Download QUIZ 2: Macro – Winter 2010 Name: Section Registered: Campus

QUIZ 2: Macro – Winter 2010
Name: ______________________
Section Registered: Campus
Evening
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.
a. Suppose that the annualized nominal interest rate on a five year bond starting today (i0,5) was
4.1%. Suppose that the annualized nominal interest rate on a three year bond starting today (i 0,3)
was 3.5%. Assuming returns are arbitraged across bonds of different maturities, the expected
annualized nominal interest rate on a two year bond starting three years from now (i3,5) will be:
i.
Less than 3.5%
ii. Between 3.5% and 4.5%
iii. Between 4.5% and 5.5%
iv. More than 5.5%
This was just like questions on the practice quiz. We know from arbitrage that investors
should be indifferent between investing in a five year security today (for 5 periods) or
investing in a three year security today (for 3 periods) and rolling over the proceeds when
the 3 year security expires into a new 2 year security at the expected interest between years
3 and 5. Specifically:
(1+i0,5)5 = (1+i0,3)3(1+i3,5)2
Given this, we can solve directly for i3,5:
i3,5
= [(1+i0,5)5/(1+i0,3)3]0.5 – 1
= [(1.041)5/(1.035)3]0.5 – 1
Given this, we get i3,5 = 5.01%
b. In a world where all contracts are indexed in nominal terms, an actual inflation rate that was
higher than the expected inflation rate will make:
i. Borrowers better off relative to lenders
ii. Lenders better off relative to borrowers
When actual inflation is higher than expected inflation, borrowers end up paying a lower
real return (real return = nominal return – inflation). Higher than expected inflation rates
redistributes wealth from lenders (who are made worse off) to borrowers (who are made
better offer). See lecture notes for full details.
c. According to our lecture last week, the annualized real appreciation rate of residential real
estate - averaged across U.S. states - between 1980 and 2000 was:
i.
Approximately 2% per year
ii.
Less than 2% per year
iii.
More than 2% per year
This came directly from the slides. The real return on housing both within U.S. states
(1980-2000) and across countries (1970-2000) averaged roughly 1.1% per year (much less
than 2% per year). See lecture notes for details.
d. According to the Cobb-Douglas production function, TFP (A) and labor (N) are:
i. Substitutes
ii. Complements
iii Neither substitutes or complements
This came directly from Supplemental Notes 2 (and was stressed in both last week’s lecture
and Friday night’s lecture).
The Cobb-Douglas production function assumes
complementarity between the inputs. That means, an increase in TFP makes labor more
valuable (from the firm’s perspective). This can be seen that the marginal product of labor
increases as A increases.
e. According to the Cobb-Douglas production function, a doubling of TFP (A) (holding K and N
constant), will:
i.
Cause the marginal product of labor to exactly double
ii. Cause the marginal product of labor to more than double
iii. Cause the marginal product of labor to less than double
From the lecture notes and supplemental notes, we know that:
MPN = .7 A (K/N).3
Taking logs of both sides, we get:
ln(MPN) = ln(.7) + ln(A) + 0.3ln(K) – 0.3ln(N)
This means that a 1% increase in A will lead to a 1% increase in the MPN. Likewise, a
doubling of A will double MPN (holding K and N constant).
This question was very similar to many of the questions on the practice quizzes. Even if you
did not think to take logs, you could have just figured this out yourself by plugging in
numbers. For example, suppose you initially set A, K, and N equal to 1. MPN will equal
0.7. If you increase A to 2 (double A) and you hold K and N constant, MPN will equal 1.4.
In other words, MPN will double from 0.7 to 1.4. This is validation by example. It is not as
elegant as a formal math proof, but it works none-the-less. You do not need to be math
geniuses to get a feel for math equations.
Question 2 (3 points): Suppose you are given the following information for an economy.
Suppose that the one year nominal interest rate, from today’s perspective, is set at 0%. Suppose
that the unemployment rate is currently 6% and suppose further that it is expected to remain at
that level for the next year. Suppose that the one year expected inflation rate, from today’s
perspective, is -4%. (Notice, the economy is expecting deflation.)
Lastly, suppose that the
expected one year growth rate in real GDP, from today’s perspective, is 3%.
Given the above information, what is the expected one year real interest rate in the economy,
from today’s perspective? Put your answer in the box. You must show your work to get full
credit. For simplicity, you should use the approximation formula. Note: Not all of the above
information may be needed to answer the question.
This was a very simple problem. From lecture, we know:
The expected real interest rate = nominal interest rates – expected inflation
Substituting in, we get the following:
=
=
0% - (-4%)
4%
The expected one year real interest rate in this economy is 4%. (The GDP growth and the
unemployment rate were irrelevant for this problem).
The reason I asked this question is to foreshadow some of the things we will do later in the
course (and to test if people knew the difference between real and nominal interest rates).
What was I trying to foreshadow? Why is deflation bad (relative to inflation)? Because,
when nominal interest rates are close to zero, deflation results in high real interest rates.
The way the Fed will usually fight high real interest rates is to lower nominal rates. But,
when nominal rates are close to zero and there is deflation, it becomes harder for the Fed to
stimulate the economy by lowering real rates.
Question 3 (4 points): In this class, we assume the Cobb-Douglas production function is a good
approximation of aggregate production. According to the Cobb-Douglas production function,
the economy wide labor demand curve will slope down. What economic concept (embedded in
the Cobb-Douglas production function) leads to a downward sloping labor demand curve?
Note: Your answer should be no more than 5-7 words (i.e., your answer is a 5-7 word phrase).
The answer, expressed succinctly, is only 5 words). We will not read anymore than 5-7 words.
Aside from this 5-7 word phrase, no additional explanation is needed.
Diminishing Marginal Product of Labor
Question 4 (3 points): In the Economist article entitled “Cycle Proof Regulation” (from
4/11/2009), Raghu Rajan (a Booth professor and former chief economist of the IMF) discusses
how the extent of regulation (imposed by government regulators) tends to be correlated with
economic conditions. According to the article – and referring to historical data - how is
regulation typically correlated with economic conditions?
Note: I am not asking what Raghu is proposing, I am asking how he views regulation to have
historically taken place in booms relative to busts. Your answer should be no more than 1
sentence (or phrase).
According to the article, policy makers often tighten regulation during busts and loosen
them during booms. During busts, the regulation is not needed because individuals are
already more risk averse. A very interesting article.