Answers to end-of-chapter problems
Chapter 1
Quick Check
1. a. True.
b. True.
c. False.
d. False/uncertain. The rate of growth was higher during the
decade beginning in 1996 than during
the previous two decades, but it is probably unrealistic to expect
productivity to continue to grow at such a fast pace.
e. False. There are problems with the statistics, but the
consensus is that growth in China has been
high.
f. False. The European "unemployment miracle" refers to the
relatively low European
unemployment rate in the 1960s and the early 1970s.
g. True.
h. True.
2. a. More flexible labor market institutions may lead to lower
unemployment, but there are questions
about how precisely to restructure these institutions. The
United Kingdom has restructured its
labor market institutions to resemble more closely U.S.
institutions and now has a lower
unemployment rate than before the restructuring. On the other hand,
Denmark and the Netherlands have relatively low unemployment rates
while maintaining relatively generous social insurance programs for
workers.
In addition, some economists argue that tight monetary policy has at
least something to do with the high unemployment rates in Europe.
b. Although the Euro will remove obstacles to free trade between
European countries, each country
will be forced to give up its own monetary policy.
Dig Deeper
3. a. The Chinese government has encouraged foreign firms to produce
in China. Since foreign firms
are typically more productive than Chinese firms, the presence of
foreign firms has lead to an increase in Chinese productivity. The
Chinese government has also encouraged joint ventures between foreign
and Chinese firms. These joint ventures allow Chinese firms to learn
from more productive foreign firms.
b. The recent increase in U.S. productivity growth has been a
result of the development and
widespread use of information technologies.
c. The United States is a technological leader. Much of U.S.
productivity growth is related to the development of new technologies.
China is involved in technological catch-up. Much of Chinese
productivity growth is related to adopting existing technologies
developed abroad.
d. It's not clear to what extent China provides a model for other
developing countries. High investment seems a good strategy for
countries with little capital, and encouraging foreign firms to
produce (and participate in joint ventures) at home seems a good
strategy for countries trying to improve productivity. On the other
hand, the degree to which China's centralized political
control has been important in managing the pace of the
transition and in protecting property rights
of foreign firms remains open to question.
4. a. 10 years: (1.018)10=1.195 or 19.5 % higher
20 years: 42.9% higher
50 years: 144% higher
b. 10 years: 31.8 % higher
20 years: 73.7 % higher
50 years: 297.8% higher
c. Take output per worker as a measure of the standard of living.
10 years: 1.195/1.318=1.103, so the standard of living would
be 10.3% higher;
20 years: 21.6 % higher
50 years: 63% higher
d. No. Labor productivity growth fluctuates a lot from year to
year. The last few years may
represent good luck. It is too soon to tell whether there has been a
change in the trend observed since 1970.
5. a. 13.2(1.034)t=2.8(1.088)t
t = ln(13.2/2.8)/[ln(1.088/1.034)]
t 30.5 yrs
This answer can be confirmed with a spreadsheet, for students
unfamiliar with the use of
logarithms.
b. No. At current growth rates, Chinese output will exceed U.S.
output within 31 years, but Chinese
output per person (the Chinese standard of living) will still
be less than U.S. output per person.
Explore Further
6. a/c. As of February 2008, there had been 5 recessions (according to
the traditional definition) since
1960. Seasonally-adjusted annual percentage growth rates of GDP (in
chained 2000 dollars) are given below.
1969:4 -1.9 1981:4 -4.9
1970:1 -0.7 1982:1 -6.4
1974:3 -3.8 1990:4 -3.0
1974:4 -1.6 1991:1 -2.0
1975:1 -4.7
1980:2 -7.8
1980:3 -0.7
With respect to the note on 2001, the growth rates for
2001 are given below.
2001:1 -0.5%
2001:2 1.2%
2001:3 -1.4%
2001:4 1.6%
7. a-b. % point increase in the unemployment rate for the 5 recessions
1969-70 0.7 1981-82 1.1
1974-75 3.1 1990-91 0.9
1980 0.6
The unemployment rate increased by 1.5 percentage points
between January 2001 and
January 2002.
Chapter 2
Quick Check
1. a. True.
b. True/Uncertain. Real GDP increased by a factor of 25; nominal
GDP increased by a
factor of 21. Real GDP per person increased by a factor of 4.
c. False.
d. True.
e. False. The level of the CPI means nothing. The rate of change
of the CPI is one measure of inflation.
f. Uncertain. Which index is better depends on what we are trying
to measure—inflation faced by consumers or by the economy as a
whole.
g. False. The underground economy is large, but by far the
majority of the measured unemployed in Spain are not employed in
the underground economy.
2. a. No change. This transaction is a purchase of intermediate
goods.
b. +$100: personal consumption expenditures
c. +$200 million: gross private domestic fixed investment
d. +$200 million: net exports
e. No change. The jet was already counted when it was produced,
i.e., presumably when Delta (or some other airline) bought it
new as an investment.
3. a. The value of final goods =$1,000,000, the value of the silver
necklaces.
b. 1st Stage: $300,000. 2nd Stage: $1,000,00-$300,000=$700,000.
GDP: $300,000+$700,000=$1,000,000.
c. Wages: $200,000 + $250,000=$450,000.
Profit: ($300,000-$200,000)+($1,000,000-$250,000-300,000)
=$100,000+$450,000=$550,000.
GDP: $450,000+$550,000=$1,000,000.
4. a. 2006 GDP: 10($2,000)+4($1,000)+1000($1)=$25,000
2007 GDP: 12($3,000)+6($500)+1000($1)=$40,000
Nominal GDP has increased by 60%.
b. 2006 real (2006) GDP: $25,000
2007 real (2006) GDP: 12($2,000)+6($1,000)+1000($1)=$31,000
Real (2006) GDP has increased by 24%.
c. 2006 real (2007) GDP: 10($3,000)+4($500)+1,000($1)=$33,000
2007 real (2007) GDP: $40,000.
Real (2007) GDP has increased by 21.2%.
d. The answers measure real GDP growth in different units. Neither
answer is incorrect, just as measurement in inches is not more
or less correct than measurement in centimeters.
5. a. 2006 base year:
Deflator(2006)=1; Deflator(2007)=$40,000/$31,000=1.29
Inflation=29%
b. 2007 base year:
Deflator(2006)=$25,000/$33,000=0.76; Deflator(2007)=1
Inflation=(1-0.76)/0.76=.32=32%
c. Analogous to 4d.
6. a. 2006 real GDP = 10($2,500) + 4($750) + 1000($1) = $29,000
2007 real GDP = 12($2,500) + 6($750) + 1000($1) = $35,500
b. (35,500-29,000)/29,000 = .224 = 22.4%
c. Deflator in 2006=$25,000/$29,000=.86
Deflator in 2007=$40,000/$35,500=1.13
Inflation = (1.13 -.86)/.86 = .31 = 31%.
d. Yes, see appendix for further discussion.
Dig Deeper
7. a. The quality of a routine checkup improves over time. Checkups
now may include EKGs, for example. Medical services are
particularly affected by this problem since there are continual
improvements in medical technology.
b. The new method represents a 10% quality increase.
c. There is a 5% true price increase. The other 10% represents a
quality increase. The quality-adjusted price of checkups using
the new method is only 5% higher than checkups using the old
method last year.
d. You need to know the relative value of pregnancy checkups with
and without ultra-sounds in the year the new method is
introduced. Still, since everyone chooses the new method, we
can say that the quality-adjusted price of checkups has risen by
less than 15%. Some of the observed 15% increase represents an
increase in quality.
8. a. Measured GDP increases by $10+$12=$22. (Strictly, this
involves mixing the final goods and income approaches to GDP.
Assume here that the $12 per hour of work creates a final good
worth $12.)
b. No. The true value of your decision to work should be less than
$22. If you choose to work, the economy produces the value of
your work plus a takeout meal. If you choose not to work,
presumably the economy produces a home-cooked meal. The extra
output arising from your choice to work is the value of your
work plus any difference in value between takeout and home-
cooked meals. In fact, however, the value of home-cooked meals
is not counted in GDP. (Of course, there are other details.
For example, the value of groceries used to produce home-cooked
meals would be counted in GDP. Putting such details aside,
however, the basic point is clear.)
Explore Further
9. a. Quarters 2000:III, 2001:I, and 2001:III had negative growth.
b. The unemployment rate increased after 2000, peaked in 2003, and
then began to fall. The
participation rate fell steadily over the period—from 67.1% in
2000 to 66% in 2004.
Presumably, workers unable to find jobs became discouraged and
left the labor force.
c. Employment growth slowed after 2000. Employment actually fell
in 2001. The
employment-to-population ratio fell between 2000 and 2004.
d. It several years after the recession for the labor market to
recover.
Chapter 3
Quick Check
1. a. True.
b. False. Government spending excluding transfers was 19% of GDP.
c. False. The propensity to consume must be less than one for our
model to make sense.
d. True.
e. False.
f. False. The increase in output is one times the multiplier.
g. False.
2. a. Y=160+0.6(Y-100)+150+150
Y=1000
b. YD=Y-T=1000-100=900
c. C=160+0.6(900)=700
3. a. Equilibrium output is 1000. Total
demand=C+I+G=700+150+150=1000. Total demand equals production.
