ANSWERS TO HOMEWORK QUESTIONS
Chapter 3
Review Questions
1. A production function shows how much output can be produced with
a given amount of capital and labor. The production function can
shift due to supply shocks, which affect overall productivity.
Examples include changes in energy supplies, technological
breakthroughs, and management practices. Besides knowing the
production function, you must also know the quantities of capital
and labor the economy has.
2. The upward slope of the production function means that any
additional inputs of capital or labor produce more output. The fact
that the slope declines as we move from left to right illustrates the
idea of diminishing marginal productivity. For a fixed amount of
capital, additional workers each add less additional output as the
number of workers increases. For a fixed number of workers,
additional capital adds less additional output as the amount of
capital increases.
3. The marginal product of capital (MPK) is the output produced per
unit of additional capital. The MPK can be shown graphically using
the production function. For a fixed level of labor, plot the output
provided by different levels of capital; this is the production function.
The MPK is just the slope of the production function.
4. The marginal revenue product of labor represents the benefit to a
firm of hiring an additional worker, while the nominal wage is the
cost. Comparing the benefit to the cost, the firm will hire additional
workers as long as the marginal revenue product of labor exceeds the
nominal wage, since doing so increases profits. Profits will be at their
highest when the marginal revenue product of labor just equals the
nominal wage.
The same condition can be expressed in real terms by dividing
through by the price of the good. The resulting equation shows that
the real wage (W/P) equals the marginal product of labor.
12. Frictional unemployment arises as workers and firms search to find
matches. A certain amount of frictional unemployment is necessary,
because it is not always possible to find the right match right away.
For example, an unemployed banker may not want to take a job
flipping hamburgers if she cannot find another banking job right
away, because the match would be very poor. By remaining
unemployed and continuing to search for a more suitable job, the
banker is likely to make a better match. That will be better both for
the banker (because the salary is likely to be higher) and for society
as a whole (because the better match means greater productivity in
the economy).
13. Structural unemployment occurs when people suffer long spells of
unemployment or are chronically unemployed. Structural
unemployment arises when the number of potential workers with low
skill levels exceeds the number of jobs requiring low skill levels, or
when the economy undergoes structural change. When there is
structural change, workers who lose their jobs in shrinking
industries may have to move to find new jobs.
14. The natural rate of unemployment is the rate of unemployment that
prevails when output and employment are at their full-employment
levels. The natural rate of unemployment is equal to the amount of
frictional unemployment plus structural unemployment. Cyclical
unemployment is the difference between the actual rate of
unemployment and the natural rate of unemployment. When cyclical
unemployment is negative, output and employment exceed their fullemployment levels.
15. Okun’s Law is a rule of thumb that tells how much output falls when
the unemployment rate rises. Specifically, it says that the percentage
change in GDP equals 3 minus 2 times the change in the
unemployment rate. If the unemployment rate increases by two
percentage points, the percentage change in GDP will be 3 – 2(2) = -1.
Numerical problems
3. (a)
N
1
2
3
4
5
6
Y
8
15
21
26
30
33
MPN
8
7
6
5
4
3
MRPN (P 5)
40
35
30
25
20
15
MRPN (P 10)
80
70
60
50
40
30
(b) P = $5.
(1) W = $38. Hire one worker, since MRPN ($40) is greater than W
($38) at N = 1. Do not hire two workers, since MRPN ($35) is
less than W ($38) at N = 2.
(2) W = $27. Hire three workers, since MRPN ($30) is greater than
W ($27) at N = 3. Do not hire four workers, since MRPN ($25) is
less than W ($27) at N = 4.
(3) W = $22. Hire four workers, since MRPN ($25) is greater than
W ($22) at N = 4. Do not hire five workers, since MRPN ($20) is
less than W ($22) at N = 5.
(c) Figure 1 plots the relationship between labor demand and the
nominal wage. This graph is different from a labor demand curve
because a labor demand curve shows the relationship between
labor demand and the real wage. Figure 2 shows the labor
demand curve.
Figure 1
Figure 2
(d) P = $10. The table in part (a) shows the MRPN for each N. At W = $38,
the firm should hire five workers. MRPN ($40) is greater than W ($38)
at N = 5. The firm shouldn’t hire six workers, since MRPN ($30) is less
than W ($38) at N = 6. With five workers, output is 30 widgets,
compared to 8 widgets in part (a) when the firm hired only one
worker. So the increase in the price of the product increases the firm’s
labor demand and output.
(e) If output doubles, MPN doubles, so MRPN doubles. The MRPN is
the same as it was in part (d) when the price doubled. So labor
demand is the same as it was in part (d). The output produced by
five workers now doubles to 60 widgets.
(f) Since MRPN = P  MPN, then a doubling of either P or MPN leads to
a doubling of MRPN. Since labor demand is chosen by setting
MRPN equal to W, the choice is the same, whether P doubles or
MPN doubles.
Analytical problems
2. (a) An increase in the number of immigrants increases the labor force,
increasing employment and increasing full-employment output.
(b) If energy supplies become depleted, it is likely to reduce
productivity, because energy is a factor of production. So the
reduction in energy supplies reduces full-employment output.
(c) Better education raises future productivity and output, but has no
effect on current full-employment output.
(d) The reduction in the capital stock reduces full-employment output
(although it may very well increase overall welfare).
