gov. 4.2 Net International Investment Position of U.S. Find the data for Net International Investment Position of U.S for years 2007, 2009 and 2011. You should observe that despite U.S. has negative net international investment position in 2007, 2009 and 2011, its net investment income is positive. Explain how could net investment income be positive when the country has a negative net international investment position. 4.3 Current Account Balance and Trade Balance of Selected Countries Replicate Table 1.2 in the notes by Stephanie Schmitt-Grohe and Martin Uribe for years 2007 and 2009. You can find data from http://www.worldbank.org. You do not need to comment on the data for this question.
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Quantitative Exercise
Make sure that you understand the accounting identities of current account well before working on the last problem. Banana Republic (fictional) was a small Island in the middle of the Pacific Ocean. Due to global warming, the island was submerged by water at the end of 2012. So Banana Republic ceased to exist at the end of 2012. At the end of 2010, Banana Republic held a positive net foreign asset position of $1 Billion. The prevailing world interest rate is 5% from 2010-2012. Banana Republic produced $.5 Billion worth of bananas and run a trade deficit of $1 Billion in 2011. No domestic investment was made in Banana Republic in 2011. Furthermore, Banana Republic had zero net international compensation to employees, zero net unilateral transfer, and no government expenditure. Answer the following questions: a). How much was domestic consumption of Banana Republic in 2011? b). How much would Banana Republic’s net foreign asset position be at the end of 2012 if the rest of the world knew in advance that the island would be submerged by water at the end of 2012? c). How much was Banana Republic’s net investment income in 2011? d). How much was the national income of Banana Republic in 2011? e). What was the level of national saving in Banana Republic in 2011? f). How much was Banana Republic’s net foreign asset position at the end of 2011? g). How much was the current account balance in 2011? h). Would Banana Republic run a current deficit or surplus in 2012, and how much would it be? i). Would Banana Republic run a trade deficit or surplus in 2012, and how much would it be? j). How would your answers to questions in parts h and i change if Banana Republic ended up with a trade deficit of $1.2 Billion in 2011 instead?
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