Econ 100B: Economic Analysis – Macroeconomics
Problem Set #2 – Solutions
Due Date: July 6, 2017
1. Comparing the output and unemployment gaps shown
... [Show More] on slide 26 of lecture 8:
(a) Would you characterize the direction of these fluctuations as generally procyclical,
countercyclical, or acyclical? Why?
The direction of these fluctuations is generally countercyclical because almost all of the
movements in the output gap have a corresponding opposite direction of movement
by the unemployment gap.
(b) Many of the relationships in our macroeconomic models are linear; two variables
are related by the equation for a straight line y = mx+b. What is the relationship
between (i) the sign of the slope m and (ii) the cyclicality (pro or counter) seen
in a time series? Briefly explain.
If variables y and x are procyclical then the direction of change of one is the same as
the other: if one increases so does the other and if one decreases so does the other.
This would imply that m > 0. Similarly, if variables y and x are countercyclical then
the direction of change in one is the opposite of that of the other: if one variable
increases the other decreases and if one variable decreases the other increases. This
would imply that m < 0.
2. Compare and contrast the timing and direction of the fluctuations of Y and CPI
inflation (shown on slide 29 of lecture 5) during (i) the recession associated with the
financial crisis just before 2010 and (ii) the recession in the mid 1970s. Read the
final paragraph on page 296 (312) of the first (second) edition of Mishkin to find the
name of the phenomenon depicted in mid-1970 recession: what is the name of this
phenomenon?
In the recent financial crisis the fluctuations of Y and CPI inflation show the fluctuation
in CPI inflation to be procyclical with a lag. By contrast, the mid-70s recession shows the
fluctuation in CPI inflation to be countercyclical and coincident. This phenomenon of a
contemporaneous increase in inflation and decrease in aggregate output is referred to as
stagflation.
3. Who cares more about short-run models: Classicals or Keynesians? Why?
The Keynesians care more about short-term models. The Classicals see return to equilibrium
as a rapid phenomenon that needs no intervention, and they consequently focus on longterm models. The Keynesians see return to equilibrium as a potentially long phenomenon
and that intervention can help shorten the time it takes to return to equilibrium, and they
consequently focus on short-term models.
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4. Beginning with the second equation for Y in the middle of slide 24 of lecture 6, carry
out the algebra needed to obtain the equation for the IS curve.
Beginning with the IS curve
Y = C + mpc × Y
d + I + G + NX − (ζC + ζI + ζNX) r , (1)
we see that the substitution Y
d = Y − T = Y − T yields
Y = C + mpc ×
Y − T
+ I + G + NX − (ζC + ζI + ζNX) r . (2)
Collecting terms in Y we find that
Y (1 + mpc) = C − mpc × T + I + G + NX − (ζC + ζI + ζNX) r , (3)
which, after dividing both sides by (1 + mpc) and moving −mpc × T to the end of the
sum of autonomous components, yields the IS curve:
Y =
C + I + G + NX − mpc × T
(1 − mpc)
−
(ζC + ζI + ζNX)
(1 − mpc)
r (4)
5. If the IS curve does not shift when autonomous investment increases by $250 MM and
autonomous taxes increase by $325 [Show Less]