Chapter 4
Review Questions
1. Saving is current income minus consumption. For a given income,
any increase in consumption means an equal decrease in saving, so
consumption and saving are inversely related. The basic motivation
for saving is to provide for future consumption.
2. When a consumer gets an increase in current income, both current
consumption and future consumption increase. That means part of
the additional current income will be spent and part will be saved.
When the consumer gets an increase in expected future income, again
both current and future consumption increase. Because current
income does not increase, but current consumption does, saving
decreases. When the consumer gets an increase in wealth, both
current and future consumption again rise. Again, there has been no
increase in current income, so saving decreases.
3. An increase in the real interest rate has two effects on desired saving:
(1) The substitution effect increases saving, because the amount of
future consumption that can be obtained in exchange for giving up a
unit of current consumption rises. (2) The income effect may increase
or reduce saving. The income effect reduces saving for a lender,
because a person who saves is better off as a result of having a higher
real interest rate, so he or she increases current consumption.
However, for a borrower, the income effect increases saving, because
the borrower is worse off with a higher real interest rate. So the
income effect works in different directions depending on whether a
person is a lender or a borrower. For a borrower, then, both the
income and substitution effects work in the same direction, and
saving definitely increases. For a lender, the income and substitution
effects work in opposite directions, so the result on desired saving is
ambiguous.
4. The expected after-tax real interest rate equals (1 – t)i – Πe , where t is
the tax rate, i is the nominal interest rate, and Πe is the expected
inflation rate. If the tax rate declines, then the expected after-tax real
interest rate will rise.
6. The two components of the user cost of capital are the interest cost
and the depreciation cost. The depreciation cost is the value lost as
the capital wears out during the period. The interest cost represents
the opportunity cost of using the funds to purchase capital instead of
another asset, such as a bond
7. The desired capital stock is the amount of capital that allows the firm
to earn the largest possible profit. The higher the expected future
marginal product of capital, the higher the desired capital stock,
because any given amount of capital will be more productive in the
future. The higher the user cost of capital, the lower the desired
capital stock, because a higher user cost yields lower profits on each
unit of capital. The higher the effective tax rate, the lower the desired
capital stock, because the firm gets lower profits on each unit of
capital.
8. Gross investment is the total purchase of new capital goods during a
specified period. Net investment is gross investment minus the
depreciation on existing capital. Net investment is the overall increase
in the capital stock. Yes, it is possible for gross investment to be
positive when net investment is negative. This occurs whenever gross
investment is less than the amount of depreciation (as happened in
the United States during World War II).
9. Equilibrium in the goods market occurs when the aggregate supply of
goods (Y) equals the aggregate demand for goods (Cd + Id + G). Since
desired national saving (Sd) is Y – Cd – G, an equivalent condition is
Sd = Id. Equilibrium is achieved by the adjustment of the real interest
rate to make the desired level of saving equal to the desired level of
investment. The relevant diagram is:
r
S
Id
$
Numerical Problems
5. (a) Desired consumption declines as the real interest rate rises
because the higher return to saving encourages higher saving;
desired investment declines as the real interest rate rises becauses
the user cost of capital is higher, reducing the desired capital
stock, and thus investment.
(b) Recall that Sd = Y – Cd – G, so Sd = 9000 – Cd – 2000 = 7000 – Cd .
r
2
3
4
5
6
Cd
6100
6000
5900
5800
5700
Id
1500
1400
1300
1200
1100
Sd
900
1000
1100
1200
1300
Cd Id G
9600
9400
9200
9000
8800
(c) Y = Cd + Id + G at equilibrium. Given Y = 9,000, the equilibrium
condition holds only at r = 5%. At r = 5% it is also true that Sd = Id
= 1200.
(d) When government purchases fall by 400 to 1600, each Sd entry in
the table is higher by 400, and each Cd + Id + G entry is lower by
400. Then Y = Cd + Id + G occurs at r = 3%, and Sd = Id = 1400 at r
= 3%.
r
2
3
4
5
6
Cd
6100
6000
5900
5800
5700
Id
1500
1400
1300
1200
1100
Sd
1300
1400
1500
1600
1700
Cd Id G
9200
9000
8800
8600
8400
Analytical Problems
1. (a) The saving curve shifts to the right from S1 to S2. Saving and
investment increase and the real interest rate falls.
(b) This is really just a transfer from the general population to
veterans. The effect on saving depends on whether the marginal
propensity to consume (MPC) of veterans differs from that of the
general population. If there is no difference in MPCs, then there
will be no shift of the saving curve; neither investment nor the real
interest rate is affected. If the MPC of veterans is higher than the
MPC of the general population, then desired national saving
declines and the saving curve shifts to the left; the real interest
rate rises and investment declines. If the MPC of veterans is lower
than that of the general population, the saving curve shifts to the
right; the real interest rate declines and investment rises.
(c) The investment tax credit encourages investment, shifting the
investment curve from I1 to I2. Saving and investment increase, as
does the real interest rate.
(d)
The increase in expected future income decreases current desired
saving, as people increase desired consumption immediately. The
rise of the future marginal productivity of capital shifts the
investment curve to the right. As a result, the real interest rate rises,
with ambiguous effects on saving and investment.
Chapter 5
Review Questions
1. Credit items in the current account are exports of goods and services,
income receipts from abroad and incoming unilateral transfers.
