Download Problem Set 5 Answers - University of Wisconsin–Madison

Economics 302
Spring 2012
University of Wisconsin-Madison
Menzie D. Chinn
Social Sciences 7418
Problem Set 5 Answers
Due in lecture on Wednesday, May 9th. Be sure to put your name on your problem set. Put
“boxes” around your answers to the algebraic questions.
Chapter 17, Problem 3
a. The IS curve shifts right.
b. The LM curve shifts right.
c. There are three effects. First, an increase in expected future taxes tends to reduce
expected future after-tax income (for any given level of income), and therefore to reduce
consumption. This effect tends to shift the IS curve to the left. Second, the increase in
future taxes (a deficit reduction program) tends to reduce real interest rates in the future.
The fall in the expected future interest rate tends to shift the IS curve to the right. Third, the
fall in future real interest rates leads to an increase in investment in the medium run and to
an increase in output in the long run. The increase in expected future output tends to shift
the IS curve to the right. The net effect on the IS curve is ambiguous. Note that the model
of the text has lump sum taxes. If taxes are not lump sum, the tax increase may increase
distortions in the economy. These effects tend to reduce output (or the growth rate).
d. The IS curve shifts to the left.
Chapter 19, Problem 7
a. Y = C + I + G + X – IM
Y=c0+c1(Y-T)+d0+d1Y+G+x1Y*-m1Y
Y=[1/(1-c1-d1+m1)][c0-c1T+d0+G+x1Y*]
b. Output increases by the multiplier, which equals 1/(1-c1-d1+m1). The condition 0< m1<
c1+d1<1 ensures that the multiplier is defined, positive, and greater than one. As compared
to the original multiplier, 1/(1+c1), there are two additional parameters: d1, which captures
the effect of an additional unit of income on investment, and m1, which captures the effect of
an additional unit of income on imports. The investment effect tends to increase the
multiplier; the import effect tends to reduce the multiplier.
c. When government purchases increase by one unit, net exports fall by m1ΔY= m1/(1-c1d1+m1). Note that the change in output is simply the multiplier.
d. The larger economy will likely have the smaller value of m1. Larger economies tend to
produce a wider variety of goods, and therefore to spend more of an additional unit of
income on domestic goods than smaller economies do.
e.
ΔY
ΔNX
1.1
0.6
small economy
(m1=0.5)
large economy
(m1=0.1)
2
0.2
f.
Fiscal policy has a larger effect on output in the large economy, but a larger effect on net
exports in the small economy.
Question 3
3.1 We have two equations for income determination:
To solve for domestic demand, we plug in
from the second equation into the first, to get:
Where
Solving for Y, we get:
1
When Δ , Δ
increase by 1, then
increases by
/ 1
.
3.2 If the foreign government decreases spending by 1 unit, but the domestic government
increases spending by 1 unit, then the multiplier is
/ 1
. Notice that this
1. In other words, if the marginal propensity to export is
multiplier is positive if
sufficiently small, then this condition holds!
3.3 Basically, what I was thinking about is that one nation’s consumption can drive another
country’s income.
Question 4
4.1 The equations are:
1
1
Which, after plugging in numbers, we get
.33
.33
1 .33
1/6
.33
.33
1 .33
.66
This is just two equations, and two unknowns, so solving this, we get Y=5/2,Y*=4.
4.2 The Marshall-Lerner conditions tell us when depreciating the currency
increases net
exports. In this case, net exports is just
/ and this is increasing when
decreases, so it does satisfy the Marshall-Lerner conditions.
4.3 The new equations are:
. 66
1
2/9
. 66
1 .5
The previous domestic trade surplus was -1/6 (which means that the foreign trade surplus is
1/6). Solving for the above two equations, Y=8/3, Y*=7/2. The new trade surplus is -1/9, so
that the trade deficit has decreased!
4.4 You want to plot Z=Y, Z=Y/3+10/6, Z=Y/3+16/9 for income determination, and NX=-Y/3+4/6,
NX=-Y/3+7/9
4.5
4.5 Notice that if the domestic country runs a deficit, then the foreign country must run a surplus
of the exact same size (though opposite sign!). Foreign GDP goes from 4 to 3.5 when the
currency depreciates!
4.6 When the currency depreciates, domestic income increases and the domestic trade deficit
decreases. On the other hand, when the currency depreciates, foreign income and the
foreign trade surplus falls. Clearly, there is an incentive for countries to depreciate their
currency!
5. Consider an economy on a flexible exchange rate, and described by the IS-LM-UIP
framework in Chapter 20 of the textbook.
5.1 Suppose autonomous investment collapses. Using the IS-LM-UIP diagrams, show what
happens to interest rates, output, and the exchange rate.
i
LM|M0 , P0
i
IRP relation
i0
i1
IS| b0
IS| b0’
Y1
Y0
LM
E1
E0
E
The reduction in autonomous investment (b0 declines to b0’) shifts the IS curve inward (gray
arrow). The interest rate declines, so with the foreign interest rate i* and the future expected
constant, the exchange rate depreciates.
exchange rate
5.2 What could monetary policy do to restore output to pre-shock levels?
i
LM|M0 , P0
i
IRP relation
LM|M1, P0
i0
i2
IS| b0
IS| b0’
Y0
LM
E2
E1
E0
E
If the monetary authority increases the money supply to M1, then the LM curve will shift out
(black arrow), driving down the interest rate to i2, driving down the exchange rate to E2. As
the interest rate drops, investment rises; and as the exchange rate drops, net exports rise.
