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Q1. Consider the IS curve from Table 11.1 (p. 274). The resulting IS curve is
Y�t = a� − b� (R t − r̅ )
1. Suppose the economy was in the long run equilibrium in period t − 1. What are the values for a� and
�
Y in period t − 1?
� =0
a� =0 Y
2. At period t, there is a permanent negative shock to total factor productivity which decreases the
marginal product of capital. Which of the following can you say about what this means for the IS curve?
① Upward movement along existing IS curve
② Downward movement along existing IS curve
③ Shift in of IS curve
④ Shift out of IS curve
Assume that 𝑏� = 2 and 𝑟̅ changes from 3% in period t − 1 to 2% in period t. To counter the negative
shock, the government uses expansionary fiscal policy, increasing government spending by 4% of
potential GDP. That is, ∆a g = 4%. Suppose the Federal Reserve Bank fixes the real interest rate at 3%
in the short run throughout parts 3-6 below.
3. Without the increase in government spending, what will Y�t be?
Y�t =0-2(3-2)= -2
4. With the increase in government spending, what will be Y�t be?
Y�t =4-2(3-2)=2
Q2. Suppose the economy is hit by an unexpected oil price shock that permanently raises oil prices by
$50 per barrel. This is a temporary increase in 𝑜̅ in the model: the shock 𝑜̅ becomes positive for one
period and then goes back to zero.
a) Using the Phillips curve and IS-MP diagrams, explain what happens to the economy in the
absence of any monetary policy action, in other words, the central bank keeps the nominal
interest rate constant.
Solution: The Phillips curve shifts upward for one period, then shifts back down. Meanwhile, the
level of inflation permanently rises. So if it was 6 percent before, it might persistently be 8
percent afterward. If the central bank instead keeps the nominal interest rate constant after the
oil shock, then things get interesting. Now, the rise in inflation turns a constant nominal rate
into a cut in the real rate; the MP curve moves down. The central bank has just unwittingly
created a boom. With positive short-run output, inflation rises persistently, year after year, as
long as the central bank keeps the nominal interest rate constant. Remember: A constant
nominal rate plus a rise in inflation equals a cut in the real rate. And the real rate is what
matters for business decisions.
b) Suppose you are in charge of the central bank. What monetary policy action would you take in
order to restore the economy back to the initial equilibrium? Use the Phillips curve and IS-MP
diagrams to illustrate your answer.
Solution: I would temporarily raise the real rate enough to create a recession that would push
inflation down to its old level. Note that this means a big increase in the nominal rate. For
example, if I need to raise real rates by 1 percent, and the oil price shock raised inflation by 3
percent, then I need to raise the nominal rate by 1% + 3% = 4%.
Q3. Reread the inflation shock example (Event #1) in Section 13.5. Suppose the size of the one-time
shock is 𝑜̅1 and answer the following:
a) In the AS/AD graphs describing the response of the economy to the inflation shock, what are the
values of the initial response of inflation 𝜋1 and the initial output 𝑌�1 in terms of the parameters
of the model? Assume that 𝑎� = 0, since there is no AD shock.
Solution: Take 𝜋𝑡−1 as 𝜋� , the steady state value. Then the AD and AS equations give you a
system of two equations and two unknowns (𝑦�𝑡 and 𝜋𝑡 ). This quickly simplifies to 𝜋𝑡 = 𝜋� +
𝑜�
then substitute this back into the AD equation, we have 𝑦�𝑡 in terms of the parameters
(1+𝑏𝑚𝑣)
of the model. Note that not all of the oil shock gets passed through immediately. That is
because, when inflation starts to rise, the Fed tightens up on the economy, reducing the
demand pressures and cooling off the willingness of businesses to raise prices.
b) Now suppose the parameters of the AS and AD curves take the following values: 𝑜̅1 = 2%,
a = 0 , b = 1 / 2 , m = 1 / 2 , v = 1 / 2 , and π = 2% . Solve for the value of short-run output and
the inflation rate for the first three years immediately following the shock. Assume that 𝑎�
remains equal to zero.
Solution: You can just plug the AD curve into the AS curve, yielding this (for a equal to zero)
(π t −1 ) / (1 + vmb) +2vmb / (1 + vmb) a simple first-order difference equation. The short-run
π=
t
output can be calculated using the AD equation given in the chapter. The table below shows the
first ten years (you are only asked to compute three years). You can see that, even after ten
years, inflation still is half a percent above target. This is a slowly converging economy: steep IS
curve, modest monetary policy rule reaction, and sluggish inflation. All these add up to supply
shocks lasting a long time.
Inflation Short-Run Output
3.78
-0.44
3.58
-0.40
3.40
-0.35
3.25
-0.31
3.11
-0.28
2.99
-0.25
2.88
-0.22
2.78
-0.19
2.69
-0.17
2.62
-0.15
2.55
-0.14