Kyoo il Kim Department of Economics University of Minnesota

Introduction to Econometrics, Econ4261 Spring 2013

P ROBLEM S ET 1 (D UE F EBRUARY 7, T HURSDAY IN CLASS )

Answer the Followings 1. Calculate: a) E[X], E[Y ] b) V ar[X], V ar[Y ] c) Cov[X, Y ] d) ρ(X, Y ) from the distribution below Y =1 X = 5000 X = 10, 000 X = 15, 000 0 1/8 1/3 Y =0 1/4 1/8 1/6 (1)

2. Suppose E[X] = 1 and E[Y ] = 2 and suppose X and Y are independent. Evaluate: a) E[2X + 1] b) E[X + Y ] c) E[X − 2Y ] d) E[XY + 1] 3. Suppose V ar[X] = 2, V ar[Y ] = 1, Cov[X, Y ] = 0. Evaluate: a) V ar[X + 2Y ] b) V ar[X − Y ] c) Cov[2X − Y, X − 1] n

i=1 [Xi

4. Suppose c)

n

i=1 Xi

= 2 and

+ 2]

n

i=1 Yi

= 3. Evaluate: a)

n

i=1 [Xi

+ Yi ]

b)

n

i=1 [Xi

− 2Yi ]

5. Let X = 1 with n = 100. What is

6. Show that V ar[X] = E[X 2 ] when E[X] = 0.

n

i=1 Xi ? What is

n

i=1 [Xi −X]? and What is

n

i=1

X +1 ?

7. Show that Cov[X, Y ] = E[XY ] when E[X] = 0 or E[Y ] = 0. 8. Suppose V ar[X] = 1, V ar[Y ] = 2, V ar[Z] = 2, Cov[X, Y ] = 0, Cov[X, Z] = −1, and Cov[Y, Z] = 2. Obtain V ar[X − Y + 3Z] 1

9. Show that (a) (b)
n n
i=1 (Xi i=1 (Xi

− X)2 =

− X)(Yi − Y ) =

n

2 i=1 Xi

10. Let b be an estimator of β. The Mean Squared Error is deﬁned as M SE(b) = E[(b − β)2 ]. Show that M SE(b) = V ar(b) + bias2 (b) = E[(b − E[b])2 ] + (E[b] − β)2

n

−X

i=1 Xi Yi

n

i=1 Xi

=

−X

n

n

2 i=1 Xi

i=1 Yi

=

n

− nX

2

i=1 Xi Yi

− nXY

11. Do questions 2.6, 2.10, 2.15, 2.24 in Stock and Watson 12. Do questions 3.3, 3.6, 3.10, 3.13, 3.19 in Stock and Watson

...ProblemSet11. (Star Wars) Real GDP = 461.0(214.5/60.6) = 1,631.76
(E.T.) Real GDP = 399.9(214.5/96.5) = 888.90
(Titanic) Real GDP = 600.8(214.5/160.5) = 802.94
(Shrek 2) Real GDP = 437.2(214.5/188.9) = 496.45
(Avatar) Real GDP = 760.5(214.5/214.5) = 760.5
Real GDP in Order of Largest to Smallest
Movies
Nominal
Box Office Receipts (millions)
CPI in Year Released
Real Box Office Receipts (millions)
Star Wars (1977)
461.0
60.6
1,631.76
E.T. The Extra-Terrestrial (1982)
399.9
96.5
888.90
Titanic (1997)
600.8
160.5
802.94
Avatar (2009)
760.5
214.5
760.50
Shrek 2 (2004)
437.2
188.9
496.45
2. Classify each of the following as employed, unemployed, or not in the labor force.
a. Juanita has two part-time jobs but hopes to get one full-time job instead.
EMPLOYED
b. Bob teaches 1 class at the University at night and volunteers 20 hours a week at the hospital.
EMPLOYED
c. Jaime babysits her younger sister while her mother works.
NOT IN THE LABOR FORCE
d. Emma is retired. She volunteers at the library 10 hours each week.
NOT IN THE LABOR FORCE
e. Alex is 15 years old and hopes to find a part-time job soon but has not applied anywhere.
NOT IN THE LABOR FORCE
f. Rolando is not working but he has submitted an application to work at the local grocery store and is available to start work immediately.
UNEMPLOYED
3. Use the following data to calculate (a) the labor force participation rate, (b) the unemployment...