Debit items in the current account are imports of goods and services,
income payments to foreigners, and outgoing unilateral transfers.
Adding all of the credit items and subtracting all of the debit items
gives the current account balance. The current account balance
equals net exports plus net income from abroad plus net unilateral
transfers.
2. The current account includes only the trade of currently produced
goods, services and resources, plus unilateral transfers. Trades of
existing assets are counted in the capital and financial account.
5. In a small open economy, saving does not have to be equal to
investment. Saving can be used to finance domestic investment or it
can be lent abroad. So saving equals investment plus net exports.
Similarly, output need not equal absorption. Absorption is a
country’s total spending on consumption, investment, and
government purchases. Absorption may be different from output
because some output may be exported. The difference between
output and absorption is net exports.
8. An increase in desired national saving in a large open economy
reduces the world real interest rate. The saving curve shifts to the
right which increases the country’s current account at the current
world real interest rate. To restore equilibrium, the world real interest
rate must fall.
An increase in desired investment has the opposite effect. The
increase in investment reduces the domestic country’s current
account and leads to an increase in the world real interest rate to
restore equilibrium.
Saving and investment in small open economies are so small relative
to saving and investment in the world that changes in them have
very little impact on world markets. On the other hand, a large open
economy may account for a substantial fraction of the world’s saving
and investment, so a change there has a significant impact.
10. The twin deficits are the government budget deficit and the current
account deficit. They are connected because an increase in the
government budget deficit reduces national saving, which leads to an
increased current account deficit. So the government budget deficit
and the current account deficit move in the same direction.
Numerical Problems
1.
Current Account
Goods
Services
Income receipts and
payments
Total
Credit
100
90
110
Debit
125
80
150
300
355
Net exports (NX) = (100 + 90) – (125 + 80) = –15.
Current account balance (CA) = 300 – 355 = –55.
Current and Financial
Account
Credit
Increase in home country
assets abroad
Debit
160
Increase in foreign assets in
home country
200
Total
200
160
Note that the increase in home reserve assets is just a subcategory of the
increase in home country assets, so it is not included separately.
Similarly, the increase in foreign reserve assets is just a subcategory of
the increase in foreign assets in the home country. The information
about the changes in home and foreign reserve assets is included for
calculation of the official settlements balance only. It does not affect the
capital and financial account.
Capital and financial account balance (KFA) = 200 – 160 = 40.
Statistical discrepancy (SD):
CA + KFA + SD = 0
–55 + 40 + SD = 0
SD = 15
Official settlements balance = 30 – 35 = -5
Analytical Problems
5.
(a) The home country’s saving curve shifts to the right, from S1 to S2.
The real world interest rate falls, so that the current account
surplus in the home country equals the current account deficit in
the foreign country. National S rises, I rises, CA rises, rw falls.
(b) The foreign country’s saving curve shifts to the right, from S1For to
S2For. The real world interest rate must fall, so the current account
surplus in the foreign country equals the current account deficit
in the home country. National S falls, I rises, CA falls, rw falls.
(c) The foreign country’s saving curve shifts to the left, from S1For to
S2For. The real world interest rate must rise, so the current
account deficit in the foreign country equals the current account
surplus in the home country. National S rises, I falls, CA rises, rw
rises.
(d) If Ricardian equivalence holds, there is no effect. If Ricardian
equivalence does not hold, then the result is the same as in part (b),
as the foreign country’s saving curve shifts to the right. That is
because all else equal, higher taxes increase government saving more
than they reduce private saving.
Chapter 6
Review Questions
1. The three sources of economic growth are capital growth, labor
growth, and productivity growth. The growth accounting approach is
derived from the production function.
5. If there is no productivity growth, then output per worker,
consumption per worker, and capital per worker will all be constant
in the long run.
6. The statement is false. Increases in the capital-labor ratio increase
consumption per worker in the steady state only up to a point. If the
capital-labor ratio is above its golden rule value, then consumption
per worker will decline as the capital-labor ratio rises.
7.
(a) As long as the capital-labor ratio is below its golden rule value, an
increase in the saving rate increases long-run living standards, as
higher saving allows for more investment and a larger capital
stock.
(b) An increase in the population growth rate reduces long-run living
standards, as more output must be used to equip the larger
number of new workers with capital, leaving less output available
to increase consumption or capital per worker.
(c) A one-time increase in productivity increases living standards
directly, by increasing output, and indirectly, because by raising
incomes it also raises saving and the capital stock.
Numerical Problems
1. Hare: $5000  (1.03)50 = $21,919.50
Tortoise: $5000  (1.01)50 = $8,223.15
2.
20 Years Ago
Today
Percent Change
Y
1000
1300
30%
K
2500
3250
30%
N
500
575
15%
(a) A/A  Y/Y – aK K/K – aN N/N
 30% – (0.3  30%)0.7  15%
 30% – 9% – 10.5%
 10.5%
Capital growth contributed 9% (aK K / K), labor growth contributed
10.5% (aN N / N), productivity growth was 10.5%.
(b) A/A  30% – (0.5  30%)(0.5  15%)
 30% – 15% – 7.5%
 7.5%
Capital growth contributed 15% (aK K / K), labor growth
contributed 7.5% (aN N / N), productivity growth was 7.5%.
