QUIZ 2: Macro – Winter 2008
Name:
______________________
Question 1(6 points)
As macroeconomists, we often use the yield curve to back out the market’s expectation of future
inflation rates. In this question, we will see how this is done.
Suppose we are given the following data on U.S. Treasuries for January 18 th, 2008 (using the
same notation we developed in class) where period 0 is today and period 1 is one year from now
(etc.):
Current annualized one year Treasury rate starting today (i0,1) = 2.7%
Current annualized two year Treasury rate starting today (i0,2) = 2.3%
Current annualized three year Treasury rate starting today (i0,3) = 2.4%
Also, for tractability, we will make the following assumptions:
1) Today’s annual real interest rate (r0,1) = 0.5%
2) Expected future annual real interest rates are constant such that: r0,1 = r1,2 = r2,3
3) There are no risk premiums associated with any Treasury security in this economy
such that ρ0,1 = ρ1,2 = ρ2,3 = 0.
4) The Treasury market in this economy is completely competitive and any excess
returns offered by investing in one security over another will be arbitraged away.
Given, the above information, what is the market’s expected one year inflation rate between
period 2 and 3 (π2,3)? You must show your work to receive full credit. Hint: Write down the
relevant 3-period arbitrage formula and solve for the missing variable. There are many relevant
3-period arbitrage formulas. One of them will make your analysis much simpler!
We did this in class.
(1+i0,3)3 = (1+i0,2)2(1+i2,3)
(1+i0,3)3/ (1+i0,2)2 – 1 = i2,3
i2,3 = 0.026
π2,3 = i2,3 – r2,3 (using an approximation formula)
π2,3 = 0.021 (or 2.1%)
Using the actual formula, the answer is essentially the same
π2,3 =(1+ i2,3) /(1+ r2,3) – 1 = 2.09%
Question 2 (10 points total – two points each)
In this question, circle all of the true statements to the following question stem. Note: There
may be multiple true answers or there may be no true answers. You should view this as a series
of true/false questions where you are suppose to circle all of the statements that are true (given
the question stem).
According to our discussion of the aggregate supply side of the economy developed in class (i.e.,
the Cobb-Douglas production function), which of the following are true?
Here is the formula for MPN (see supplemental notes and class notes for discussion):
MPN = .7 A (K/N) .3 = .7 (Y/N) (see class notes for the derivation)
or, in percentage changes
%ΔMPN = %ΔA + .3%ΔK - .3%ΔN (to get this, just take the log difference of the MPN
definition above).
Likewise,
%ΔMPK = %ΔA + .7%ΔN - .7%ΔK
a.
All else equal, a doubling of TFP will double the marginal product of labor.
Yes. See above. The percentage change in A will lead to an exactly similar percentage
change in MPN (holding N and K constant).
b.
All else equal, a doubling of the capital stock (K) will double the marginal product of
labor.
False. See above. Doubling K will only lead to a 30% (0.3) increase in MPN. This comes
from the math above. Intuitively, it is because of the diminishing marginal product
of capital. Adding more and more machines (holding A and N constant) leads to
less and less extra amount of output.
c.
All else equal, a doubling of labor (N) will cause the marginal product of labor to fall by
half.
False. See above. A doubling of N causes MPN to fall by 30%.
d.
All else equal, a doubling of the marginal product of labor will imply a doubling of
output per worker (Y/N).
True. See above. MPN and Y/N grow at exactly the same rate (take log differences of both
and the 0.7 will be differenced out leaving the percentage growth in MPN to be exactly
equal to the percentage growth in Y/N).
e.
All else equal, a doubling of the marginal product of capital will imply a doubling of the
marginal product of labor.
False. This may be the case (if A is changing). But, it is not necessarily the case if N or K
are changing. For example, an increase in K will INCREASE MPN and DECREASE MPK
(all else equal).
Question 3 (4 points)
In the article from the Economist entitled “A Strange Recovery” (8/9/2003), the author
pointed out that there was something strange about the U.S. recovery out of the 2001
recession. Usually, as economies recover from a recession, this variable increases rapidly
in the subsequent 2 years. However, in the 2 years after the 2001 recession ended, this
variable actually declined. What was this variable that behaved “strangely”? Your
answer should be no more than 1- 2 words. Any more than 1-2 words and points will be
deducted.
We did this in class. The answer is Employment (or employment rate). Many of you put
Unemployment rate. I will give you 3 out of 4 for that. The unemployment rate continued
to rise after the recession was over (I even highlighted the words increase and decrease
above so as to focus you towards the employment rate and not the unemployment rate).