We used this equilibrium condition to solve for output.
b. Output falls by (40 times the multiplier) = 40/(1-.6)=100. So,
equilibrium output is now 900. Total
demand=C+I+G=160+0.6(800)+150+110=900. Again, total demand
equals production.
c. Private saving=Y-C-T=900-160-0.6(800)-100=160. Public saving =T-
G=-10. National saving (or in short, saving) equals private
plus public saving, or 150. National saving equals investment.
This statement is mathematically equivalent to the equilibrium
condition, total demand equals production. In other words,
there is an alternative (and equivalent) equilibrium condition:
national saving equals investment.
Dig Deeper
4. a. Y increases by 1/(1-c1)
b. Y decreases by c1/(1-c1)
c. The answers differ because spending affects demand directly,
but taxes affect demand
indirectly through consumption, and the propensity to consume
is less than one.
d. The change in Y equals 1/(1-c1) - c1/(1- c1)=1. Balanced
budget changes in G and T are
not macroeconomically neutral.
e. The propensity to consume has no effect because the balanced
budget tax increase aborts the multiplier process. Y and T both
increase by one unit, so disposable income, and hence
consumption, do not change.
5. a. Y=c0+c1YD+I+G implies
Y=[1/(1-c1+c1t1)][c0-c1t0+I+G]
b. The multiplier=1/(1-c1+c1t1)<1/(1-c1), so the economy responds
less to changes in autonomous spending when t1 is positive.
After a positive change in autonomous spending, the increase in
total taxes (because of the increase in income) tends to lessen
the increase in output. After a negative change in autonomous
spending, the fall in total taxes tends to lessen the decrease
in output.
c. Because of the automatic effect of taxes on the economy, the
economy responds less to changes in autonomous spending than in
the case where taxes are independent of income. Since output
tends to vary less (to be more stable), fiscal policy is called
an automatic stabilizer.
6. a. Y=[1/(1-c1+c1t1)][c0-c1t0+I+G]
b. T = t0 + t1[1/(1-c1+c1t1)][c0-c1t0+I+G]
c. Both Y and T decrease.
d. If G is cut, Y decreases even more. A balanced budget
requirement amplifies the effect
of the decline in c0. Therefore, such a requirement is
destabilizing.
7. a. In the diagram representing goods market equilibrium, the ZZ
line shifts up. Output
increases.
b. There is no effect on the diagram or on output.
c. The ZZ line shifts up and output increases. Effectively, the
income transfer increases the
propensity to consume for the economy as a whole.
d. The propensity to consume is likely to be higher for low-income
taxpayers. Therefore,
tax cuts will be more effective at stimulating output if they
are directed toward low-income taxpayers.
8. a. Y=C+I+G
Y=[1/(1-c1-b1)]*[c0-c1T+b0+G]
b. Including the b1Y term in the investment equation increases the
multiplier. Increases in
autonomous spending now create a multiplier effect through two
channels: consumption and investment. For the multiplier to be
positive, the condition c1+b1<1 is required.
c. Output increases by b0 times the multiplier. Investment
increases by the change in b0
plus b1 times the change in output. The change in business
confidence leads to an increase in output, which induces an
additional increase in investment. Since investment increases,
and saving equals investment, saving must also increase. The
increase in output leads to an increase in saving.
Explore Further
9. a. Output will fall.
b. Since output falls, investment will also fall. Public saving
will not change. Private
saving will fall, since investment falls, and investment equals
saving. Since output and consumer confidence fall, consumption
will also fall.
c. Output, investment, and private saving would have risen.
d. Clearly this logic is faulty. When output is low, what is
needed is an attempt by
consumers to spend more. This will lead to an increase in
output, and
therefore—somewhat paradoxically—to an increase in private
saving. Note, however,
that with a linear consumption function, the private saving rate
(private saving divided by output) will fall when c0 rises.
10. Answers will vary depending on when students visit the website.
Chapter 4
Quick Check
1. a. False.
b. False.
c. False. Money demand describes the portfolio decision to hold
wealth in the form of
money rather than in the form of bonds. The interest rate on
bonds is relevant to this decision.
d. True.
e. False.
f. False.
g. True.
h. True.
2. a. i=0.05: money demand = $18,000
i=0.10: money demand = $15,000
b. Money demand decreases when the interest rate increases because
bonds, which pay interest, become more attractive.
c. The demand for money falls by 50%.
d. The demand for money falls by 50%.
e. A 1% increase (decrease) in income leads to a 1% increase
(decrease) in money demand. This effect is independent of the
interest rate.
3. a. i=100/$PB –1; i=33%; 18%; 5% when $PB =$75; $85; $95.
b. When the bond price rises, the interest rate falls.
c. $PB =100/(1.08) $93
4. a. $20=MD=$100(.25-i)
i=5%
b. M=$100(.25-.15)
M=$10
Dig Deeper
5. a. BD = 50,000 - 60,000 (.35-i)
If the interest rate increases by 10 percentage points, bond
demand increases by $6,000.
b. An increase in wealth increases bond demand, but has no effect
on money demand, which
depends on income (a proxy for transactions demand).
c. An increase in income increases money demand, but decreases
bond demand, since we
implicitly hold wealth constant.
d. First of all, the use of "money" in this statement is
colloquial. "Income" should be substituted for "money."
Second, when people earn more income, their wealth does not
change right away. Thus, they increase their demand for money
and decrease their demand for bonds.
6. Essentially, the reduction in the price of the bond makes it more
attractive. A bond promises fixed nominal payments. The opportunity
to receive these fixed payments at a lower price makes a bond more
attractive.
7. a. $16 is withdrawn on each trip to the bank.
Money holdings are $16 on day one; $12 on day two; $8 on day
three; and $4 on day
four.
b. Average money holdings are ($16+$12+$8+$4)/4=$10.
c. $8 is withdrawn on each trip to the bank.
Money holdings are $8, $4, $8, and $4.
d. Average money holdings are $6.
e. $16 is withdrawn on each trip to the bank. Money holdings are
$0, $0, $0, and $16.
f. Average money holdings are $4.
g. Based on these answers, ATMs and credit cards have reduced
money demand.
8. a. All money is in checking accounts, so demand for central bank
money equals demand for
reserves. Therefore, demand for central bank money=0.1($Y)(.8-
4i).
b. $100B = 0.1($5,000B)(.8-4i)
i=15%
c. Since the public holds no currency,
money multiplier = 1/reserve ratio = 1/.1=10.
M=(10)$100B=$1,000B
M= Md at the interest derived in part (b).
d. If H increases to $300B the interest rate falls to 5%.
e. The interest rate falls to 5%, since when H equals $300B,
M=(10)$300B=$3,000B.
9. The money multiplier is 1/[c+((1-c)], where c is the ratio of
currency to deposits and ( is the ratio of reserves to deposits. When
c increases, as in the Great Depression, the money multiplier falls.
Explore Further
10. Answers will vary depending on when students visit the FOMC website.
Chapter 5
Quick Check
1. a. True.
b. True.
c. False.
d. False. The balanced budget multiplier is positive (it equals
one), so the IS curve shifts right.
e. False.
f. Uncertain. An increase in government spending leads to an
increase in output (which tends to increase investment), but
also to an increase in the interest rate (which tends to reduce
investment).
g. True.
2. a. Y=[1/(1-c1)][c0-c1T+I+G]
The multiplier is 1/(1-c1).
b. Y=[1/(1-c1-b1)][c0-c1T+b0-b2i+G]
The multiplier is 1/(1-c1-b1). Since the multiplier is larger
than the multiplier in part (a), the effect of a change in
autonomous spending is bigger than in part (a). An increase in
autonomous spending now leads to an increase in investment as
well as consumption.
c. Substituting for the interest rate in the answer to part (b),
Y=[1/(1-c1-b1+b2d1/d2)][c0-c1T+b0+(b2/d2)(M/P)+G].
The multiplier is 1/(1-c1-b1+b2d1/d2).
d. The multiplier is greater (less) than the multiplier in part (a)
if (b1-b2d1/d2) is greater (less) than zero. The multiplier as
measured in part (c) measures the marginal effect of an increase
in autonomous spending on equilibrium output. As such, the
multiplier is the sum of two effects: a direct effect of output
on demand and an indirect effect of output on demand via the
interest rate. The direct effect is equivalent to the
horizontal shift of the IS curve. The indirect effect depends
on the slope of the LM curve (since the equilibrium moves along
the LM curve in response to a shift of the IS curve) and the
effect of the interest rate on investment demand.
The direct effect is captured by the sum c1+b1, which measures
the marginal effect of an increase in output on the sum of
consumption and investment demand. As this sum increases, the
multiplier gets larger.
The indirect effect is captured by the expression b2d1/d2 and
tends to reduce the size of the multiplier. The ratio d1/d2 is
the slope of the LM curve, and the parameter b2 measures the
marginal effect of an increase in the interest rate on
investment. Note that the slope of the LM curve becomes larger
as money demand becomes more sensitive to income (i.e., as d1
increases) and becomes smaller as money demand becomes more
sensitive to the interest rate (i.e., as d2 increases).
3. a. The IS curve shifts left. Output and the interest rate fall.
The effect on investment is ambiguous because the output and
interest rate effects work in opposite directions: the fall in
output tends to reduce investment, but the fall in the interest
rate tends to increase it.
b. From the answer to 2(c), Y=[1/(1-c1-b1+b2d1/d2)][c0-
c1T+b0+(b2/d2)(M/P)+G].
c From the LM relation, i=Y(d1/d2)–(M/P)/d2.