6. Consider the same economy as in problem 5, but assume that it is a small economy relative to
the other economy in the world (with interest rate i*).
6.1 Suppose the foreign economy’s interest rate rises. What happens to the home economy?
Show using the IS-LM-UIP framework.
Recall the IRP relationship is given by:
Et =
(1 + it ) e
Et +1
(1 + it* )
(20.4)
Rearranging:
(1 + it ) =
(1 + it* ) Et
Ete+1
So when the foreign interest rate i* rises, then IRP relationship rises by
Et
. This is shown in
Ete+1
the figure below.
i
LM|M0 , P0
IRP relation| i*’
i
IRP relation | i*
i1
i0
IS| i*’
IS| i*
Y0 Y1
LM
E1
E0
E
The shift up in the IRP relation (gray arrow) induces a depreciation of the exchange rate, E0
to E1; with price levels fixed, the real rate depreciates, inducing a shift outward in the IS
curve (gray arrows). Output rises from Y0 to Y1.
6.2 Suppose the home economy’s government is committed to keeping the exchange rate, E,
constant against the foreign country’s. What does the home country have to do in order to
achieve that objective?
LM|M1 , P0
i
LM|M0 , P0
IRP relation| i*’
i
IRP relation | i*
i1
i0
IS| i*
Y1
Y0
LM
E0
E
The same upward shift in the IRP relation occurs (gray vertical arrow). The central bank is
committed to keeping the exchange rate at E0 (and Ete+1 remains constant), and can only do
that by raising the interest rate to i1. And that requires the central bank shrink the money
supply to M1 thereby shifting the LM curve back (gray horizontal arrow).
7. Suppose the economy is given by AD and AS equations 21.1 and 21.2 in the textbook,
assuming the economy is on a fixed exchange rate. You can assume the current period’s
expected price level equals the previous period’s price level.
7.1 Draw the AD AS diagram.
7.2 Suppose autonomous investment collapses. What happens, both in the short run, and over the
long run?
P
AS
AS’
ASfinal
P0
PFinal
AD | b0
P1
P2
AD | b0’
Y1
Y2 Yn
Y
The answer to 7.1 is the original solid lines, with output at Yn and price level at P0. The
answer to 7.2 is shown by the inward shift of the AD curve (gray arrow), in the short run.
The price level falls to P1. In period 2, the AS curve shifts down to intersect the Yn line at P1,
and the output level rises to Y2. Over time, the price level keeps on falling, and the AS curve
shifts out, until output returns to Yn.
7.3 What happens to investment in the medium run?
As the price level falls, the real money supply increases, and so the interest rate falls.
Hence, investment rises.
7.4 What happens to the real exchange rate in the medium run?
The real exchange rate is EP/P*, so as P falls, the real exchange rate falls.
7.5 What is an alternative approach to restoring full employment?
P
AS
P0
AD | b0 = AD | G’, b0’
P1
AD | b0’
Y1
Yn
Y
As the AD curve shifts in, expansionary fiscal policy can be implemented, so the AD shifts
back to where it started from, so output is restored.
Chapter 12, Problem 6
a.
i. People have asked questions about this one. We talked primarily about capital and
steady-states when population was not growing. To think about a model where there is
population and technology growth, we have to have I=δK+(gA+gN ) K . This is because
depreciation lowers the stock of capital, while increasing population and technology requires
that you increase the capital stock to match the new population. Hence, solving for the
balance equation s(Y/N)=[δ+(gA+gN )]( K/(AN)), we get K/(AN) = (s/(δ+gA+gN))2 = 1
ii. Y/(AN)= (K/AN)1/2=1
iii. gY/(AN) = 0
iv. gY/N = gA=4%
v. gY = gA+gN=6%
b.
i.
ii.
iii.
iv.
v.
K/(AN) = (s/(δ+gA+gN))2 = 0.64
Y/(AN)= (K/AN)1/2=0.8
gY/(AN) = 0
gY/N = gA=8%
gY = gA+gN=10%
An increase in the rate of technological progress reduces the steady-state levels of capital
and output per effective worker, but increases the rate of growth of output per worker.
c.
i.
ii.
iii.
iv.
v.
K/(AN) = (s/(δ+gA+gN))2 = 0.64
Y/(AN)= (K/AN)1/2=0.8
gY/(AN) = 0
gY/N = gA=4%
gY = gA+gN=10%
People are better off in case a. Given any set of initial values, the level of technology is the
same in cases (a) and (c), but the level of capital per effective worker is higher at every point
in time in case (a). Thus, since Y/N=AY/(AN)=A(K/(AN))1/2=A1/2(K/N)1/2, output per worker is
always higher in case (a).
e302ps5a_s12.doc
7.5.2012