QUIZ 1: Macro – Winter 2014
Name: __ANSWERS______________
Section Registered:
Friday a.m
Friday afternoon
Saturday a.m.
Question 1 (11 points total)
For parts A and E, put your answers in the boxes provided. For parts B, C, and D, circle the answer that
is correct. For this problem, there is only one correct answer to each question stem.
Suppose the economy is represented by the following aggregate production function:
1
Y    K 0.45 N 0.55
 A
A. Given the above production function, what is the expression for the marginal product of labor? (3
points)
Put answer in box
To solve for the MPN, take the partial derivative of the
Aggregate production function with respect to N.
0.55(1/A)(K/N).45
Some of you report not knowing how to take derivatives. Again, this production function is nearly
identical to the one we did in class. For that one, I told you to memorize the marginal product of capital.
To make the analogy simpler, define A' = (1/A). In that case, the above production function can be
expressed as:
Y  A ' K 0.45 N 0.55
This production function is the same as you used in class aside from A' = (1/A) and the coefficients on
capital and labor changed (although they still both sum to 1).
Given that, you should have been able to use what you memorized in class to write the marginal product
of labor as:
Y
K
 0.55 A '  
N
N
0.45
[Note, to get the answer above, just re-substitute A'=(1/A)]
The only way this differs from what we did in class is the coefficient on labor which shows up out in front
changed from 0.7 to 0.55 and the coefficient on the capital-labor ratio changed from 0.3 to 0.45 (because
the coefficient on capital changed from 0.3 to 0.45).
Some people get scared of math. However, this question was all intuition and knowing how to express
the marginal product of labor for the Cobb-Douglas production function. Even if you didn't know any
calculus, you should have been able to answer this question using what you learned.
B. Given the above production function, which of the following is true: (2 points)
When we think about returns to scale, we want to think about what happens if we increase all
variable (non-technology) inputs proportionately.
Consider the above production function Y = (1/A)K0.45N0.55 .
Suppose A, K, and N all equal 1. If that is true, then Y = 1. Now, suppose we double K and N
such that K=N=2. In that case, we get Y = 2. A doubling of all variable inputs resulted in a
doubling of output (holding TFP constant). If Y more than doubled when we double both K and
N, we would refer to this as "increasing returns to scale". If Y less than doubled when we double
both K and N, we would refer to his as "decreasing returns to scale".
Here is a rule for determining whether a production function determines increasing, decreasing or
constant returns to scale. Suppose we can express the production function as follows:
Y = AKαNβ
If we change K and N by some factor X, we can re-express the production function as
Y = A(X*K)α(X*N)β
Using some simple algebra, we can also write this expression as:
Y= (X)α+β *AKαNβ
Constant returns to scale exists when α+β = 1 (an increase in K and N by X will increase Y by
exactly X).
Increasing returns to scale exist when α+β > 1
Decreasing returns to scale exists when α+β < 1
Given this, you can answer the question.
a.
b.
c.
d.
There is constant returns to scale in production (XX)
There is decreasing returns to scale in production
There is increasing returns to scale in production.
You cannot tell about the returns to scale in production.
C. Given the above production function, which of the following is true: (2 points)
From the expression MPN = 0.55(1/A)(K/N)0.45 if you increase A, MPN will fall. An increase in
technology with this production actually reduces the marginal product of labor. In other words,
with this production function, workers become less valuable as technology increases. This is how
we define "substitutes" in production. See supplemental notes (3) for more details.
Likewise, an increase in K will increase the marginal product of a worker (given this production
function). Given this, we say K and N are complements. This is how we define complements in
production. See supplemental notes (3) for more detais.
a. TFP and labor are complements
b. TFP and labor are substitutes
c. TFP and labor are neither complements nor substitutes
D. Given the above production function, which of the following is true: (2 points)
a. Capital and labor are complements
b. Capital and labor are substitutes
c. Capital and labor are neither complements nor substitutes
E. Given the above production function, what is the labor share of income? Your answer should be
a numerical value. (2 points)
Put answer in box
This comes from the exponent on N in the production function.
55%
This came directly from the class and supplemental notes.
Question 2 (3 points)
Use the available information to infer the annualized nominal interest rate on a three year loan
starting two years from now (i2,5).
Nominal interest rate on one year loan starting today (i0,1):
Nominal interest rate on two year loan starting today (i0,2):
Nominal interest rate on three year loan starting today (i0,3):
Nominal interest rate on five year loan starting today (i0,5):
0.11%
0.40%
0.79%
1.64%
To answer this question, you need to exploit the information provided within the yield curve. This
question is similar to the question asked on most of the recent practice quizzes. Given this, the question
will be graded on the 0/3 scale. No partial credit will be given (although, we would like to see your work
how you came to your answer). Either the answer is correct or not. Take care to make sure you do not
make any simple math mistakes. Put your answer in the box provided. Express your answer in X.XXX%
form. Hint: You can answer this problem using one equation where there is one unknown.
Arbitrage implies:
(1+ i0,5)5=(1+i0,2)2 (1+i2,5)3
Plugging in (1+.0164)5=(1+.0040)2(1+i2,5)3
2.475%
So i2,5 = (1.0761)1/3 – 1 = .02475 or 2.475%
As an investor, you should be indifferent between investing in a five year security starting in year 0
(today) or investing in a 2 year security in year 0 (today) and then re-investing in a three-year security
beginning in year 2 and ending at beginning of year 5.
Question 3 (3 points)
In class, we talked about how – in practice – economists often measure TFP. Briefly describe the process
we use to measure TFP (within a country over time or across countries at a given point in time). Your
answer should be no more than 2 well-constructed sentences.
In practice, economists often measure TFP by running the following regression which follows from
taking logs of the Cobb-Douglas production function: Y = ANαKβ:
ln(Y) = ln(A) + α ln(N) + β ln(K)
where Y, N and K are data (observed). To turn this into a regression, we simply add an error term and
estimate the regression using the observed data. A (our measure of TFP) is the residual from the
regression (i.e., the amount of GDP that is NOT predicted by N and K). Often, we also add other
control variables such as raw materials or education of the local labor force to the regression. The TFP
measure is still the residual from the regression.
As we will talk about in class, some researchers (like me) are trying to use models and data to infer the
importance of certain components to TFP. In particular, we are looking at the role of better labor market
allocation of minorities and women to contributing to U.S. productivity growth during the last 50 years.
Question 4 (3 points)
In “Will Obamacare Destroy Jobs?” (Economist, 8/21/2013), the article mentions that Obamacare will
require firms with 50 or more full-time employees to offer them affordable health insurance or pay a fine
of $2,000-3,000 per worker. The article then spoke about ways that firms can get around this law. What
did the article mention as the way in which firms can get around this aspect of the heath care law? Your
answer should be no longer than 12 words. My ideal answer was 8 words.
They reduce hours/ rely more on part-time labor.
[Note - this came directly from the readings. Moreover, it was in the first paragraph. Even if you didn't
read the whole article, this would have been obvious from the first part of the reading.]