5. The condition for the steady state is:
sAf(k) = (n + d)k
(a) .3(3k.5) = (.05 + .1)k
.9k.5 = .15k
6k.5 = k so k = 36
y = 3k.5 = 3(6) = 18
c = y – i = y – sy = 18 - .3(18) = 12.6
(b) Using the same method as in (a),
k = 64, y = 24, c = 14.4
(c) Using the same method as in (a),
k = 25, y = 15, c = 10.5
(d) Using the same method as in (a),
k = 64, y = 32, c = 22.4
6. In the steady state, sAf(k) = (n + d)k, so
(a) .1(6k.5) = (.01 + .14)k
.6k.5 = .15k
4k.5 = k
k = 16
y = 6k.5 = 6(4) = 24
c = y – i = y – sy = 24 - .1(24) = 21.6
i = sy =.1(24) = 2.4
(b) To double output per worker, y must rise from 24 to 48.
y = 6k.5 so k must satisfy the equation 48 = 6k.5. That implies
that k = 64. To raise k to 64, s must rise. The new steady state
requires that
s6(64.5) = (.01 + .14)64
s48 = 9.6
s = .2
Analytical problems
1. (a) The destruction of some of a country’s capital stock in a war would
have no effect on the steady state, because there has been no
change in s, f, n, or d. Instead, k is reduced temporarily, but
equilibrium forces eventually drive k to the same steady-state
value as before. The rapid recovery of Germany and Japan after
WWII illustrate the point.
(b) Immigration raises n from n1 to n2 in the figure below. The rise in
n lowers steady-state k, leading to a lower steady-state
consumption per worker.
(c) The rise in energy prices reduces the productivity of capital per
worker. This causes sf(k) to shift down from sf1(k) to sf2(k) in the
figure below. The result is a decline in steady-state k. Steady-state
consumption per worker falls for two reasons: (1) Each unit of
capital has a lower productivity, and (2) steady-state k is reduced.
(d) A temporary rise in s has no effect on the steady-state
equilibrium.
(e) The increase in the labor force participation rate does not affect
the growth rate of the labor force, so there is no impact on the
steady-state capital-labor ratio or on consumption per worker.
However, because a larger fraction of the population is working,
consumption per person increases.
2. (a) The rise in capital depreciation shifts up the (n + d)k line from (n +
d1)k to (n + d2)k, as shown in the figure below. The equilibrium
steady-state capital-labor ratio declines. With a lower capital-labor
ratio, output per worker is lower, so consumption per worker is
lower. There is no effect on the long-run growth rate of the total
capital stock, because in the long run the capital stock must grow
at the same rate (n) as the labor force grows, so that the capitallabor ratio is constant.
(b) In an endogenous growth model, the growth rate of output is y/y 
sA – (n + d), so the rise in the depreciation rate reduces the
economy’s growth rate. Similarly, the growth rate of capital equals
k/k  sA – (n+ d), which also declines when the depreciation rate
rises. Since consumption is a constant fraction of output, its
growth rate declines as well. So the increase in the depreciation
rate reduces the long-run growth rate of the capital stock, as well
as long-run capital, output, and consumption per worker.
Chapter 7
Review Questions
2.
(1) The medium of exchange function allows people to make trades at
a lower cost in time and effort than in a barter economy. (2) The unit
of account function provides a single, uniform measure of value. (3)
The store of value function provides a way of holding wealth that has
high liquidity and little risk.
4. The four characteristics of assets that are most important to wealth
holders are (1) expected return, (2) risk, (3) liquidity, and (4) time to
maturity. Money has a low expected return compared to other assets.
The level of risk associated with money depends on the probability of
unexpected inflation. Money is the most liquid of all assets, and has
zero time to maturity.
6. The macroeconomic variables that have the greatest impact on
money demand are the price level, real income, and the nominal
interest rate on other assets. The higher the price level, the higher
the demand for money, because more units of money are needed to
carry out transactions. The higher the level of real income, the
greater the volume of transactions, and so money demand is higher.
The higher the nominal interest rate on other assets, the lower is
money demand. That is because the rate of interest is the
opportunity cost of holding money.
9. In equilibrium, the price level is proportional to the nominal money
supply. Specifically, the price level equals the nominal money supply
divided by real money demand. The inflation rate is equal to the
growth rate of the nominal money supply minus the growth rate of
real money demand.
Numerical problems
2. (a) Real money demand is
Md/P = 500 + 0.2Y – 1000i
= 500 + (0.2  1000) – (1000  0.10)
= 600.
Nominal money demand is
Md = (Md/P)  P = 600  100 = 60,000.
In equilibrium, Md = Ms, so velocity is
V = PY/Md = 100  1000/60,000 = 1.67.
(b) Real money demand is unchanged, because neither Y nor i have
changed.
Nominal money demand is
Md = (Md/P)  P = 600  200 = 120,000.
Velocity is unchanged, because neither Y nor Md/P has changed,
and we can write the equation for velocity as
V = PY/Md = Y/(Md/P).
7. (a) With a constant real interest rate and zero expected inflation,
inflation is given by the equation
  M/M – Y Y/Y.
To get inflation equal to zero, the central bank should set money
growth so that
M/M  Y Y/Y  2/3  .045  .03  3%.
The interest elasticity isn’t relevant, since interest rates are expected to
remain constant.