To obtain the equilibrium interest rate, substitute for
equilibrium Y from part (b).
d. I= b0+b1Y-b2i=b0+(b1-b2d1/d2)Y+(b2/d2)(M/P)
To obtain equilibrium investment, substitute for equilibrium Y
from part (b).
e. From part (b), holding M/P constant, equilibrium Y decreases by
[1/(1-c1-b1+b2d1/d2)] when G decreases by one unit. From part
(d), holding M/P constant, I decreases by
(b1- b2d1/d2)/(1-c1-b1+b2d1/d2) when G decreases by one unit.
So, if G decreases by one unit, investment will increase when
b1
f. A fall in G leads to a fall in output (which tends to reduce
investment) and to a fall in the interest rate (which tends to
increase investment). Therefore, for investment to increase,
the output effect (b1) must be smaller than the interest rate
effect (b2d1/d2).
Note that the interest rate is the product of two factors: (i)
d1/d2, the slope of the LM curve, which gives the effect of a
one-unit change in equilibrium output on the interest rate, and
(ii) b2, which gives the effect of a one-unit change in the
equilibrium interest rate on investment.
4. a. Y=C+I+G=200+.25(Y-200)+150+.25Y-1000i+250
Y=1100-2000i
b. M/P=1600=2Y-8000i
i=Y/4000-1/5
c. Substituting from part (b) into part (a) gives Y=1000.
d. Substituting from part (c) into part (b) gives i=5%.
e. C=400; I=350; G=250; C+I+G=1000
f. Y=1040; i=3%; C=410; I=380. A monetary expansion reduces the
interest rate and increases output. Consumption increases
because output increases. Investment increases because output
increases and the interest rate decreases.
g. Y=1200; i=10%; C=450; I=350. A fiscal expansion increases
output and the interest rate. Consumption increases because
output increases. Investment is affected in two ways: the
increase in output tends to increase investment, and the
increase in the interest rate tends to reduce investment. In
this example, these two effects exactly offset one another, and
investment does not change.
Dig Deeper
5. Firms deciding how to use their own funds will compare the return on
bonds to the return on investment. When the interest rate on bonds
increases, bonds become more attractive, and firms are more likely to
use their funds to purchase bonds, rather than to finance investment
projects.
6. a. If the interest rate were negative, people would hold only
money, and not bonds. Money would be a better store of value
than bonds.
b. See hint.
c. See hint.
d. The increase the money supply has little effect on the interest
rate. If the interest rate is actually zero, than the increase
in the money supply literally has no effect.
e. No. If there is no effect on the interest rate, which affects
investment, monetary policy cannot affect output.
7. a. The reduction in T shifts the IS curve to the right. The
increase in M shifts the LM curve
down. Output increases.
b. The Clinton-Greenspan policy mix was (loosely) contractionary
fiscal policy (IS left) and expansionary monetary policy (LM
down).
c. In 2001, there was a recession, which was triggered by a fall in
investment spending following the decline in the stock market.
The events of September 11, which came after the recession had
begun, had only a limited effect. In fact, the economy had
positive growth in the fourth quarter of 2001. The expansionary
monetary and fiscal policies tended to weaken the recession, but
the policies came too late to avoid a recession.
8. a. Increase G (or reduce T), which shifts the IS curve to the
right, and increase M, which
shifts the LM curve down.
b. Reduce G (or increase T), which shifts the IS curve to the left,
and increase M, which shifts the LM curve down. The interest
rate falls. Investment increases, since the interest rate falls
while output remains constant.
9. a. The IS curve shifts left. Output and the interest rate fall.
b. Consumption falls. The change in investment is ambiguous: the
fall in output tends to
reduce investment, but the fall in the interest rate tends to
increase investment. The change in private saving equals the
change in investment. So, private saving could rise or fall in
response to a fall in consumer confidence.
Explore Further
10. a. The fall in G and the increase in T shift the IS curve to
the left. The increase in M shifts
the LM curve down. The interest rate falls, and
investment increases.
b. Receipts rose, outlays fell, and the budget deficit fell.
c. On September 4, 1992, the FOMC reduced the federal funds rate by
25 basis points. Subsequent changes in federal funds rate over
the period 1993-2000 are given below.
Changes in the Federal Funds Rate
September 4, 1992 3 March 25, 1997
5.5
February 4, 1994 3.25 September 29, 1998
5.25
March 22, 1994 3.5 October 15, 1998 5
April 18, 1994 3.75 November 17, 1998
4.75
May 17, 1994 4.25 June 30, 1999
5
August 16, 1994 4.75 August 24, 1999 5.25
November 15, 1994 5.5 November 16, 1999
5.5
February 1, 1995 6 February 2, 2000
5.75
July 6, 1995 5.75 March 21, 2000 6
December 19, 1995 5.5 May 16, 2000
6.5
January 31, 1996 5.25
d. Investment was 12.1% of GDP in 1992 and increased every
year over the period to reach 17.7% of GDP in 2000.
e. Over the period 1993-2000, the average annual growth rate of
GDP per person was
2.49%. Over the period first four years of the period, the
average annual growth rate was 1.98%; over the second four
years, the average annual growth rate was 3%.
11. a. Growth was negative in 2000:III, 2001:I, and 2001:III.
b. Investment had a bigger percentage change, and unlike
consumption, growth in
investment was negative for every quarter in 2000 and 2001,
except 2000:II. Overall
investment was generally more variable than nonresidential fixed
investment in 2000 and 2001. Moreover, nonresidential fixed
investment had positive growth during 2000, but negative growth
in 2001.
c. Investment had a substantially larger decline in its
contribution to growth in 2000 and
2001. The proximate cause of the recession of 2001 was a fall
in investment demand.
d. Investment fell in the last two quarters of 2001, but began
growing again in the first
quarter of 2001. Consumption growth was slow for the first
three quarters of 2001, but
grew rapidly in the fourth quarter. As mentioned in the text,
the Fed reduced the federal
funds rate several times during the fourth quarter of 2001.
Moreover, automobile manufacturers offered large discounts.
These actions may have helped to generate strong consumer
spending. In any event, it is clear that the events of
September 11 did not cause the recession of 2001. The
recession had started well before these events.
CHAPTER 6
Quick Check
1. a. False. The participation rate has increased over time.
b. False.
c. False.
d. True.
e. False.
f. Uncertain/False. The degree of bargaining power depends on the
nature of the job and
the employee's skills.
g. True.
h. False.
2. a. (Monthly hires + monthly separations)/monthly employment
=(4.4+4.6)/122=7%
b. 1.4/6.2=23%
c. (1.4+1.4)/6.2=45%. Duration is 1/.37 or 2.2 months.
d. (3+2.8+1.4+1.4)/57.3=15%.
e. new workers: 0.4/(3+1.4)=9%.
3. a. W/P=1/(1+()=1/1.05=.952
b. Wage setting: u=1-W/P=4.8%
c. W/P=1/1.1=.91; u=1-.91=9%. The increase in the markup lowers
the real wage. Algebraically, from the wage-setting equation,
the unemployment rate must rise for the real wage to fall. So
the natural rate increases. Intuitively, an increase in the
markup implies more market power for firms, and therefore less
production, since firms will use their market power to increase
the price of goods by reducing supply. Less production implies
less demand for labor, so the natural rate rises.
Dig Deeper
4. a. Answers will vary.
b-c. Most likely, the difference between your actual wage and your
reservation wage will be higher for the job you will have ten
years later.
d. The later job is more likely to require training, which means
you will be costly to replace, and will probably be a much
harder job to monitor, which means you may need an incentive to
work hard. Efficiency wage theory suggests that your employer
will be willing to pay a lot more than your reservation wage for
the later job, to make the job valuable to you, so you will stay
at it and work hard.
5. a. The computer network administrator has more bargaining power.
She is much harder to replace.
b. The rate of unemployment is the most important indicator of
labor market conditions. When the rate of unemployment
increases, it becomes easier for firms to find replacements, and
worker bargaining power falls.
c. In our model, the real wage is always given by the price-setting
relation: W/P=1/(1+().
Since the price-setting relation depends on the actual price
level and not the expected one, this relation holds in the short
run and the medium run of our model
6. a. When the unemployment rate is very low, it is very difficult
for firms to find workers to
hire and very easy for workers to find jobs. As a result, the
bargaining power of workers is very high when the unemployment
rate is very low. Therefore, the wage gets very high as the
unemployment rate gets very low.
b. Presumably, the real wage would grow without bound as the
unemployment rate
approached zero. Since a worker could always find a job, there
would be nothing to constrain aggressive wage bargaining. At
any positive rate of unemployment, however, there is some
constraint on worker bargaining power.
7. a. EatIn Eat out
Population 100 Population 100
Labor Force 75 Labor Force
100
Employment 50 Employment 75
Unemployment 25 Unemployment
25
Unemployment Rate 33% Unemployment Rate
25%
Participation Rate 75% Participation Rate
100%
b. The measured labor force and participation rate rise.
