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.

1

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?

2

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.

3

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.

4

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.

2

5

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?

3

1 Math Review Problem 2 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 ...

93KB Sizes 0 Downloads 273 Views

Recommend Documents

Problem 1 Problem 2 Problem 3 -
roads through the forest are both extremely important, so a boy who reaches the age of manhood is not designated ... first hike is a 5 kilometer hike down the main road. The second hike is a 51. 4 kilometer ..... from one state to another with two cl

The Isoperimetric Problem - Penn Math
Mar 1, 2012 - with the assumption that a solution exists, that is, that there is a simple ... points of C which lies entirely (except for its endpoints) outside of C .

1 Site Zoning Vignette: 1 hour total 1 problem with 2 tasks Problem ...
General notes / Tips: • Exact problem w/ single answer. • Follow the program exactly. • Be aware of sun exposure planes; corner of building will likely be clipped.

Problem Set 1: C
Sep 17, 2010 - Simply email [email protected] to inquire; be sure to mention your full name, your ..... Now let's add those products' digits (i.e., not the products themselves) .... http://code.google.com/apis/chart/docs/gallery/bar_charts.html.

Problem Set 1: C
Sep 17, 2010 - on cloud.cs50.net as well as filling out a Web-‐based form, which may take a ... virtual terminal room) or lifting material from a book, website, or.

problem 1 -
The table PERSON contains the attributes namely driver_id, name & address ... The table CAR contains the attributes such as model, year & register number ..... The average order amount can be obtained by considering the total cost per order. ...... e

Problem Set 1: C
Problem Set 1: C due by 7:00pm on Fri 9/17. Per the directions at this document's end, submitting this problem set involves submitting source code.

problem 1 -
Hence ONO and INO act as the foreign keys for this relation. Warehouse : This relation contains information about the warehouses of the company. It keeps track ...

problem 1 -
This relation contains information about the warehouses of the company. It keeps .... COURSES OFFERED BY THE CS DEPARTMENT THAT USE MORE THAN.

1 Problem -
Page 1. 1 Problem. Find the solution of the following differential equation: dy dx. + ycotx = 2x + x2cotx x = 0, given y = 0 when x = π. 2. 1.

Problem Set 1: C
Sep 17, 2010 - Nor may you provide or make available solutions to problem sets to individuals who .... Simply email [email protected] to inquire; be sure to mention your full name, your ..... 21 http://www.nist.gov/dads/HTML/greedyalgo.html .... Anyhow,

problem 1 -
The table PERSON contains the attributes namely driver_id, name & address where ... The table CAR contains the attributes such as model, year & register number ...... each attribute is given a name, a data type to specify its domain of values ...

Review Unit Math 3 Exam Review #1.pdf
Review Unit Math 3 Exam Review #1.pdf. Review Unit Math 3 Exam Review #1.pdf. Open. Extract. Open with. Sign In. Main menu.

Math Problem Solving Worksheet.pdf
Washington. has 120 state parks. Which state has. more state parks? 2. John Kennedy became president. when he was 43 years old. George W. Bush became ...

An Incentive Solution to the Peer Review Problem
the Internet has brought forward. Some people review quickly, while ... that his next submission sits in the editorial office for ten weeks before being sent out for ...

The symbol-grounding problem in numerical cognition A review of ...
The symbol-grounding problem in numerical cognition A review of theory evidence and outstanding questions.pdf. The symbol-grounding problem in numerical ...