Analytical problems
1. (c) Stocks are an alternative asset to money. When the expected
return to stocks falls, money demand will increase. People will
invest less in stocks and more in cash, checking accounts, and
other items that provide liquidity and safety, so the demand for M1
and M2 will rise.
4. For all of these, it is useful to remember that in equilibrium, the price
level equals the nominal money supply divided by real money demand.
(a) An increase in government purchases reduces national saving,
causing the real interest rate to rise for a fixed level of income. If
the real interest rate is higher, then real money demand will be
lower. The price level must rise. The result is that output is
unchanged, the real interest rate increases, and the price level
increases.
(b) When expected inflation falls, real money demand increases. There
is no effect on employment, saving or investment, so output and
the real interest rate remain unchanged. With higher real money
demand and an unchanged nominal money supply, the
equilibrium price level must decline.
(c) When labor supply rises, full-employment output increases. Higher
output means higher income, so saving will increase. More saving
means the real interest rate will decline. Both higher output and a
lower real interest rate increase real money demand. Higher
money demand with a constant money supply means the price
level must decline.
(d) When the interest rate paid on money increases, real money
demand rises. That is because the cost of holding money falls.
With no effect on employment or saving and investment, output
and the real interest rate remain unchanged. With higher real
money demand and an unchanged nominal money supply, the
equilibrium price level must decline.
Chapter 9
Review Questions
1. The labor market and the production function determine the position
of the FE line. The equilibrium level of employment is determined in
the labor market. Plugging the equilibrium level of employment into
the production function gives the full-employment level of output.
The FE line is vertical at that point. The FE line shifts to the right if
there is an increase in labor supply, an increase in the capital stock
or if there is a beneficial supply shock.
2. The IS curve shows combinations of the real interest rate (r) and
output (Y) where the goods market is in equilibrium. Equilibrium in
the goods market occurs when the aggregate supply of goods (Y)
equals the aggregate demand for goods (Cd  Id  G). Since desired
national saving (Sd) is Y – Cd – G, an equivalent condition is Sd  Id.
Equilibrium is achieved by the adjustment of the real interest rate to
make the desired level of saving equal to the desired level of
investment. For different levels of output, there are different desired
saving curves, with different equilibrium interest rates. The derivation
of the IS curve is illustrated in Figure 9.2 in the textbook (page 312).
The curve slopes downward because as output rises, the saving curve
shifts along the investment curve and the real interest rate declines.
The IS curve could shift down and to the left if: (1) government
purchases fall, (2) the expected future marginal product of capital
falls (or the MEI falls), (3) taxes increase, or (4) the average propensity
to consume falls.
3. The LM curve shows the combinations of output and the real interest
rate where there is equilibrium in the asset market. Equilibrium in
the asset market occurs when real money demand equals the real
money supply.
Figure 9.4 in the textbook (page 317) shows the derivation of the LM
curve and why it slopes upward. An increase in output raises money
demand, shifting the money demand curve to the right. With the
money supply fixed, there will be a higher real interest rate in
equilibrium. This gives two points of the LM curve, plotted on the
right half of the figure. The result is that higher output increases the
real interest rate along the LM curve, so the LM curve slopes upward.
The LM curve would shift down and to the right if the real money
supply increased. That could occur if the nominal money supply
increased or if the price level decreased. In addition, the LM curve
would shift down and to the right if real money demand fell. That
could occur if there were a decrease in the risk of alternative assets
relative to the risk of holding money, an increase in the liquidity of
alternative assets, or an increase in the efficiency of payment
technologies.
5. General equilibrium is a situation in which all markets in an
economy are simultaneously in equilibrium. This is shown in Figure
9.7 in the textbook (page 325) as the point at which the FE line and
the IS and LM curves intersect. If the economy is not initially in
general equilibrium, output and the real interest rate are determined
by the intersection of the IS and LM curves. In the long run, the
adjustment of the price level moves the LM curve until it intersects
the FE line and IS curve.
Numerical problems
1. (a) Sd  Y – Cd – G
 Y – (4000 – 4000r  0.2Y) – 2000
 – 6000  4000r  0.8Y.
(b) Y  Cd  Id  G
Y  (4000 – 4000r  0.2Y)  (2400 – 4000r)  2000
Y  8400 – 8000r  0.2Y
0.8Y  8400 – 8000r, or
8000r  8400 – 0.8Y
Using the equivalent equation that desired saving equals desired
investment gives us
Sd  Id, or – 6000  4000r  0.8Y  2400 – 4000r
0.8Y  8400 – 8000r, or
8000r  8400 – 0.8Y
So we can use either equilibrium condition to get the same result.
When Y  10,000,
8000r  8400 – (0.8 × 10,000)  400, so r  0.05.
When Y  10,200,
8000r  8400 – (0.8 × 10,200)  240, so r  .03
(c) When G  2400, desired saving becomes Sd  – 6400  4000r  0.8Y.
Sd is now 400 less for any given r and Y.
Setting Sd  Id, we get
– 6400  4000r  0.8Y  2400 – 4000r
8000r  8800 – 0.8Y.
Similarly, using the alternative form of the equation gives:
Y  Cd  Id  G
Y  (4000 – 4000r  0.2Y)  (2400 – 4000r)  2400
Y  8800 – 8000r  0.2Y
So 0.8Y  8800 – 8000r, or
8000r  8800 – 0.8Y
At Y = 10,000, this is 8000r = 8800 – (0.8 × 10,000) = 800, so r = 0.10.
