WEEK 6
CH14, Problem 1 – You are given the following two IS curves that show how real GDP (Yt)
in the current time period t depends on the current interest rate and interest rates in
previous periods, where rt is the interest rate in time period t. Furthermore each time
period corresponds to a quarter or three months.
1. Yt= 8800-25Rt-25Rt-t
- 25Rt-2 - 25Rt-3 - 20Rt-4 - 20Rt-5
- 20Rt-6 - 15Rt-7 - 15Rt-8 - 10Rt-9
2. Yt= 8400 - 5Rt - 5Rt-1
- 5Rt-2 - 5Rt-3 - 5Rt-4 - 10Rt-5
- 15Rt-6 - 15Rt-7 - 15Rt-8 - 20Rt-9
(a) Verify that initially real GDP equals 8,000 for both IS curves.
Given that the interest rate has been 4 percent for the last ten quarters, then for IS curve I, real
GDP equals 8,800 − 25(4) − 25(4) − 25(4) − 25(4) − 20(4) − 20(4) − 20(4) − 15(4) − 15(4) −
10(4) = 8,000. For IS curve II, real GDP equals 8,400 − 5(4) − 5(4) − 5(4) − 5(4) − 10(4) −
15(4) − 15(4) − 15(4) − 20(4) = 8,000.
(b) Suppose that the Fed lowers the interest rate to 3% and keeps it there for the next 10
quarters. Calculate real GDP for the next 10 quarters for each IS curve.
For IS curve I, real GDP in the first quarter equals 8,800 − 25(3) − 25(4) − 25(4) − 25(4) −
20(4) − 20(4) − 20(4) − 15(4) − 15(4) − 10(4) = 8,025. Using the same IS curve, it is easy to
show that for quarters two through ten, real GDP equals 8,050, 8,075, 8,100, 8,120, 8,140,
8,160, 8,175, 8,190, and 8,200, respectively. For IS curve II, real GDP in the first quarter equals
8,400 − 5(3) − 5(4) − 5(4) − 5(4) − 5(4) − 10(4) − 15(4) − 15(4) − 15(4) − 20(4) = 8,005. Using
the same IS curve, it is easy to show that for quarters two through ten, real GDP equals 8,010,
8,015, 8,020, 8,025, 8,035, 8,050, 8,065, 8,080, and 8,100, respectively.
(c) For each IS curve, what is the total increase in real GDP?
Real GDP increases by 200 billion for IS curve I. The increase in real GDP for IS curve II equals
100 billion.
(d) For each IS curve, how many quarters does it take for the incease in real GDP to equal
one-half of the total increase?
For IS curve I, it takes four quarters, or twelve months, for real GDP to increase by 100 billion
or one-half of the total increase in real GDP. For IS curve II, it takes seven quarters, or twentyone
months, for real GDP to increase by 50 billion or one-half of the total increase in real GDP.
WEEK 6
(e) Using Figure 14-2 above, explain which one of the IS curves resembles the economy’s
response to a change in the interest rate prior to 1991 and which one resembles its response
since 1991. Explain how your answer is related to the interest-rate parameters in each IS
equation.
IS curve I resembles the economy’s response prior to 1991. The increase in output in response to
a decline in the interest rate is larger than for IS curve II and one-half of the total increase in
output occurs much sooner with IS curve I as compared to IS curve II. IS curve II resembles the
economy’s response to a change in the interest rate since 1991.
The reasons why IS curve I resembles the economy’s response prior to 1991 is that its interest
rate parameters for the first six quarters are larger than those of IS curve II, and it is only for that
last quarter that IS curve I has a smaller interest rate parameter than that of IS curve II. These
parameters reflect the fact that since 1991, the monetary policy effectiveness lag has been longer
and the interest-rate multiplier has been smaller.
(f) Given your answers to parts b-d, explain how the changes in the monetary policy
effectiveness lag and the interest-rate multiplier affects how much and how long monetary
policymakers must change interest rates in response to any given demand shock.
The answers to Parts b through d indicate that for IS curve II, real GDP rises less than it does for
IS curve I during any of the first seven time periods, for any given increase in the interest rate.
Therefore, the changes in the policy effectiveness lag and the interest-rate multipliers mean that
monetary policymakers now have to change interest rates more in response to a given demand
shock than they did previously.
WEEK 6
CH17, Problem 2 – Suppose that the equation for the aggregate demand is Y = $9,000 + Ms
/ P, where Ms is the nominal money supply and P is the price level. Initially the nominal
money supply equals $3,000. In addition, suppose that the expectations of firms and
workers are rational in the sense when people make the best forecasts they can with the
available data.