Measured employment
rises. Measured unemployment does not change, but
the measured
unemployment rate falls. Measured GDP will rises.
c. To adjust the labor market statistics, you would have to
estimate the number of
workers informally employed at home and add them to the measured
employed. To the extent that workers employed informally at
home were measured as unemployed, you would have to reduce
measured unemployment accordingly. To the extent that workers
employed informally at home were considered out of the labor
force, counting these workers as employed would increase the
size of the labor force.
To adjust the GDP statistics, you would have to estimate the
value-added of final goods produced at home. You could make
comparisons to similar goods produced outside the home, or make
comparisons to workers involved in similar industries outside
the home, estimate the relevant wage and hours worked, and
calculate value-added as the cost of labor, as is done for
government services. In either case, you need to calculate
value-added, since intermediate goods—groceries, cleaning
supplies, child care supplies, and so on—involved in the
production of at-home goods are already counted in GDP as final
goods in the formal sector.
Explore Further
8. a. 55%; (0.55)2= 30%; (0.55)6 = 2%
b. 55%
c. second month: (0.55)2=30%; sixth month: (0.55)6 = 2%
d. Average proportion 27 weeks or more over 1990-1999= 16.1%
1996: 17% 2000: 11%
1997: 16% 2001: 12%
1998: 14% 2002: 18%
1999: 12% 2003: 22%
The long-term unemployed exit unemployment less frequently than
the average
unemployed worker.
9. a-b. Answers will depend on when the page is accessed.
c. The decline in unemployment does not equal the increase in
employment, because the labor force is not constant.
CHAPTER 7
Quick Check
1. a. True.
b. True. In the AS relation, if P=Pe, Y=Yn. Note that Pe must be
known to graph the AS curve.
c. False. The AD curve slopes down because an increase in P leads
to a fall in M/P, so the
nominal interest rate increases, and I and Y fall.
d. False. There are changes in autonomous expenditure and supply
shocks, both of which
cause output to deviate from the natural level in the short run.
e. True.
f. False. Fiscal policy affects the interest rate in the medium
run and therefore affects
investment.
g. False. The natural level of output changes in response to a
permanent supply shock
(other than a change in Pe). The price level changes in the
medium run in response to either a demand or a supply shock.
2. a. IS shifts right, and LM shifts up. AD shifts right, and AS
shifts up.
b. Y returns to its unchanged natural level. The interest rate and
the price level increase.
3. a. SR: short run WS: wage-setting curve
MR: medium run PS: price-setting curve
" "WS "PS "AS "AD "IS "LM "
"SR "up "no "up "no "no "up "
" " "change" "change"change" "
"MR "same "no "up "no "no "up "
" "as SR "change"furthe"change"change"furthe"
" " " "r " " "r "
WS PS AS AD LM IS
b.
" "Y "i "P "
"SR "falls "rises "rises "
"MR "falls "rises "rises "
" "furthe"furthe"furthe"
" "r "r "r "
i P
4. a. Money is neutral in the sense that the nominal money supply has
no effect on output or the interest rate in the medium run.
Output returns to its natural level. The interest rate is
determined by the position of the IS curve and the natural level
of output. Despite the neutrality of money in the medium run,
an increase in the money supply will increase output and reduce
the interest rate in the short run. Therefore, expansionary
monetary policy can be used to speed up the economy's return to
the natural level of output when output is low.
b. In the medium run, fiscal policy affects the interest rate and
investment, so fiscal policy is
not considered neutral.
c. False. Labor market policies, such as the degree of
unemployment insurance, can affect the natural level of output.
Dig Deeper
5. a. SR: short run
MR: medium run
" "IS "LM "AD "AS "
"SR "left "down "left "no "
" " " " "change"
"MR "same "down "same "down "
" "as SR "furthe"as SR " "
" " "r " " "
WS PS AS AD LM IS
b-c.
" "Y "i "P "
"SR "falls "falls "falls "
"MR "back to "falls "falls "
" "original "further "further "
" "Yn " " "
" "C "I "Private S"
"SR "falls "ambiguous"ambiguous"
"MR "back to "rises "rises "
" "original "(above "(above "
" "level "original "original "
" " "level) "level) "
The short-run change in investment is ambiguous, because the
interest rate falls, which tends to increase investment, but
output also falls, which tends to reduce investment. In the
medium run, investment must rise (as compared to its short-run
and original levels), because the interest rate falls but output
returns to its original level.
Since the budget deficit does not change in this problem, the
change in private saving equals the change in investment. It is
possible that private saving will fall in the short run, but
private saving must rise (above its short-run and original
levels) in the medium run.
6. a. Open answer. Firms may be so pessimistic about sales that they
do not want to borrow at any interest rate.
b. The IS curve is vertical; the interest rate does not affect
equilibrium output.
c. The LM curve is unaffected.
d. The AD curve is vertical; the price level does not affect
equilibrium output.
e. The increase in z reduces the natural level of output and shifts
the AS curve up. Since the AD curve is vertical, equilibrium
output does not change, but the price level increases. Note
that output is above its natural level.
f. Since Y>Yn, P>Pe. Therefore, Pe rises and theAS curve shifts
up. In fact, the AS curve shifts up forever, and the price
level increases forever. Output does not change; it remains
above its natural level forever.
7. a. The LM has a flat segment at i=0 and then slopes up.
b. The IS slopes down as before. There is no flat segment at i=0.
Arguably, the IS curve is
undefined for nominal interest rates below zero.
c. As P falls, M/P rises, and the nominal interest rate falls.
Eventually, when P falls far enough, the nominal interest
reaches zero. The AD curve slopes down until P reaches the
level consistent with i=0. For levels of P below this
threshold, the AD curve is vertical.
d. There is no effect on output in the short run or the medium run.
Since the money stock does not affect the interest rate, it
does not affect output.
8. a. The AD curve shifts left in the short run. Output and the
price level fall in the short run.
In the medium run, the expected price level falls, and AS shifts
right, returning the economy to the original natural level of
output, but at a lower price level.
b. The unemployment rate rises in the short run, but returns to its
original level (the natural rate, which is unchanged) in the
medium run.
c. The Fed should increase the money supply, which shifts the AD
curve right. A monetary expansion of the proper size exactly
offsets the effect of the decline in business confidence on the
AD curve. The net effect is that the AD curve does not move in
the short run or medium run, and neither does the AS curve.
d. Under the policy option in part (c), output and the price level
are higher in the short run. In the medium run, output is the
same in parts (a) and (c), but the price level is higher in part
(c).
e. The unemployment rate is lower in the short run in part (c). In
the medium run, the unemployment rate is the same in parts (b)
and (c).
9. a. The AS curve shifts up in the short run and shifts up
further in the medium run.
Output falls in the short run and falls further in the medium
run. The price level rises in the short run and rises further
in the medium run.
b. The unemployment rate rises in the short run and rises
further in the medium run.
c. The Fed could increase the money supply in the short run
and shift the AD curve to the
right. The AS curve would shift up over time.
d. Output and the price level are higher in the short run in
part (c). Output is the same in the
medium run in parts (a) and (c), but the price level
is higher in part (c).
e. The unemployment rate in the short run is lower in part
(c), but the same in the medium
run in parts (a) and (c).
10. The Fed's job is not so easy. It has to distinguish changes in
the actual rate of unemployment from
changes in the natural rate of unemployment. The Fed can use monetary
policy to keep the unemployment rate near the natural rate, but it
cannot affect the natural rate.
11. a. The unemployment rate rises in the short run and rises
further in the medium run. The
real wage falls immediately to its new medium-run
level.
b. The unemployment rate falls in the short run but returns
to the original natural rate in the medium run. The real wage
is unaffected. However, after tax income rises.
c. In our model, the real wage depends only upon the markup.
A fall in the markup increases the real wage. Policy measures
that improve product market competition—for example, more
vigorous anti-trust enforcement—could increase the real wage.
d. The fall in income taxes tended to increase the after-tax
real wage. The increase in oil prices tended to reduce the
after-tax real wage. Intuitively, the immediate effect of an
oil price increase is to reduce the real wage by increasing gas
prices. Thus, the increase in gas prices tends to absorb the
extra after-tax income provided by the tax cut.
Explore Further
12. a. P=(1+()(Pe)a(F(u,z))a(PE)1-a
b. P=(1+()(Pe)a(F(u,z))a(Px)1-a
P= Pe(1+()1/aF(u,z)x(1-a)/a
c. The AS curve slopes up in Y-P space.
d. If P= Pe, then 1=(1+()1/aF(u,z)x(1-a)/a.
An increase in x implies that F must fall to
maintain the equality. F falls when u rises.
So, an increase in the relative price of energy resources leads
to an increase in the natural rate of unemployment.
e. The AS curve shifts up in the short run and shifts up
further in the medium run. The
unemployment rate and the price level rise in the short run and
rise further in the medium run. Output falls in the short run
and falls further in the medium run.
f. An increase in the relative price of energy resources
causes the AS curve to shift up in the short run. If Pe remains
constant, the AS curve will not shift further after the initial,
short-run shift. In order for Pe to remain constant, wage
setters must be expecting the Fed to reduce the money supply,
thereby shifting the AD curve left. This monetary policy moves
output to its new, lower natural level right away, and maintains
the original price level, so there will be no price adjustment
in the transition to the new medium-run equilibrium.