The market-clearing real interest rate increases from 0.05 to 0.10.
Thus the IS curve shifts up and to the right from IS1 to IS2 in the
figure below.
2. (a) Md/P  3000  0.1Y – 10,000i
 3000  0.1Y – 10,000(r  e)
 3000  0.1Y – 10,000(r  .02)
 2800  0.1Y – 10,000r
Setting M/P = Md/P:
6000/2  2800  0.1Y – 10,000r
10,000r  – 200  0.1Y
r  – 0.02  (Y/100,000)
When Y  8000, r  0.06.
When Y  9000, r  0.07.
(b) M = 6600, so M/P = 3300. Setting money supply equal to money
demand:
3300  2800  0.1Y – 10,000r
10,000r  –500  0.1Y
r  –0.05  (Y/100,000)
When Y  8000, r  0.03.
When Y  9000, r  0.04.
The LM curve is shifted down and to the right because the same
level of Y gives a lower r at equilibrium.
(c) Md/P  3000  0.1Y – 10,000(r  e)
 3000  0.1Y – 10,000r – (10,000  .03)
 2700  0.1Y – 10,000r.
Setting money supply equal to money demand:
3000  2700  0.1Y – 10,000r
10,000r  – 300  0.1Y
r  – 0.03  (Y/100,000).
When Y  8000, r  0.05.
When Y  9000, r  0.06.
The LM curve is shifted down and to the right
3. Step 1: Find the IS Curve. Begin by finding the savings curve:
S=Y–C–G
S = Y – (200 + .8Y - .8T – 500r) – 196
S = Y – 200 - .8Y + .8(20 + .25Y) + 500r – 196
S = .2Y – 396 + 16 + .2Y + 500r
S = .4Y – 380 + 500r
Next set S = I:
.4Y – 380 + 500r = 200 – 500r
.4Y = 580 – 1000r
Y = 1450 – 2500r (This is the equation for the IS curve.)
Step 2: Find the LM curve
Ms/P = Md/P
9890/P = .5Y –250(r + .1)
9890/P + 250r + 25 = .5Y
Y = 19780/P + 500r + 50 (This is the equation for the LM curve)
Step 3: Solve for r, P, C and I
The economy is at full employment output, which is given as 1000.
Using the IS curve, we can find r:
Y = 1450 – 2500r
1000 = 1450 – 2500r
2500r = 450 so r = 450/2500 = .18
Given Y and r, we can find P on the LM curve:
Y = 19780/P + 500r + 50
1000 = 19780/P + 500(.18) + 50
1000 = 19780/P + 140
860 = 19780/P
P = 19780/860 = 23
Step 4: Find C and I
C = 200 + .8[1000 – (20 + .25(1000)] –500(.18)
C = 694
I = 200 – 500(.18) = 110
Analytical problems
3. (a) The decrease in expected inflation increases real money demand,
which shifts the LM curve left (up). The real interest rate rises and
output declines, as illustrated in the following diagram:
(b) The increase in desired consumption shifts the IS curve up and to
the right, as shown below. The real interest rate and output both
rise.
(c) The increase in government purchases shifts the IS curve up and
to the right. The result is the same as in part (b).
(d) If Ricardian equivalence holds, the increase in taxes has no effect
on either the IS or LM curves, so there is no change in either the
real interest rate or output. If Ricardian equivalence doesn’t hold,
the increase in taxes reduces consumption spending. The IS
curve shifts down and to the left. as shown in the following
diagram. Both the real interest rate and output decline.
(e) An increase in the expected future marginal productivity of capital
will increase investment. The IS curve shifts right, with the same
result as in part (b).
Chapter 11
Review Questions
1. The efficiency wage is the real wage that maximizes effort or efficiency
per dollar of real wages. It assumes that workers will exert more
effort, the higher the real wage. The real wage will remain rigid even if
there is an excess supply of labor, because firms won’t reduce the
wage they pay; doing so would reduce their profits, since workers
wouldn’t work as hard.
2. Full-employment output is the amount of output produced by firms
with employment determined by the labor demand curve at the point
where the marginal product of labor equals the efficiency wage.
A productivity shock does not lead to a change in the efficiency wage,
since it does not affect work effort. But it does affect the marginal
product of labor, so employment changes. A beneficial productivity
shock, for example, leads to an increase in employment. Both the
employment increase and the increase in productivity lead to an
increase in full-employment output.
Labor supply changes have no effect on the efficiency wage or
employment; they simply affect the amount of unemployment. So
they have no impact on full-employment output.
3. Price stickiness is the tendency of prices to adjust only slowly to
changes in the economy. Keynesians believe it is important to allow
for price stickiness to explain why monetary policy is not neutral.
4. Menu costs are the costs of changing prices. Menu costs may lead to
price stickiness in monopolistically competitive markets but not in
perfectly competitive markets, because a monopolistically competitive
firm’s demand is not as sensitive to the price as is a perfectly
competitive firm’s demand. Monopolistically competitive firms may
meet the demand at a fixed price when demand increases, because
price exceeds marginal cost, so that profits still rise, and because the
cost of changing prices may exceed the additional profit earned from
doing so. A perfect competitor would lose all of its customers if its
price were a little above the price charged by its competitors. But a
monopolistically competitive firm would lose only some of its
customers in this case.
