Download Economics 407: Topics in Macroeconomics

Economics 407: Topics in Macroeconomics
Homework #2
This homework is due on Tuesday, February 4th.
1.
Assume that people have rational expectations and that the economy is described by the
sticky-price model discussed in class (see Chapter 13 of Mankiw for a discussion of rational
expectations). Explain why each of the following propositions is true:
a. Only unanticipated changes in the money supply affect real GDP. Changes in the money
supply that were anticipated when prices were set do not impact real variables.
At the time when sticky price firms choose their future prices, if they know the money supply
will change they can adjust their prices accordingly. This price adjustment immediately shifts
the aggregate supply curve and, if firms correctly anticipate the impact of the money supply on
the price level, the aggregate supply curve move cancels the GDP impact of the aggregate
demand curve move.
Of course, this doesn’t happen if the change in money supply is unanticipated. If sticky price
firms set their prices and are then surprised by changing money supply, the firm’s prices will be
out of adjustment relative to the overall price level and these firms will have to compensate by
changing their production levels.
b. If the Fed chooses the money supply at the same time as people are setting prices, so that
everyone has the same information about the state of the economy, then monetary policy cannot
be used systematically to stabilize output. Hence, a policy of keeping the money supply constant
will have the same real effects as a policy of adjusting the money supply in response to the state
of the economy (this is called the policy irrelevance proposition).
If both groups, the Fed and the public, have the same information and make decisions
simultaneously, then monetary policy cannot be used to influence real variables. Consider the
sticky price model. In this case, flexible price firms can change their price at a moments notice
and can thereby adjust instantly to changes in the economy. Because of this, Fed policy changes
will not influence flexible price firm’s decision to produce goods and services.
With regard to sticky price firms, since they receive information about the economy at exactly
the same time the Fed does, they make their price decisions with no extra (or less information)
than the Fed does. If there are expectations of higher future prices, then the sticky price firms
(and the Fed) react by setting their prices high and generate no additional output impacts.
2.
Consider a Phillips Curve given by:
+ v
Π = Π − βU − U
Π represents the inflation rate, U represents the unemployment rate, and vt represents a supply
shock. A positive v can be thought of as a negative supply shock (inflation is higher than it
should be given U) and a negative v can be thought of as a positive supply shock (inflation is
lower than it should be given U). One could imagine v’s occur randomly according to a normal
distribution centered at zero and having some variance σ2.
= 6, U1 = 6, U2 = 6, Π = 0,Π = 0, v1 = 0 and
For the following problem imagine that β= 1, U
v2 = 0.
a. {Adaptive expectations I} As is evident from the Phillips Curve, the formation of inflation
expectations is an important component in the determination of the inflation rate. One method of
modeling expectations are through adaptive expectations. An example of an adaptive
expectation would be to expect future inflation to equal the inflation over the past year, or
Π = Π . Consider an economy which, in period 3, experiences a supply shock equivalent to
an additional 1% of inflation (v3 = 1, U3 = 6). Starting with period 3, sketch the evolution of
inflation over subsequent years (assume subsequent U’s are 6).
Period
v
Π
Π
1
0
0
0
2
0
0
0
3
1
0
1
4
1
1
0
5
1
1
0
6
1
1
0
b. {Adaptive expectations II} Using the same setup as part a, consider a slightly more complex
system of adaptive expectations given by Π = .5Π + .5Π . These expectations could be
thought of as those formed through averaging the past two period’s worth of inflation. Again,
starting with period 3, sketch the evolution of inflation over subsequent years.
Period
v
Π
Π
1
0
0
0
2
0
0
0
3
1
0
1
4
.5
.5
0
5
.75
.75
0
6
.625
.625
0
c. {Rational expectations} Unlike adaptive expectations which “look backwards” to form
beliefs of future inflation, one might believe economic agents consider the fundamentals in an
economy when setting their expectations. Imagine that agents understand that v is drawn from a
normal distribution with mean zero and have no reason to believe future unemployment rates
will differ from 6%. If v3 = 1, sketch the evolution of inflation over subsequent years.
Period
v
Π
Π
1
0
0
0
2
0
0
0
3
1
0
1
4
0
0
0
5
0
0
0
6
0
0
0
d. Okun’s law states that for every one percent increase in the unemployment rate, real GDP will
fall by 2%. For each of parts a, b, and c, imagine the Fed wanted to force Π4 = 0. How much
real GDP will the economy need to sacrifice for the Fed to achieve its goal? Under which
scenario is this sacrifice higher? Why?
a)
Π = 1 − 1U − 6. For Π = 0, Ut must be 7. Since each additional increase in
unemployment rate leads to 2% less GDP, under this scheme of adaptive expectations, the
economy must forego 2% GDP.
b)
Π = .5 − 1U − 6. For Π = 0, Ut must be 6.5. This economy would give up 1%
GDP to eliminate inflation in period 4. However, note that this does not eliminate inflation
permanently. Even if Π = 0, Π = .5 and the economy would have to give up another 1% GDP
to eliminate the resulting inflation. Ultimately, the same amount of GDP would have to be given
up to get rid of inflation as in part a, but it would have to give it up over 2 years.
c)
In this case there is no sacrifice made since inflation in period 4 will be zero anyway.
3.
Explain hysteresis and why it is important in connection with the Phillips Curve.
Hysteresis is the idea that in a system of equations, a shock to one variable (x) leading to a
change in another (y) is not reversible. In other words, if x were to fall to its original value y
would not return to its original value.