13. a. 1959:IV – 1969:IV 52.9%
1969:IV – 1979:IV 38.2%
1979:IV – 1989:IV 35.1%
1989:IV – 1999:IV 37.6%
1999:IV – 2007:IV 20.7%
b. The 70s, 80s, and 90s look remarkably similar. The 60s
had by far the highest growth.
Clearly, the first decade of the 21st century will
have the lowest growth.
Note, although the problem did not ask for the growth rates of
GDP per person, the ranking of the decades would be similar.
The growth rates of GDP per person are given below.
1959:IV – 1969:IV 34.4%
1969:IV – 1979:IV 24.0%
1979:IV – 1989:IV 23.0%
1989:IV – 1999:IV 21.8%
1999:IV – 2007:IV 11.7%
CHAPTER 8
Quick Check
1. a. True.
b. False.
c. False.
d. True.
e. False.
f. True.
2. a. No. In the 1970s, we experienced high inflation and high
unemployment. The expectations-augmented Phillips curve is a
relationship between inflation and unemployment conditional on
the natural rate and inflation expectations. Given inflation
expectations, when the natural rate of unemployment increases
(i.e., when there is an increase in z or (), there is also an
increase in both the actual unemployment rate and the inflation
rate. In addition, increases in inflation expectations imply
higher inflation for any level of unemployment. In the 1970s,
both the natural rate and expected inflation increased, so both
unemployment and inflation were relatively high.
Note that increases in inflation expectations also tend to
increase the unemployment rate in the short run from the supply
side—think of an increase in the expected price level, given
last period's price, in the AD-AS framework. However, increases
in inflation expectations may tend to increase short run output
from the demand side, because of the real interest rate effect.
The real interest rate is introduced in Chapter 14.
b. No. The expectations-augmented Phillips curve implies that
maintaining a rate of unemployment below the natural rate
requires not merely high inflation but increasing inflation.
This is because inflation expectations continue to adjust to
actual inflation.
3. a. un=0.1/2 =5%
b. πt =0.1-2(0.03) = 4% every year beginning with year t.
c. πet= 0 and πt=4% forever. Inflation expectations will be
forever wrong. This is unlikely.
d. ( might increase because inflation expectations adapt to
persistently positive inflation. The increase in ( has no
effect on un.
e. π5= π 4+0.1-2(0.03)=4%+4%=8%
For t>5, π t= 8% + (t - 5)(4%). So, π 10=28%; π 15=48%.
Inflation increases by four percentage points every year.
f. Inflation expectations will again be forever wrong. This is
unlikely.
4. a. A higher cost of production means a higher markup of the price
level over wages. In the simple model of the text, the markup
reflects all nonwage components of the price of a good.
b. un=(0.08+0.1()/2
The natural rate of unemployment increases from 5% to 6% as (
increases from 20% to
40%.
Dig Deeper
5. a. un=01./2=.05
π t = π t-1 - 2(ut - .05) = π t-1 + 2%=2%
π t = 2%; π t+1 = 4%; π t+2 = 6%; π t+3 = 8%.
b. π t = 0.5 π t + 0.5 π t-1 - 2(ut - .05)
or, π t = π t-1 - 4(ut - .05)
c. π t = 4%; π t+1 = 8%; π t+2 = 12%; π t+3 = 16%
d. As indexation increases, inflation becomes more sensitive to the
difference between the unemployment rate and the natural rate.
6. a. Yes. The average rate of unemployment was lower in the 1990s.
Indeed, even though the unemployment rate was at a historical
low, inflation rose very little.
b. The natural rate of unemployment probably decreased.
7. a. (=1: uu=6%; (=2: uu=3%
As wages become more flexible, more of the effect of supply
shocks (changes in ( and z) is transmitted to changes in wages
and less to changes in the natural rate of unemployment.
b. (=1: uu=9%; (=2: uu=4.5%
In an environment with more wage flexibility (higher (), the
natural rate of
unemployment rises less in response to an increase in the price
of oil.
Explore Further
8. a-d. As of 2006, the equation that seems to fit well is πt – πt-1 =
4.4% –0.73ut, which implies a
natural rate of approximately 6%.
9. The relationships imply a lower natural rate in the more recent
period.
CHAPTER 9
Quick Check
1. a. False. The unemployment rate rises when output growth is less
than the normal rate and
rises when output growth is greater than the normal rate.
b. True.
c. True.
d. False. The Phillips curve relates the change in inflation to
the difference between the
unemployment rate and the natural rate. Okun's law relates the
change in the unemployment rate to the difference between output
growth and the normal rate. The aggregate demand relation
equates inflation to real money growth. It is true that the
aggregate demand relation implies that inflation equals adjusted
money growth, which is the difference between money growth and
output, but this is only a relation between inflation and output
growth conditional on money growth.
e. False. In the medium run, inflation equals adjusted money
growth, which is the
difference between nominal money growth and output growth.
f. True.
g. Uncertain. In principle, the statement is true, but nominal
rigidities may make even fully
credible policy costly.
h. True.
i. True.
2. a. The unemployment rate will increase by 1% per year when g=0.5%.
Absent output growth, productivity growth tends to increase the
unemployment rate, since fewer workers are required to produce a
given quantity of goods. Absent output growth, labor force
growth also tends to increase the unemployment rate, since more
workers are competing for the same number of jobs. Therefore,
unemployment will increase unless the growth rate exceeds the
sum of productivity growth and labor force growth.
b. For the unemployment rate to decrease by 0.5% per year for the
next four years, output must grow at 4.25% per year for each of
the next four years.
c. Okun's law is likely to become ut-ut-1=-0.4*(gyt-5%)
3. a. un= 5%
b. Assume the economy has been at the natural rate of unemployment
for two years (this year and last year). Then, gyt = 3%; gmt =
gyt + πt = 11%.
c. π u gyt gmt
t-1: 8% 5% 3% 11%
t: 4% 9% -7% -3%
t+1: 4% 5% 13% 17%
t+2: 4% 5% 3% 7%
t+3: 4% 5% 3% 7%
4. a. See text for full answer. Gradualism reduces the need for
large policy swings, with effects that are difficult to predict,
but immediate reduction may be more credible and encourage
rapid, favorable changes in inflation expectations.
Nevertheless, the staggering of wage decisions suggests that a
gradual disinflation—as long as it is credible—is the option
consistent with no change in the unemployment rate.
b. The answer is not clear. Based in Ball's evidence, a fast
disinflation probably results in a
lower sacrifice ratio, depending on the features listed in part
(c).
c. Relevant features include the degree of indexation, the nature
of the wage-setting process,
and the initial rate of inflation.
5. a. Inflation will start increasing.
b. It should let unemployment increase to its new, higher, natural
rate.
Dig Deeper
6. a. sacrifice ratio=1
b. πt = 11%; πt+1 = 10%; πt+2 = 9%; πt+3 = 8%; πt+4 = 7%; . . . ;
πt+9 = 2%
c. 10 years; sacrifice ratio=
(10 point years of excess unemployment)/(10 percentage point
reduction in inflation)=1
d. πt = 8.5%; πt+1 = 5.9%; πt+2 = 3.9%; πt+3 = 2.4%; πt+4 = 1.3%
Less than 5 years are required.
sacrifice ratio=5/(12-1.3)=0.47
The sacrifice ratio is lower because people are somewhat forward-
looking and incorporate the target inflation rate into their
expectations.
e. The central bank can let the unemployment rate return to the
natural rate beginning at time t+1. The ex post sacrifice ratio
from this scenario = (1 point year of excess unemployment)/(10
point reduction of inflation) = 0.1
f. Take measures to enhance credibility.
7. a. πt-πt-1= -(ut-.05)
ut- ut-1= -0.4(gmt-πt-.03)
b. Assuming gm,t-1=13%, πt-1= 10%, ut-1=5%, and beginning in year
t, gm=3%, the economy
evolves as follows.
π u
t: 7.1% 7.9%
t+1: 3.1% 9.1%
t+2: -0.7% 8.8%
t+3: -3.2% 7.5%
t+4: -4.1% 5.9%
t+5: -3.5% 4.4%
t+6: -2.1% 3.6%
t+7: -0.5% 3.4%
t+8: 0.8% 3.7%
t+9: 1.5% 4.3%
t+10: 1.6% 4.9%
c. Inflation does not decline smoothly. In the early years, the
large unemployment rates (relative to the natural rate) reduce
inflation to negative values. In this example, money growth
equals the normal growth rate of output, so negative inflation
drives real money growth (and hence output growth) above the
normal output growth rate, and unemployment falls. Eventually,
when unemployment falls below the natural rate, inflation begins
to increase again. These cycles continue, with decreasing
amplitude.
d. u=5% and π=0% in the medium run.
Explore Further
8. a. Yes.
b. The unemployment rate increased from 5.7% in January 2002 to
6.3% in June 2003.
c. Although growth was positive, it well below the normal rate of
3% for most of the period.
Therefore, growth was too low to prevent the unemployment rate
from rising.
d. Employment fell.
e. Yes.
f. Productivity grew.
9. a. Actually, according to non-seasonally adjusted data,
the level of unemployment fell in
five months of 2001, although it rose over the entire year.
Nevertheless, in several months in which the level of
unemployment rose (e.g., July), the level of employment also
rose, which is the point of the problem.
b. The levels of employment and unemployment can both
rise if the participation rate
increases.
Chapter 10
Quick Check
1. a. True.
b. True.
c. False.
d. False.
e. True.
f. False.
g. True.