6. In the Keynesian model in the short run, output and the real interest
rate increase due to an increase in government purchases. In the
long run, the real interest rate is higher, but output returns to its
full-employment level. Since the real interest rate is higher in the long
run, investment is lower and consumption is lower.
10. In Keynesian analysis, a supply shock may reduce output in two
ways: (1) a reduction in output, because the supply shock reduces
the marginal product of labor, shifting the FE line to the left; and (2)
a further reduction in output if the supply shock is something like an
oil price shock that is large enough to cause many firms to raise
prices, shifting the LM curve up and to the left so much that it
intersects the IS curve to the left of the FE line. Supply shocks create
problems for stabilization policy because: (1) policy can do nothing to
affect the location of the FE line; and (2) using expansionary policy
risks worsening the already-high rate of inflation.
Numerical Problems
1. The following table shows the real wage (w), the effort level (E), and
the effort per unit of real wages (E/w).
w
8
10
12
14
16
18
E
7
10
15
17
19
20
E/w
0.875
1.00
1.25
1.21
1.19
1.11
The firm will pay a wage of 12, since that wage provides the
maximum effort per unit of the real wage (E/w = 1.25). The firm will
employ 88 workers, since that is the number of workers for which
w = MPN. That’s because MPN = E(100 – N)/15. When w = 12, E =
15, so w = MPN implies 12 = 15(100 – N)/15. N therefore = 88. As
long as the supply of labor exceeds the demand for labor, labor
supply has no effect on the firm’s decision.
3. The IS curve is Y = Cd + Id + G = [600 + 0.8(Y – 1000) – 500r] +[400 –
500r] + 1000, so 0.2Y = 1200 – 1000r. This is plotted in Figure 11.12.
Figure 11.12
Since e 0, the nominal interest rate (i) equals the real interest rate
(r).
(a) Can the economy reach full employment? Since full-employment
output is Y = 8000, for the economy to be on the IS curve, 0.2Y =
1200 – 1000r, so (0.2  8000) = 1200 – 1000r, or 1000r = –400, so
r = i = –.4. But since the nominal interest rate can’t be negative,
this isn’t possible. Thus, the requirement that i be non-negative
means that there’s no way to satisfy the goods markets
equilibrium condition at full employment. Assuming that the
result is that i = 0 and that output is determined along the IS
curve, 0.2Y = 1200 – (1000  0), so Y = 6000. Note that this is the
best result possible, no matter what the money supply is, so
monetary policy can’t restore full employment.
(b) To restore full employment while the nominal interest rate is zero
clearly requires a shift in the IS curve. If we return to the original
derivation and put G in the equation instead of using the original
value of G = 1000, we get:
Y = Cd + Id + G = [600 + 0.8(Y – 1000) – 500r] +[400 – 500r] + G, so
0.2Y = 200 + G – 1000r. To get Y = 8000 and r = 0, we have 0.2 
8000 = 200 + G – (1000  0), so G = 1400. Then the IS curve is
0.2Y = 1600 – 1000r. This is plotted in Figure 11.13 as IS2, while
the original IS curve is IS1.
Figure 11.13
Thus, raising G to 1400 can generate full employment, if the money
supply is chosen so that the LM curve intersects the IS curve at the
right point. Note that taxes are 1000, so the government must run a
large budget deficit.
What must the money supply be? Since P = 2, we need money supply
(M/P) = money demand (L), so M/2 = 0.5Y – 200i = (0.5  8000) – (200
 0) = 4000, so M = 8000.
This situation is quite similar to the situation in Japan in the 1990s
and suggests that to get out of the liquidity trap, Japan will need to
use expansionary monetary policy, along with expansionary fiscal
policy.
Analytical Problems
1. a. The tax incentive for investment shifts the IS curve to the right.
The short-run effect is to increase output, employment and the
real interest rate; the price level is unaffected. In the long-run,
the price level will rise, and that will shift the LM curve left.
Relative to the starting point, output and employment will be the
same, but the price level and interest rate will be higher.
b. The tax incentive for saving reduces consumption, so the IS curve
shifts left. The short-run effect is to reduce output, employment
and the real interest rate; the price level is unaffected. In the
long-run, the price level will fall, and that will shift the LM curve
right. Relative to the starting point, output and employment will
be the same, but the price level and interest rate will be lower.
c. Investor pessimism about future profits will reduce investment
and shift the IS curve left. The short-run effect is to reduce
output, employment and the real interest rate; the price level is
unaffected. In the long-run, the price level will fall, and that will
shift the LM curve right. Relative to the starting point, output and
employment will be the same, but the price level and interest rate
will be lower.
d. Higher consumer confidence will increase consumption and shift
IS to the right. The short-run effect is to increase output,
employment and the real interest rate; the price level is
unaffected. In the long-run, the price level will rise, and that will
shift the LM curve left. Relative to the starting point, output and
employment will be the same, but the price level and interest rate
will be higher.
Chapter 13
Review questions
1. The nominal exchange rate is the rate at which two currencies can be
exchanged for each other in the market. The real exchange rate is the
price of domestic goods relative to foreign goods. Changes in the two
exchange rates are related as follows:
% change in enom= % change in e + for - US
2. The two major types of exchange-rate systems are fixed exchange
rates and flexible exchange rates. In a fixed-exchange-rate system,
exchange rates are set at officially determined levels. In a flexibleexchange-rate system, exchange rates are determined by conditions
of demand and supply in the foreign exchange market. Currently, the
major currencies of the world are on a flexible-exchange-rate system
(more or less).