...ProblemSet1Problem1
Which project should the firm select? Why?
Project B: Managers should try to maximize their stock’s intrinsic value while also bringing in revenue. The P/E ratio shows the dollar amount investors will pay for $1 of current earnings.
Problem 2
If most investors expect the same cash flows from Companies A and B but are more confident that A’s cash flows will be closer to their expected value, which company should have the higher stock price? Explain.
The primary goal of a corporation should be to maximize its owner’s value. If a manager is to maximize shareholder wealth, he/she must know how that wealth is determined. Fundamentally, shareholder wealth is the number of shares outstanding at times the market price per share. A stock’s price at any given time depends on the cash flows a “marginal” investor expects to receive after buying the stock. With that being said, Company A’s cash flow would increase the stock price and the risk would be minimal. Management’s goal should be to make decisions designed to maximize the stock’s price.
Problem 3
The president of Southern Semiconductor Corporation (SSC) made this statement in the company’s annual report: “SSC’s primary goal is to increase the value of our common stock holders’ equity.” Later in the report, the following announcements were made:
a. The company contributed...

...INSTRUCTIONS: You must show all of your work where calculations are required and you must include a brief explanation of approximately 50 words for each answer to receive full credit:
1. Markets, Demand and Supply, part 1 (10pts):
a. What effect will each of the following have on the DEMAND for coffee (i.e. Increase Demand, Decrease Demand, or NO CHANGE)? You must include a brief explanation of approximately 50 words for each answer to receive full credit:
i. There is an increase in the price of coffee.
(a) Increase in Demand for coffee. In general, an increase in price of coffee will engender a concomitant decrease in demand. Also of importance is the amount of this change in demand and the affect on total revenue. These changes (demand and total revenue) will be determined by the price elasticity of demand.
ii. There is an increase in the price of tea, which consumers view as a substitute for coffee.
(a) Increase in the Demand for Coffee. In general, an increase in the price of tea will engender a concomitant increase in the demand for coffee. As a close substitute
iii. There is an increase in consumer incomes, assuming coffee is a normal good.
iv. There is a decrease in the number of consumers who buy coffee.
b. What effect will each of the following have on the SUPPLY of soybeans? (i.e. Increase Supply, Decrease Supply, or NO CHANGE)? You must include a brief explanation of approximately 50 words for each answer to...

...YOUR TAs NAME:___________________________ YOUR DISCUSSION #_____________
THE GEORGE WASHINGTON UNIVERSITY
Department of Economics
Economics 011
Section 14
Prof. Steve Suranovic
Fall 2012
ProblemSet #2 – Answers
Answer all of the following questions from the book and those below. HW #2 is due in class on
Wednesday Feb 22nd .
A. Questions from Text and Readings
R&T Chapter 2-5 (online), Chapter 2.4 Review and Practice (in printed textbook);
Concept Problems 2, 3;
(for Extra Practice complete Numerical Problems1 – 5 (not required for HW1))
CP2. Why does the downward-sloping production possibilities curve imply that factors of
production are scarce?
CP2. A downward-sloping production possibilities curve shows that in order to obtain
more of one good (or service), another must be forgone. That is the meaning of
scarcity—the situation where we are forced to choose among alternatives.
CP3 In what ways are the bowed-out shape of the production possibilities curve and the law of
increasing opportunity cost related?
Answers to Extra Practice Numerical Problems
Numerical Problems1.
a. The production possibilities curve is a straight line from a point at twenty trees per
day on the vertical axis to four lawns per day on the horizontal axis.
b. Nathan must forgo 1/5 of a lawn mowed for each tree he plants.
c. Mowing a...

...ProblemSet1
Name: Christen Brown
ProblemSet1 is to be completed by 11:59 p.m. (ET) on Monday of Module/Week 2.
1. Based on the information provided for the market for video games, answer the following questions.
PRICE
Q DEMANDED
Q SUPPLIED
$50
5
9
$45
7
7
$40
9
5
$35
11
3
$30
13
1
a.) Draw and properly label the demand and supply graphs (this means you must label the axes and any lines you include on the graph).
b.) What is the equilibrium price and quantity?
a.)
b.) PRICE: $45.00 QUANTITY: #7
Now, assume that a new government report claims that video game play stimulates the brain.
c.) What will this do to the demand curve? Of the available list of things in the text that causes a change in demand, which best fits here as the cause of the demand shift?
d.) What will happen to the equilibrium price and quantity?
c.) With claims that the video game is stimulating, the demand curve will shift to the right. Of all the reasons for change in demand listed in our text, the one that best describes this situation is changes in consumer tastes and preferences. This fits most appropriately because it describes changes due to new information. In this situation with the video game, the government released new, positive information to the consumers, which increased demand.
d.) P: The price will increase. Q: The equilibrium quantity will increase....