2. The table should read as follows.
" "Food "Transportation"
" " "Services "
" "Price "Quantit"Price "Quanti"
" " "y " "ty "
"Mexico "5 "400 "20 "200 "
" "pesos " "pesos " "
"United "$1 "1,000 "$2 "2,000 "
"States " " " " "
a. U.S. consumption per person = $1(1000) + $2(2,000)=$5000
b. Mexican consumption per person=5(400) pesos + 2(2000) pesos =
6000 pesos
c. From the U.S. point of view, the exchange rate (E)=10 pesos/$.
Mexican consumption per person in dollars = 6000 pesos/E=$600
d. Mexican consumption per person ($PPP)=$1(400)+$2(200)=$800
e. Mexican standard of living relative to the United States
Exchange rate method: 600/5000 =0.12
PPP method: 800/5000=0.16
3. a. Y=63
b. Y doubles.
c. Yes.
d. Y/N=(K/N)1/2
e. K/N=4 implies Y/N=2. K/N=8 implies Y/N=2.83. Output less than
doubles.
f. No.
g. No. In part (f), we are essentially looking at what happens to
output when we increase capital only, not capital and labor in
equal proportion. There are decreasing returns to capital.
h. Yes.
Dig Deeper
4. a. (Y/Y = .5 ((K/K)
growth rate of output = 1/2 growth rate of capital
b. 4% per year
c. K/Y increases.
d. No. Since capital is growing faster than output, the saving
rate will have to increase to maintain the same pace.
Eventually, the required saving will exceed output. Capital
must grow faster than output because there are decreasing
returns to capital in the production function.
5. Even though the United States was making the most
important technical advances, the other countries were
growing faster because they were importing technologies previously
developed in the United States. In other words, they were
reducing their technological gap with the United States.
Explore Further
6. The figures on GDP per person are chained ($2000) PPP numbers.
a. Version 6.2 of the Penn World Table through 2003 yields the
following average growth
rates.
1951-1973 1974-2003 1991-2003
U.S. 2.19% 1.97% 1.97%
Japan 4.70% 1.98% 0.80%
b. Had the United States and Japan maintained the growth rates
they achieved over the
period 1951 to 1973, Japanese real output per person would have
surpassed U.S. output per person by 2003. Instead, in 2003 U.S.
real output per person ($34,875) was substantially higher than
Japanese real output per person ($24,037).
7. The figures on GDP per person are chained ($2000) PPP numbers.
a. There was substantial convergence for the France, Belgium, and
Italy through 1991.
Since then, the standard of living of these countries relative
to the U.S. standard of living has fallen somewhat.
b. Argentina, Chad, Madagascar, and Venezuela have not converged to
the United States.
In fact, they have grown steadily poorer relative to the United
States.
8. The figures on GDP per person are chained ($2000) PPP numbers.
a. 10 Richest Countries in 1970
Qatar $66, 763
Kuwait $64,914
Brunei $30,749
Bermuda $21,492
Switzerland $21,111
United States $17,321
Bahamas $16,911
Luxembourg $16,806
Denmark $16,584
Sweden $15,785
b. 10 Richest Countries in 2003
Luxembourg $49,262
Qatar $36,157
Bermuda $35,738
United Arab Emirates $35,658
United States $34,875
Norway $34,011
Macao $30,420
Switzerland $28,792
Ireland $28,248
Denmark $27,970
c. 10 Richest Countries in 1970: Proportional Increase in the Standard
of Living 1970-2003
Luxembourg 2.93
United States 2.01
Denmark 1.69
Bermuda 1.66
Sweden 1.66
Switzerland 1.36
Bahamas 1.09
Brunei 0.85
Qatar 0.54
Kuwait 0.40
d. The dataset includes 152 countries with observations for both 1970
and 2003.
biggest proportional increase in standard of living: China
9.94
smallest proportional increase in standard of living: Liberia
0.17
fraction with negative growth: 18/152=18%
Chapter 11
Quick Check
1. a. True, if saving includes public and private saving.
b. False.
c. True. In the model without depreciation, there is no steady
state. A constant saving rate produces a positive but declining
rate of growth. In the infinite-time limit, the growth rate
equals zero. Output per worker rises forever without bound. In
the model with depreciation, if the economy begins with a level
of capital per worker below the steady-state level, a constant
saving rate also produces a positive but declining rate of
growth, with a limit of zero. In this case, however, output
per worker approaches a fixed number, defined by the steady-
state condition of the Solow model. Note that depreciation is
not needed to define a steady state if the model includes labor
force growth or technological progress.
d. Uncertain. See the discussion of the golden-rule saving rate.
e. Uncertain/False. It is likely the U.S. rate is below the golden
rule rate and that transforming Social Security to a pay-as-you-
go system would ultimately increase the U.S. saving rate.
These premises imply that such a transformation would increase
U.S. consumption in the future, but not necessarily in the
present. Indeed, if the only effect of such a transformation
is to increase the saving rate, we know that consumption per
worker will fall in the short run. Moreover, moving to a pay-as-
you-go system requires transition costs. If these costs are
borrowed, then the reduction in public saving will offset the
increase in private saving during the transition. If these
costs are not borrowed, then transitional generations must
suffer either a reduction in promised benefits or an increase in
taxes to finance their own retirement (at least to some degree)
in addition to the retirement of a previous generation. Thus,
whether the U.S. "should" move to a pay-as-you-go system depends
on the likely resolution of intergenerational distributional
issues and your view about the equity of such a resolution.
f. Uncertain. The U.S. capital stock is below the golden rule,
but that does not necessarily
imply that there should be tax breaks for saving. Even if the
tax breaks were effective in stimulating saving, the increase in
future consumption would come at the cost of current
consumption.
h. False. Even if you accept the premise (that educational
investment increases output, as would be implied by the Mankiw,
Romer, Weil paper), it does not necessarily follow that
countries should increase educational saving, since future
increases in output will come at the expense of current
consumption. Of course, there are other arguments for
subsidizing education, particularly for low-income households.
2. Disagree. An increase in the saving rate does not affect growth in
the long run, but does increase
growth in the short run. In addition, an increase in the saving rate
leads to an increase in the long-
run level of output per worker. Finally, since the evidence suggests
that the U.S. saving rate is below the golden-rule rate, an increase
in the saving rate would increase steady-state consumption per worker.
3. Assume that the economy begins in steady state. One decade after an
increase in the saving rate, the growth rate of output per worker will
be higher than it was in its initial steady state. Five decades after
an increase in the saving rate, the growth rate of output per worker
will be close to its value in the initial steady state (this value is
zero in the absence of technological progress). The level of output
per worker will be higher, however, than it was in the initial steady
state.
Dig Deeper
4. a. This would likely lead to a higher saving rate, so output per
worker and output per person
will be higher in the long run.
b. Treat an increase in female participation as a one-time increase
in employed labor. In this case, an increase in female
participation would have no effect on the level of output per
worker, but would lead to a higher level of output per person,
since a greater fraction of the population is employed.
5. A transformation to a fully funded system leads to an increase in the
saving rate. Ignoring any
short-run transition costs, in the long run an increase in the saving
rate leads to a higher level of output per worker, but has no effect
on the growth rate of output per worker.
6. a. K/N=(s/(2())2; Y/N=s/(4()
b. C/N=(1-s)Y/N=s(1-s)/(4()
c-e. Y/N increases with s. C/N increases until s=0.5, then
decreases.
7. a. Yes.
b. Yes.
c. Yes.
d. Y/N = (K/N)1/3
e. In steady state, sY//N = (K/N, which, given the production
function in part (d), implies
K/N=(s/()3/2
f. Y/N =(s/()1/2
g. Y/N = 2
h. Y/N = 21/2
8. a. Substituting from problem 7 part (e) implies K/N=1.
b. Substituting from problem 7 part (f), Y/N=1.
c. K/N=0.35; Y/N=0.71
d. K/N Y/N
t 1.00 1.00
t+1 0.90 0.97
t+2 0.80 0.93
t+3 0.71 0.89
9. b. K/N = (0.15/.075)2 = 4
Y/N= (4)1/2=2
c. K/N=(0.2/0.075)2 =7.11
Y/N=(7.11)1/2=2.67
Capital per worker and output per worker increase.
Explore Further
10. a. For 2006, the national saving rate was approximately 14.1%.
In steady state, K/N = (0.141/0.075)2 =3.56, and Y/N=(3.25)1/2
=1.89.
b. For 2006, the budget deficit (including the off budget items)
was 1.9% of GDP.
Eliminating the deficit increases the national saving rate to
16% (14.1% + 1.9%). As a
result, in steady state, K/N = (0.16/.075)2=4.55, and
Y/N=(4.55)1/2 =2.13. Steady-state output per worker increases
by 12.7%.
CHAPTER 12
Quick Check
1. a. True.
b. True.
c. False. In steady state, there is no growth of output per
effective worker.
d. True.
e. False. The steady-state rate of growth of output per effective
worker is zero. A higher
saving rate leads to higher steady-state level of capital per
effective worker, but has no effect on the steady-state rate of
growth of output per effective worker.
f. True.
g. False.
h. False/Uncertain. Even pessimists about technological progress
typically argue that the
rate of progress will decline, not that it will be zero.
Strictly, however, the truth of this statement is uncertain,
because we cannot predict the future.