3. Purchasing power parity, PPP, is the idea that similar foreign and
domestic goods, or baskets of goods, should have the same price
when priced in terms of the same currency. Purchasing power parity
does seem to explain exchange rates in the long run, but over shorter
periods it doesn’t work well because countries produce very different
sets of goods, because some goods aren’t traded internationally, and
because there are transportation costs and legal barriers.
4. The J curve shows the response of net exports to a real depreciation.
At first the real depreciation reduces net exports, as the decline in the
real exchange rate means that a country pays more for its imports
and receives less for its exports. But as time passes, the higher price
of imports reduces the demand for imports, while the lower price of
the country’s exports increases their demand abroad. So eventually
net exports begin to increase.
5. An increase in domestic income leads people to buy more goods,
including imported goods, so net exports decline. An increase in
foreign income leads foreigners to buy more goods, including goods
exported from the domestic country, so net exports increase. An
increase in the domestic real interest rate makes domestic assets
more attractive and foreign assets less attractive to both domestic and
foreign investors. This causes a reduction in the supply of the
domestic currency on the foreign exchange market and an increase in
demand for the domestic currency on the foreign exchange market.
The result is an appreciation of the domestic currency, which leads to
a decline in net exports.
6. Foreigners demand dollars in the foreign exchange market to be able
to buy U.S. goods and services (U.S. exports) and U.S. real and
financial assets (U.S. capital inflows). Americans supply dollars to the
foreign exchange market to be able to buy foreign goods and services
(U.S. imports) and real and financial assets in foreign countries (U.S.
capital outflows). The demand for dollars increases if the demand for
U.S. goods increases, the domestic real interest rate increases,
foreign income increases, or the foreign real interest rate decreases.
The supply of dollars increases if the demand for foreign goods
increases, the domestic real interest rate decreases, domestic income
increases, or the foreign real interest rate increases.
7. The IS-LM model for the open economy differs from the closedeconomy IS-LM model in that international influences may shift the
IS curve. Factors that raise a country’s net exports, given domestic
output and the domestic real interest rate, shift the IS curve upward,
while factors that reduce a country’s net exports shift the IS curve
downward. A recession could be transmitted from one country to
another because a recession in one country reduces the net exports
of other countries, shifting their IS curves down. In the Keynesian
model in the short run, this would lead to a reduction in output in
the other countries.
8. Expansionary fiscal policy increases output and the real interest rate
in the short run, both of which lead to a reduction of net exports.
Expansionary monetary policy increases output in the short run,
which tends to reduce net exports, but reduces the real interest rate,
which tends to increase net exports (by reducing the exchange rate).
The overall effect is potentially ambiguous, but the effects of changes
in the real exchange rate on net exports may be weak in the short
run, so it is likely that net exports will decline.
Numerical problems
4. a. General equilibrium output is given as 1,000.
The IS curve is given by the equation
S – I = NX
S = Y – C – G = Y – [200 + .6(Y – T) – 200r] – 152
S = Y – 200 - .6Y + .6(20 + .2Y) + 200r – 152
S = .52Y – 340 + 200r
S – I = .52Y – 340 + 200r – 300 + 300r
S – I = .52Y – 640 + 500r
NX = 150 - .08Y – 500r (given)
S – I = NX
.52Y – 640 + 500r = 150 - .08Y – 500r
.6Y = 790 – 1000r
Y = 1316.67 – 1666.67r (IS curve)
Since Y is given at 1000, one can solve for r with only the IS curve:
1000 = 1316.67 – 1666.67r
r = .19
The LM curve is given by the equation
Ms/P = Md/P
924/P = .5Y – 200r
Given Y and r, one can solve for P using the LM curve:
924/P = .5(1000) – 200(.19)
P=2
Plugging Y = 1000 and r = .19 into the C, I and NX:
C = 630
I = 243
NX = -25
b. G = 214 changes S to
S = .52Y – 402 + 200r
repeating the derivation in part (a), the new saving functions gives:
S – I = NX
.52Y – 702 + 500r = 150 - .08Y – 500r
.6Y = 852 – 1000r
Y = 1420 – 1666.67r (new IS curve)
The LM curve is the same. In the short run P = 2 so
924/2 = .5Y – 200r
Y = 924 + 400r (LM curve with P = 2)
The IS and LM curves together give us two equations and two
unknowns. Solve them together to find short run equilibrium Y
and r:
IS: Y + 1666.67r = 1420
LM: Y – 400r = 924
Subtract LM from IS
2066.67r = 496
r = .24
Plugging r into either equation gives us Y = 1020
Plugging r and Y into the appropriate equations gives:
C = 629.6
I = 228
NX = - 51.6
In the long run, Y returns to 1000, so
The IS curve is Y = 1420 – 1666.67r or
1000 = 1420 – 1666.67r so
r = .25
Plugging Y and r into the LM curve gives us
924/P = .5Y – 200r or
924/P = .5(1000) – 200(.25)
so P = 2.055
The long run values for C, I and NX are:
C = 618
I = 225
NX = -55