QUIZ 1: Macro – Winter 2012
Name: __SOLUTIONS_________________
Section Registered:
Tuesday a.m
Tuesday p.m
Wednesday a.m.
Question 1 (10 points – 2 points each)
For each of the following questions, CIRCLE the answer that makes the statement true. There is
only ONE true answer to each of the following question stems. When answering the question
consider the model of labor demand that we built in class. Also, assume that the capital stock (K) is
fixed and that exogenous variables (e.g., TFP and tax rates) only change when I tell you they change.
A. A permanent increase in TFP (A) today will unambiguously shift today’s labor demand
curve:
i.
To the right
ii. To the left
iii. Neither to the right or left.
Recall from Topic 2 and the Supplemental Notes 4, we said we can draw the labor demand curve
(Nd):
Nd = real wages (W/P) = marginal product of labor (MPN)
If we consider the Cobb-Douglas production function: Y = AK.3N.7, we can define:
MPN= .7A(K/N).3
From this identity, we can clearly see that increasing A will unambiguously increase MPN and
therefore shift the labor demand curve out (to the right). Furthermore, when the effects of a TFP
(A) increase are permanent, we also know that the labor supply (Ns) curve will unambiguously
shift in (to the left) from the income effect. We didn’t ask about the labor supply curve in this
problem – but, that will be important for next week.
B. A temporary increase in TFP today will unambiguously shift today’s labor demand curve:
i.
To the right
ii. To the left
iii. Neither to the right or left.
By the same logic as the previous question—an increase in TFP increases MPN which means
the labor demand curve must shift out. It is important to note that when increases in TFP (A)
are temporary, there will be no shift in the labor supply curve (by definition, a temporary
change is a change in which there is no income effect). Again, we will deal with the labor
supply curve next week on the quiz.
C. A permanent decline in real wages today will unambiguously shift today’s labor demand
curve:
i.
To the right
ii. To the left
iii. Neither to the right or left.
As discussed in Topic 2 and in Supplemental Notes 4, changes in capital (K) or TFP (A) will
shift the labor demand curve. Recall that we draw the labor market in {W/P, N} space.
Changes in labor stock (N) or real wages (W/P) will cause a movement along the labor
demand curve.
D. A temporary increase in labor income tax rates (tn) will unambiguously shift today’s labor
demand curve:
i.
To the right
ii. To the left
iii. Neither to the right or left.
Again, only changes in capital (K) or TFP (A) will shift the labor demand curve.
variables will affect the labor supply curve.
These
E. A permanent increase in labor income tax rates will unambiguously shift today’s labor
demand curve:
ii.
To the right
ii. To the left
iii. Neither to the right or left.
Again, changes in capital (K) or TFP (A) will shift the labor demand curve. This will be a change
in labor supply curve.
Question 2 (3 points)
In the article “Which one of these is not like the other” (from the Economist blog), research by
Alberto Cavollo and Roberto Rigobon (both of MIT Sloan) was discussed. Alberto and Roberto
are now computing alternative price indices for many industrialized countries (including the U.S.
and Argentina). How do they collect the prices used to compute their price index? Your answer
should not be more than 8 words (my preferred answer is one word).
Internet (or internet scraping or grocery prices on internet or even just grocery prices)
Question 3 (4 points):
As mentioned in class (and supplemental notes 2), we can use the yield curve to infer
expectations of inflation over time.
When doing this problem we will make the following
assumptions:

The one year real interest rate in all periods is zero (r0,1 = r1,2 = .. = r4,5 = 0).
Additionally, we will assume that there are no risk-premiums associated with U.S. Treasuries and
that the Treasury market in this economy is completely competitive such that any excess returns
offered by investing in one security over another will be arbitraged away.
Here is some information on the current yield curve in the U.S.
One Year Treasury (i0,1) =
0.14%
Five Year Treasury (i0,5) =
0.77%
Three Year Treasury starting two years from now (i2,5) = 1.11%
Given this information, what is the expected inflation rate in the U.S. between now and two
years from now (π0,2). (There is no need to annualize your answer – leave it as π0,2).
Hint: Write down the relevant arbitrage formula and solve for the missing variable (it will be one
equation and one unknown. This is nearly identical to the questions on the practice quizzes).
Express your answer to at least three significant digits (i.e., x.xx%).
We want to solve for π0,2 and we know i0,5, i2,5 but we don’t know i0,2. We have a tool we can
use to find i0,2 (I even gave you a hint in the set up).
Arbitrage implies:
(1+ i0,5)5=(1+i0,2)2 (1+i2,5)3
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 in year 5.
Using the arbitrage equation above, we can solve for i0,2:
(1.0077)5 = (1+i0,2)2 (1+0.0111)3
1.0391 = (1+ i0,2)2(1.0337)
i0,2= 0.0026
From the assumptions, we know that r0,2 = 0 and that ρ0,2 = 0. This implies that
i0,2 = π0,2 = 0.0026 or 0.26%
That was the only tricky part of this question!
Put Answer Here
0.26%
Question 4 (3 points)
Consider the following information.


The June CPI in 1980, 2000, and 2012 were, respectively: 82.5; 172.2 ; and 228.6
Nominal wages of non-college men in June of those same years were, respectively: $6.50
per hour ; $11.00 per hour ; and $12.00 per hour.
What were the real wages of non-college men in 1980? Report your answer in terms of June20012 dollars.
Let’s first anchor our price indices in 1980 by dividing each year’s June CPI by 82.5 so we get:
June 1980/June 1980 = 1
June 2000/June 1980 = 172.2/82.5 = 2.087
June 2012/June 1980= 228.6/82.5 = 2.771
So once we normalize in this fashion, we can say real wages in June 1980 in terms of
June 1980 dollars = June 1980 nominal wages / (June 1980 prices/June 1980 prices) = $6.50/1 =
$6.50
In this question, we have asked you for real 1980 wages in terms of June 2012 dollars.
So let’s take that real wage number we just computed and scale it up by the 2012/1980
conversion factor that we calculated when we normalized the index:
(June 1980 nominal wages)/(June 1980 prices/June 1980 prices) * (June 2012 prices/June 1980
prices)
Plugging in:
($6.50/1) *(228.6/82.5) = $6.50 * 2.771 = $18.01
Put Answer Here
$18.01