2. a. Most technological progress seems to come from R&D activities.
See discussion on fertility and appropriability in Chapter
12.2.
b. This proposal would probably lead to lower growth in poorer
countries, but higher
growth in rich countries.
c. This proposal would lead to an increase in R&D spending. If
fertility did not fall, there
would be an increase in the rates of technological progress and
output growth.
d. Presumably, this proposal would lead to a (small) decrease in
the fertility of applied
research and therefore to a (small) decrease in growth.
e. This proposal would reduce in the appropriability of drug
research. Presumably, there would be a reduction in the
development of new drugs, a reduction in the rate of
technological progress, and a reduction in the growth rate.
3. a. The economic leaders typically achieve technological progress
by generating new ideas
through research and development.
b. Developing countries can import technology from the economic
leaders by copying this
technology or by receiving a transfer of technology as a result
of joint ventures with firms headquartered in the economic
leaders. Even in the absence of technology transfer, foreign
direct investment can increase technological progress in the
host country by substituting more productive foreign production
techniques for less efficient domestic ones.
c. Poor patent protection may facilitate a more rapid adoption of
new technologies in developing countries. The costs of such a
policy are relatively small, since developing countries generate
relatively few new technologies.
Dig Deeper
4. a. The growth rate of output per worker falls in the short run and
continues to fall over time.
In the long run, the growth rate approaches a new steady state
with a permanently lower (but still positive) growth rate.
Output per worker continues to rise over time, just at a slower
rate.
b. A permanent reduction in the saving rate has no affect on the
steady-state growth rate of output per worker. The growth rate
of output per worker falls (but remains positive) in the short
run but in the long run it approaches its original steady-state
rate.
5. a. Nominal GDP
Year 1: 10(100)+10(200)=3000
Year 2: 12(100)+12(230)=3960
b. Year 2 Real GDP (Year 1 Prices)=10(100)+10(230)=3300
growth rate of real GDP=3300/3000 – 1 = 10%
c. GDP deflator
Year 1=1; Year 2=3960/3300=1.2
inflation=20%
d. Real GDP/Worker
Year 1 = 3000/100=30; Year 2 = 3300/110=30
Labor productivity growth is zero.
e. Year 2 Real GDP (Year 1 Prices)=10(100)+13(230)=3990
output growth=3990/3000 – 1 = 33%.
f. GDP deflator
Year 1=1; Year 2=3960/3990=0.992
inflation=0.992/1 – 1 = -0.8%
g. Real GDP/worker=36.3 in year 2. Labor productivity growth is
36.3/30=21%.
h. This statement is true, assuming there is progress in the
banking services sector.
6. a. i. K/(AN) = (s/((+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. K/(AN) = (s/((+gA+gN))2 = 0.64
ii. Y/(AN)= (K/AN)1/2=0.8
iii. gY/(AN) = 0
iv. gY/N = gA=8%
v. 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. K/(AN) = (s/((+gA+gN))2 = 0.64
ii. Y/(AN)= (K/AN)1/2=0.8
iii. gY/(AN) = 0
iv. gY/N = gA=4%
v. gY = gA+gN=10%
(K/(AN)) = (4/5)2; (Y/(AN)) = (4/5); gY/(AN) = 0; gY/N = 4%; gY
= 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).
7. a. Probably affects A. Think of climate.
b. Affects H and possibly A, if better education improves the
fertility of research.
c. Affects A. Strong protection tends to encourage more R&D but
also to limit diffusion of technology.
d. May affect A through diffusion.
e. May affect K, H, and A. Lower tax rates increase the after-tax
return on investment, and thus tend to lead to more accumulation
of K and H and to more R&D spending.
f. If we interpret K as private capital, than infrastructure
affects A (e.g., better transportation networks may make the
economy more productive by reducing congestion time).
g. Assuming no technological progress, a reduction in population
growth implies an increase in the steady-state level of output
per worker. A reduction in population growth leads to an
increase in capital per worker. If there is technological
progress, there is no steady-state level of output per worker.
In this case, however, a reduction in population growth implies
that output per worker will increase at every point in time, for
any given path of technology. See the answer to problem 6(c).
Explore Further
8. a. The quantity gY – gN is the growth rate of output per worker.
The quantity gK – gN is the
growth rate of capital per worker.
b. gK – gN = 3(gY – gN) – 2gA
c. gY – gN gA gK – gN
U.S. 1.8% 2.0% 1.4%
France 3.2% 3.1% 3.4%
Japan 4.2% 3.8% 5.0%
UK 2.4% 2.6% 2.0%
Chapter 13
Quick Check
1. a. False. Productivity growth is unrelated to the natural rate of
unemployment. If the
unemployment rate is constant, employment grows at same rate as
the labor force.
b. False.
c. True.
d. True.
e. True.
f. True.
g. False.
2. a. u = 1-(1/(1+())(A/Ae)
b. u = 1-(1/(1+0.05)) = 4.8%
c. No. Since wages adjust to expected productivity, an increase
in productivity eventually leads to equiproportional increases
in the real wage implied by wage setting and the real wage
implied by price setting, at the original natural rate of
unemployment. Thus, equilibrium can be maintained without any
change in the natural rate of unemployment.
3. An increase in labor productivity has no effect on the natural rate
of unemployment, because the
wage ultimately rises to capture the added productivity. The increase
in the wage also implies that an increase in labor productivity has no
permanent effect on inflation. From the price setting equation,
P=(1+()W/A. If the wage (W) increases by the same proportion as
productivity (A), the price level will not change.
4. a. Reduce the gap, if this leads to an increase in the relative
supply of high-skill workers.
b. Reduce the gap, since it leads to a decrease in the relative
supply of low-skill workers.
c. Reduce the gap, if it leads to an increase in the relative
supply of high-skill workers.
d. Increase the gap, if it leads U.S. firms hire low-skill workers
in Central America, since this reduces the relative demand for
U.S. low-skill workers.
Dig Deeper
5. Technological change has led to a reduction in agricultural
employment, but evidently has had no effect on the natural rate of
unemployment.
6. a. P = Pe(1+()(Ae/A)(Y/AL)
The new variables are technology variables, A and Ae. An
increase in A has two effects.
i. For a given level of Y, an increase in A reduces Y/A,
which implies a reduction in N and in increase in u. The
increase in u tends to reduce W and therefore to reduce P.
This is the effect that tends to increase the actual rate
of unemployment in the short run.
ii. To the extent that Ae lags behind A, Ae/A falls. In
effect, workers do not receive as much of an increase in
wages as warranted by the increase in productivity. This
is the effect that tends to reduce the actual and natural
rates of unemployment for a time.
The effects in (i) and (ii) both shift the AS curve down, so
output increases in the short run. The effect on short-run
unemployment depends on the relative strength of the effects in
(i) and (ii).
b. AS shifts down. Given Ae/A=1, only effect (i) is relevant.
c. In this case, effects (i) and (ii) from part (a) are relevant.
Compared to part (b),
the AS curve shifts down further.
7. a. W/P=F(1-N/L,z)
b. Labor supply slopes up. As N increases, u falls for given L,
so W/P increases.
c. W/P=MPL/(1+()
d. Labor demand slopes down. As N increases, the MPL falls, so
W/P falls.
e. An improvement in technology increases the MPL, so the labor
demand curve shifts right. The real wage increases when
technology improves.
8. a. The real wage of high-skill labor increases. The real wage of
low-skill labor falls.
b. Since there is a binding minimum real wage, a fall in labor
demand has no effect on the
real wage of low-skill workers. Employment of low-skill workers
falls, however, and the unemployment rate increases.
c. Wage inequality will increase by a greater amount in the United
States. Unemployment
will increase by a greater amount in Europe.
d. The United States has had a large increase in wage inequality
over the past 30 years, and Europe has had a large increase in
the unemployment rate.
Explore Further
9. a. Projections for job decline from 2006-2016
Some examples:
Stock clerks and order fillers – technological change
Electrical and electronic equipment assemblers – perhaps
foreign competition
b. Projections for job growth from 2006-2016
Some examples:
Home health aides – aging of the population
Computer systems analysts – technological change
c. More occupations that are forecast to grow require degrees as
opposed to on-the-job
training.
10. a. For a given markup, the real wage grows at the rate of
technological progress. Clearly,
there has been technological progress since 1973.
b. 1973: $8.98; 2006: $8:24
c. The real wage of low-skill workers has fallen markedly, which
suggests that the relative
demand for low skill workers has fallen markedly.
d. Other benefits, particularly health care benefits, might be
missing from this calculation.
CHAPTER 14
Quick Check
1. a. True.
b. True.
c. True.
d. False.
e. True.
f. False.
g. True.
h. True. The nominal interest rate is always positive.
i. False. The real interest rate can be negative.
2. a. Real. Nominal profits are likely to move with inflation; real
profits are easier to forecast.
b. Nominal. The payments are nominal.
c. Nominal. Car lease and car loan payments are usually stated in
nominal terms.
3. a. exact: r = (1+.04)/(1+.02)-1 = 1.96%; approximation: r (.04-.02
= 2%
b. 3.60%; 4%
c. 5.48%; 8%
4. a. No. If the nominal interest rate were negative, nobody would
hold bonds. Money would be more appealing since it could be
used for transactions and would earn zero—as opposed to
negative—interest.
b. Yes. The real interest rate is negative if expected inflation
exceeds the nominal interest rate. Even in this case, the real
interest rate on bonds (which pay nominal interest) exceeds the
real interest rate on money (which does not pay nominal
interest) by the nominal interest rate.
c. A negative real interest rate makes borrowing very attractive
and leads to a large demand for investment.
d. Answers will vary.