(a) Calculate points on the aggregate demand curve when the price level equals 0.8, 1/0,
1.2, 1.25, and 1.5, given the initial value of the nominal money supply.
The equation for the aggregate demand curve is Y = 9,000 + 3,000/P, given that the nominal
money supply is initially 3,000. If the price level equals 0.8, the point on the aggregate demand
curve is Y = 9,000 + 3,000/0.8 = 9,000 + 3,750 = 12,750. The same calculation shows that the
following points are on the aggregate demand curve: (12,000, 1.0), (11,500, 1.2), (11,400, 1.25),
and (11,000, 1.5).
(b) Suppose that natural real GDP equals $12,000 and that the short-run supply curve is
given in the table below, where the price surprise equals P – Pe and Pe is the expected price
level: Price surprise
-0.2
0.0
0.2
0.25
0.5
Real GDP
11,900
12,000
12,100
12,125
12,250
Given that the expected price level is initially 1.0, explain why the economy is in long-run
equilibrium when the price level equals 1.0 and real GDP equals $12,000.
The long-run equilibrium values of real GDP and the price level are where aggregate demand
and long-run aggregate supply are equal. Long-run equilibrium also requires the price level to
equal the expected price level or equivalently that the price surprise is zero. Since the long-run
aggregate supply curve is vertical at natural real GDP and since natural real GDP equals 12,000,
the long-run equilibrium values of real GDP and the price level are also 12,000 and 1.0, given
that the expected price level is initially 1.0.
(c) Suppose that the real exchange rate declines as it did in 2006-2007 and as a result,
aggregate demand increases. Also assume that the decline in the real exchange rate will
persist over time. As a result of this decline, the new equation for the aggregate demand is
Y = $9,600 + Ms / P. Given no change in the nominal money supply, calculate the points on
the new aggregate demand curve when the price level equals 0.8, 1.0, 1.2, 1.25, and 1.5,
given the initial value of the nominal money supply. Using the table given in part b, explain
what the new equilibrium price level and level of real GDP are in the short run, given the
price surprise induced by the decline in the real exchange rate?
The decrease in the real exchange results in an increase in aggregate demand so that the new
equation for the aggregate demand curve is Y = 9,600 + 3,000/P, given the initial value of the
nominal money supply. Therefore, if the price level equals 0.8, the point on the new aggregate
demand curve is Y = 9,600 + 3,000/0.8 = 9,600 + 3,750 = 13,350. The same calculation shows
that the following points are on the new aggregate demand curve: (12,600, 1.0), (12,100, 1.2),
(12,000, 1.25), and (11,600, 1.5).
The new level of aggregate demand and short-run aggregate supply are equal at real GDP equal
to 12,100 and a price surprise equal to .2. Therefore, the new equilibrium price level equals 1.2
in the short run.
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(d) Monetary policymakers respond to the decline in the real exchange rate in one of three
ways: (i) they do nothing and leave the nominal money supply as is; (ii) they change the
money supply so as to return the price level to its level as given in part b; or (iii) they
change the money supply so as to maintain the price level as determined by your answer to
part c. For each of these cases, assume that this is how monetary policymakers have
behaved in the past and this is how firms and workers expect them to behave in response to
the decline in the real exchange rate. Calculate what the long-run equilibrium price level is
and what the expected price level is under each response by monetary policymakers.
Calculate by how much monetary policymakers must change the nominal money supply
for the expectations of firms and workers to be realized.
If monetary policymakers respond to the decline in the real exchange rate by doing nothing and
leaving the nominal money supply at its current level of 3,000, then the long-run equilibrium
price level is 1.25, since that is where aggregate demand and the long-run aggregate supply are
equal at the natural real GDP level of 12,000.
If monetary policymakers change the money supply so as to return the price level to 1.0,
which is what it was equal to in Part b, then the nominal money supply, Ms, must be such that
12,000 = 9,600 + Ms/1.0 or Ms = 12,000 − 9,600 = 2,400. That is, monetary policymakers must
reduce the nominal money supply to 2,400 for the price level and the expected price level to be
equal at P = 1.0.
If monetary policy changes the money supply so as to keep the price level equal to 1.2, which is
what it was in Part c, then the nominal money supply, Ms, must be such that 12,000 = 9,600 +
Ms/1.2 or Ms/1.2 = 12,000 − 9,600 = 2,400. Therefore, Ms = 1.2(2,400) = 2,880. That is,
monetary policymakers must reduce the nominal money supply to 2,880 for the price level
and the expected price level to be equal at P = 1.2.
CH17, Problem 3 – Suppose that instead of persisting as is assumed in problem 2, the
decline in the real exchange rate is only temporary in that the real exchange rate is only
temporary in that after the initial change in the price level that you found in part c of
problem 2, aggregate demand returns to its original level.