...73-240 | Recitation A
ProblemSet1Problem1: Nominal GDP, Real GDP, Price Indices, and Inflation
A. Nominal GDP in Year 1 = $430
Nominal GDP in Year 2 = $617.50
Growth Rate of Nominal GDP = 44%
B. RGDP(1) in Year 1 = $430
RGDP(1) in Year 2 = $410
RGDP(1) growth = -4.65%
RGDP(2) in Year 1 = $655
RGDP(2) in Year 2 = $617.50
RGDP(2) growth = -5.73%
The answer differs depending on which base year you use because the relative prices of the goods in comparison to each other (price of coffee in relation to price of donuts), and thus different ratios are being worked with depending on which year you choose, meaning the answer will be different.
C. Nominal GDP in Year 1 = $430
Nominal GDP in Year 2 = $617.50
RGDP(1) in Year 1 = $430
RGDP(1) in Year 2 = $410
GDP Deflator in Year 1 = $430/$430 * 100 = 100
GDP Deflator in Year 2 = $617.50/$410 * 100 = 150.6
Rate of Inflation = 50.6%
D. CPI(1) in Year 1 = $430/$430 * 100 = 100
CPI(1) in Year 2 = $655/$430 * 100 = 152.3
CPI Based Rate of Inflation = 52.3%
E. These are different because in C what you’re measuring is the change in quantities across years, and in D you’re looking at the change in prices across the years, keeping the...

...PROBLEMSET # 1
Instructions:
1) Open book, open notes limited to only class materials.
2) Unlimited time.
3) This must be reflective of your individual effort. GMU Honor Code applies.
4) The ProblemSet #1 (only the question solutions portion) is due at the end of the day on September 24th.
5) Show all work, as partial credit will be given for each question’s answer. Organize your work so it is easy to follow. You can use word, power point, excel or combinations of the above.
6) Return the Solutions pages to be graded. Put a copy in the course folder and send me an electronic copy that I will grade and return to you along with the approved solution.
7) The exercise is worth 100 points.
8) GOOD LUCK
Name: ________________________________
1) You are savings for the college education of your two children. They are two years apart in age; one will begin college 15 years from today and the other will begin 17 years from today. You estimate your children’s college expenses to be $21,000 per year per child, payable at the end of each school year. The annual interest rate is 15%. Your deposits begin one year from today. You will make your last deposit when your oldest child enters college. (15 points)
How much money must you deposit in an account to fund your children’s...

...ProblemSet1
Macroeconomics, ECON 2123
(Instructor: Partha Sen; TA: Peter Tsui)
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Posted: Friday, 19 September 2014
Due: 5:00 PM Friday, 26 September 2014
(Submit your homework into the homework collection box outside the department office)
100 marks total
Part I: True/False/Uncertain (20 marks, 4 marks each)1. GDP is the value of all goods and services produced in the economy during a given period.
2. When disposable income equals zero, consumption equals zero.
3. The multiplier is greater than 1 if T = 0 and G = 0.
4. Paradox of saving occurs when the attempts by people to save more lead to a decline in output and an increase in saving in the short run.
5. When MPC (marginal propensity to consume) increases and investment decreases, goods market equilibrium output increases.
Part II: NATIONAL ACCOUNTS (25 marks)
For Part II, consider an artificial economy and assume the following:
1. Fill in the following table: (6 marks)
year
Output of Rice
Price (per ton of rice)
Nominal GDP
Real GDP
(in 1990 $)
Real GDP
(in 2000 $)
1990
600
1,000
2000
1800
10,000
2001
2,000
10,500
2002
2,200
11,500
2. Find the growth rate of real GDP (using 2000$ as common price) for 2001 and 2002. (Express as percentage change and round to the nearest tenth, i.e.,...