QUIZ 1: Macro – Fall 2014
Name: ___ANSWERS____________
Section Registered:
Tuesday a.m
Tuesday p.m
Wednesday a.m.
Question 1 (6 points total - 3 points each)
Suppose you are given the following data for the labor market status of individuals (over the age of 16) in
an economy. For this problem, grades will either be 3 or 0 for each part (no partial credit). However, we
do want to see your work to get full credit.
75 million people are employed full time
15 million people are employed part time
20 million people are retired
8 million people are students
12 million people are disabled
10 million people are unemployed
25 million people are in the "other" labor market category
A. Given the above information, what is the labor force participation rate for this economy (for
individuals over the age of 16)? Express your answer in XX.XX%.
Labor force participation = labor force/ population where labor force = employed + unemployed
This measure gives us an idea of who is currently in the employment ranks and who is actively trying to
join the employment ranks/ still has some attachment to the labor market.
Start by calculating the population: 75+15+20+8+12+10+25 = 165 million
Total employed: 75 + 15 = 90 million (we count both the full time and part time employed)
Total unemployed: 10 million (this was given)
Putting it together the labor force participation rate = (90+10)/165 = 60.60%
B. Given the above information, what is the employment rate for this economy? Express your
answer in XX.XX%.
In comparison, this measure reports who is actively in the employment ranks now.
Employment rate = employed/ population where employed = full-time employed + part-time employed
Start by calculating the population: 75+15+20+8+12+10+25 = 165 million
Total employed: 90 million (see above)
Putting it together the employment rate = (90)/165 = 54.55%
From Carolyn: At home exercise: How do we think about search intensity in this economy? Are
discouraged workers a problem in this economy?
Question 2 (4 points total)
For the statement below, assess whether it is True, False or Uncertain. Your explanation determines the
entire grade. If you state "true" and provide no support for your answer, you will receive no credit even if
your answer is true. Given the nature of this question, your explanation should include the mathematical
definition of the marginal product of labor. Your answers should not be more than 4 sentences total
(where an equation counts as a sentence). An ideal answer could include one equation and one sentence.
According to the Cobb-Douglas production function, doubling both capital (K) and labor (N) will double
the marginal product of labor (MPN). Assume that TFP (A) is held fixed when answering this question.
Let’s start with our Cobb-Douglas production function:
Y=AK0.3N0.7
Now, take the partial derivative with respect to N to get an expression for MPN (you all should know how
to derive this identity, you’ll be using it a lot in the weeks to come!)
MPN = 0.7A(K/N)0.3
Let’s say K/N originally was 1. If we double both K and N, K/N is still 1 so, there is no change in MPN
(holding A fixed). This is the constant returns to scale assumption embedded in the Cobb-Douglas
production function. So, this answer is definitely false.
Suppose, we only double K (holding N fixed). This is a different question, but still worth exploring.
Continuing our example from above, now K/N = 2 (if it was 1 before, it is now 2). What happens to
MPN? By scaling K/N by 2, MPN only scales by a factor of 20.3 which is strictly less than 2. So, while
MPN increases, it increases by a factor less than 2. Here is the intuition: because of diminishing
marginal product of capital, if the capital intensity of an economy increases, without increasing TFP, the
marginal benefit of the extra capital gets smaller and smaller over time. This means the extra effect of
capital on worker productivity is getting smaller and smaller over time. Diminishing marginal product of
capital is why an increase in the capital to labor ratio does not increase the marginal product of a worker
one-for-one. So, when countries try to grow only by increasing K/N, the effect on MPN diminishes over
time.
Question 3 (6 points total - 3 points each)
For this problem, grades will either be 3 or 0 for each part (no partial credit). However, we do want to see
your work to get full credit.
Below, column 1 shows the nominal level of the Case-Shiller Price Index for the Chicago MSA in June
2000, June 2007, and June 2014. Column 2 shows the CPI for the entire U.S. for the same time periods.
2000
2007
2014
a.
Case Shiller Index
106.08
165.94
129.94
CPI
172.2
207.2
237.9
Deflating by the U.S. CPI, what was real average annual house growth in Chicago between
June 2000 and June 2007. Make sure your answer is presented as an average annual growth rate
- adjusted for compounding. Additionally use the exact formula to compute real growth.
Let’s get started by getting the 2007 C-S Index in real 2000$:
165.94*(172.2/207.2) = 137.91.
The 2000 C-S Index is already in 2000$.
Now compute the real growth rate between 2000 and 2007: (137.91-106.08)/106.08 = 30.01%
Now, we want to annualize the growth rate over the seven year period. Basically, you are asking what
annual growth rate (compounded over seven years) gives you 30.01% over seven years.
annualized real growth = (1+real growth rate)1/7-1
=(1+.3001)1/7-1 = 3.82%
According to the C-S index, real growth rate of housing in Chicago between 2000 and 2007 was 3.82%
per year (smaller than Las Vegas but higher than Des Moines).
b.
Deflating by the U.S. CPI, what was real average annual house growth in Chicago between
June 2000 and June 2014. Make sure your answer is presented as an average annual growth rate
- adjusted for compounding. Additionally use the exact formula to compute real growth.
Let’s get started by getting the 2014 C-S Index in real 2000$.
129.94*(172.2/237.9) = 94.05
Now compute the real growth rate between 2000 and 2014: (94.05-106.08)/106.08 =-11.34 %
Now, we want to annualize:
annualized real growth = (1+real growth rate)1/14-1
=(1-.1134)1/14-1 = -0.86%
Real house prices in Chicago - according to the Case Shiller index fell slightly over the last 14 years.
Question 4 (4 points)
In Jeff Sommer's NYT's article "Getting Creative with GDP" (July 23, 2013), the article talked about
changes in the measurement of one country's GDP calculation in July of 2013. Your task is simple. Name
the country and tell how the measurement of GDP changed.
Your answer should not be more than 12 words (including a country name). (Note: my total answer will
include only 7 words). Remember our goal is to just get a sense if you are reading the articles. You do
not need to write an essay on the details of the change. Just name the country and tell what broad change
was made to changing GDP. If you are in the ball park, you will get full credit.
The U.S.: We changed the way we measured intangible capital.
From Carolyn: For those of you who are particularly interested in intangible capital and growth
accounting, you can also check out Corrado, Hulten and Sichel (2009), a Fed paper about this.
http://www.conference-board.org/pdf_free/IntangibleCapital_USEconomy.pdf