(a) Given that monetary policymakers, firms, and workers all recognize that the decline in
the real exchange rate is only temporary and given the three policy responses described in
part d of problem 2, again calculate what the long-run equilibrium price level is and what
the expected price level is under response by monetary policymakers. Again calculate by
how much monetary policymakers must change the nominal money supply for the
expectations of firms and workers to be realized.
If the decline in the real exchange rate is only temporary, so that the aggregate demand curve
returns to its original level, then given no change in the nominal money supply, the economy is
long-run equilibrium when the expected price level and the actual price level at 1.0. On the other
hand, if monetary policymakers change the nominal money supply so as to maintain a price level
equal to 1.2 when aggregate demand returns to its original level, then they must change the nominal
money supply to Ms′so that 12,000 = 9,000 + Ms′/1.2 or Ms′/1.2 =12,000 − 9,000 or Ms′ =1.20(3,000)
= 3,600. That is, monetary policymakers would have to increase the nominal money supply to 3,600
to keep the price level and expected price level equal to 1.2.
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(b) Compare your answers to part d of problem 2 with those of part a of this problem and
explain why they are different.
If monetary policymakers do nothing in the sense of not changing the nominal money supply, then
expected and actual price level rise if the decline in the real exchange rate persists. The reason both
price levels rise is that firms and workers know it takes a higher price level to offset the increase in
aggregate demand caused by the decline in the real exchange rate, given that they expect monetary
policymakers to take no steps to offset that increase in aggregate demand. On the other hand, if firms
and workers know that the decline in the real exchange rate is only temporary, then they understand
that the increase in aggregate demand is also only temporary. So if they expect that monetary
policymakers are not going to take any steps to respond to the temporary changes in the real exchange
rate and aggregate demand, then they also know that the price level returns to 1.0, so that is the price
level they expect.
Note, however, that if the decline in the real exchange rate is expected to persist, so that the increase
in aggregate demand is also expected to persist and firms and workers also expect monetary
policymakers to take actions to reduce the price level to 1.0 in the face of that increase in aggregate
demand, then monetary policymakers must reduce the nominal money supply enough to shift the
aggregate demand curve back to its original level.
Finally, if firms and workers expect that monetary policy makers will maintain the price level at 1.2,
then when the decline in the real exchange rate is expected to persist, monetary policymakers must
take action so as to reduce aggregate demand so that aggregate demand and long-run aggregate supply
are equal to 12,000 at a price level of 1.2. That reduction in aggregate demand would require a
decrease in the nominal money supply. On the other hand, if the decline in the real exchange is only
temporary and so also is the increase in aggregate demand, then monetary policymakers would have
to increase aggregate demand so as to keep aggregate demand and long-run aggregate supply equal to
12,000 at a price level of 1.2. That would require an increase in the nominal money supply.
(c) Explain what data or other factors that monetary policymakers, firms, workers might
analyze in attempting to determine if the decline in the real exchange rate is temporary or
will persist. Finally, suppose that monetary policymakers are better able than firms and
workers to determine if a change in the real exchange rate is temporary or will persist and
that firms and workers know this. Given your answer to part d of problem 2 and part a of
this problem, explain how once monetary policymakers have determined whether the
change in the real exchange rate is only temporary or will persist, they could signal their
findings to firms and workers.
Policymakers, workers, and firms would look to data from the foreign exchange markets and
economic conditions in the rest of the world in an attempt to determine if there were changes in any of
these areas that would cause the decline in the real exchange rate to either persist or only be temporary
in nature.
If monetary policymakers have always responded to changes in aggregate demand by not doing
anything, then there is nothing that they can do to signal to workers and firms whether the change in
the real exchange rate is going to persist or is only temporary. On the other hand, if monetary policymakers have responded to changes in aggregate demand so as to either maintain the price level at its
pre- or post-surprise level, then what they do to the nominal money supply signals to firms and
workers what they have discovered concerning the nature of change in the real exchange rate. For
example, if workers and firms expect that monetary policymakers act so as to maintain the price level
equal to 1.0, its pre-surprise level, then monetary policymakers can signal to workers and firms that
the decline in the real exchange is only temporary by maintaining the nominal money supply at its
pre-surprise level. On the other hand, if monetary policy makers discover that the decline in the real
exchange rate is going to persist, then they can signal that to workers and firms by reducing the
nominal money supply. Finally, you should be able to figure out how monetary policymakers can
WEEK 6
signal to firms and workers what they know about the change in the real exchange rate via a change in
the nominal money supply if workers and firms expect monetary policymakers to maintain the price
level at 1.2.