5. a. The discount rate is the interest rate. So, in case (i), the
EPDV is $2,000(1-0.25) under either interest rate, and in case
(ii) the EPDV is (1-0.2)$2,000 under either interest rate.
b. The interest rate does not enter the calculation. Hence, you
prefer (ii) to (i) since 20%<25%.
Note that the answer to part (a) does not imply that saving will
not accumulate. By retirement, the initial investment will have
grown by a factor of (1+i)40 in nominal terms and (1+r)40 in
real terms. As long as r is positive, the purchasing power of
the initial investment will grow.
Moreover, this problem assumes that the tax rate you will pay
upon retirement (25%) is higher than the tax rate you pay when
you establish the IRA (20%). This assumption may be false for
some taxpayers.
6. a. $V=$100/0.1=$1000
b. Since the first payment occurs at the end of the year,
$V = $z[1- 1/(1+i)n]/[1-(1+i)] - $z.
10 years: $575.90; 20 years: $836.49; 30 years: $936.96; 60
years: $996.39
c. i = 2%: PV of consol=$5000; 10 years: $816.22; 20 years:
$1567.85; 30 years: $2184.44; 60 years: $3445.61
i = 5%: PV of consol=$2000; 10 years: $710.78; 20 years:
$1208.53; 30 years: $1514.11; 60 years: $1887.58
7. a. The Fisher hypothesis is that in the medium run, changes in
inflation are reflected one- for-one in changes in the nominal
interest rate. In other words, in the medium run, changes in
inflation have no effect on the real interest rate.
b. Support.
c. The line should not go through the origin, because the real
interest rate is positive: when
inflation equals zero, the nominal interest rate is positive.
d. No. Even if monetary policy does not affect output or the real
interest rate in the medium
run, it can be used in the short run.
Dig Deeper
8. a. The IS shifts right. At the same nominal interest rate, the
real interest rate is lower, so output is higher.
b. The LM curve shifts down because the increase in money growth
leads to an increase in the real money stock. The increase in
expected inflation has no effect on the LM curve, because money
demand depends on the nominal interest rate, not the real
interest rate.
c. Output increases. The nominal interest rate is higher than in
Figure 14-5. Whether the nominal interest rate is lower or
higher than before the increase in money growth is ambiguous.
Thinking in terms of the money market equilibrium, the increase
in the nominal money supply tends to reduce the nominal interest
rate, but the increase in nominal money demand (because of the
increase in output) tends to increase the nominal interest rate.
d. Output is higher than in Figure 14-5. Reasoning from the IS
relation, the real interest rate must be lower, since no
exogenous variables in the IS relation have changed. (In other
words, while the nominal interest rate may increase relative to
Figure 14-5, it increases by less than the increase in expected
inflation, so the real interest rate decreases.)
Explore Further
9. Answers will vary depending upon when the website is accessed.
CHAPTER 15
Quick Check
1. a. False.
b. True.
c. True.
d. False.
e. True.
f. True.
g. False.
h. Uncertain/False. Some of the increase in the stock market was
probably justified. However, most economists believe that there
was a bubble in the stock market as well. A
stock market correction followed.
2. a. (1+i)n=$F/$P
1+i =($F/$P)1/n
i =(1000/800)1/3-1 = 7.7%
b. 5.7%
c. 4.1%
3. The yield is approximately the average of the short-term interest
rates over the life of the bond.
a. 5%.
b. 5.25%
c. 5.5%
4. a. The LM curve shifts down unexpectedly. There is unexpected
fall in the interest rate and an unexpected increase in output.
Both of these changes lead to an increase in the stock price.
b. There is no change in the stock price.
c. The effect on the stock price is ambiguous. Unexpected
expansionary fiscal policy means the interest rate is higher
than expected (after the expected expansionary monetary policy)
but so is output. The interest rate effect tends to reduce the
stock price; the output effect to increase them.
Dig Deeper
5. a. See Figure 14-5 in Chapter 14.
b. Initially after the increase, the yield curve will slope down
out to one-year maturities, then slope up. After one year, the
yield curve will slope up. After three years, the yield curve
will be flat.
6. a. This question should have read: "Explain why an inverted
(downward-sloping) yield curve may indicate that a recession is
coming."
An inverted yield curve implies that the expected future
interest rate is lower than the current interest rate. These
expectations could arise from a belief that the IS curve is
going to shift to the left in the future, say because future
investment is expected to fall. If the IS curve shifts left in
the future, output will fall.
b. Given the Fisher effect, a steep yield curve probably implies
that financial market participants believe that future inflation
will be substantially higher than current inflation.
7. Let r be the real interest rate, g the growth rate of dividends, and
x the risk premium. The price is given by the following expression.
Q=1000/(1 + r + x) + 1000(1 + g)/(1 + r + x)2 + 1000(1 + g)2/(1 + r +
x)3 . . .
= [1000/(1 + r + x)][1 + (1 + g)/(1 + r + x) + (1 + g)2/(1 + r +
x)2 + . . .] = 1000/(r + x - g)
a. $50,000; $20,000
b. $10,000; $7692.31
c. $16,666.67; $11,111.11
d. The stock price increases when the risk premium falls. A fall
in the risk premium is like
a fall in the real interest rate.
Explore Further
8. a. The Fed can reduce the growth rate of money. The nominal
interest rate increases in the short run, but falls in the
medium run.
b. Inflation was highest in early 1980. The 12-month inflation
rate peaked at 14.6% in March and April of 1980.
d. A positive spread means that expected future interest rates are
higher than current interest rates. A declining spread means
that the expected increase in future short-term interest rates
is falling. The one-year T-bill rate increased from 7.28% to
12.6% between January 1978 and January 1980, but the spread
declined from 0.9 percentage points to –1.46 percentage points
over the same period. Financial market participants were not
expecting short-term interest rates to continue to increase.
Indeed, by the end of the 1970s, the negative spread indicates
that short-term interest rates were expected to decline in the
future.
e. There spread declined by almost one percentage point in October
1979. The decline is
consistent with expectations of lower inflation in the future.
f. The one-year interest rate fell.
g. During the rate cut in the recession, spreads went up, as short-
term rates declined. However, long-term rates did not increase,
which suggests that inflation expectations did not increase.
Instead, the increase in spreads is consistent with the
expectation that the anti-inflationary policy would continue
with high short-term interest rates after the recession. This
is indeed what happened.
9. Answers will vary.
10. Answers will vary.
CHAPTER 16
Quick Check
1. a. False.
b. False.
c. False.
d. False.
e. False.
f. True.
g. True.
2. a. 0.75(1+1.05+1.052)$40,000=$94,575
b. $194,575
c. The consumer works for three more years and will be retired for
seven years, so there are 10 more years of consumption. So,
since the real interest rate is zero, the consumer can consume
one-tenth of her total wealth, or 19,457.50, this year.
d. Consumption could increase by $2,000 annually.
e. Benefits imply extra annual consumption of
0.6(1.052)$40,000(7/10)=$18,522.
3. The EPDV of purchasing the machine is (/(r+() = $18,000/(r+0.08)
a. Buy. EPDV=$138,462>$100,000
b. Break-even. EPDV=$100,000
c. Do not buy. EPDV=$78,261<$100,000
4. a. $44,000(1-0.4)36-$40,000(1-0.4)38=$38,400
b. $44,000(1-0.3)36-$40,000(1-0.3)38=$44,800
Dig Deeper
5. a. EPDV of future labor income = $30. Consumption=$10 in all
three periods.
b. youth: -5; middle age: 15; old age: -10
c. Total saving =n(-5+15-10)=0
d. 0 – 5n + 10n = 5n
6. a.. youth: 5; middle age: 12.5; old age: 12.5
The consumer cannot borrow against future income when young.
b. 0 + 12.5n - 12.5n = 0
c. 0 + 0 + 12.5n = 12.5n
d. By allowing people to borrow to consume when young, financial
liberalization may lead to less overall accumulation of capital.
7. a. Expected value of earnings during middle age is
0.5($40,000+$100,000)=$70,000.
EPDV of lifetime earnings = $20,000 + $70,000=$90,000.
The consumption plan is $30,000 per year.
The consumer will save -$10,000 (i.e., the consumer will borrow
$10,000) in the first
period of life.
b. In the worst case, the EPDV of lifetime earnings = $60,000.
Consumption = $20,000 and saving=0 in the first period of life.
Consumption is lower than part (a), and saving is higher.
c. Consumption in youth is $20,000; in middle age is $50,000; and
in old age is $50,000.
Consumption will not be constant over the consumer's lifetime.
d. The uncertainty leads to higher saving by consumers in the
first period of life.
Explore Further
8. a-c. Between 1959 and 2006, consumption accounted for 66% of GDP on
average and investment for about 13%, so consumption is about
five times bigger than investment. Relative to average
changes, movements in consumption and investment are of similar
magnitude, which implies investment is much more volatile than
consumption.
9. a. Consumers may be more optimistic about the future (and spend
more) when disposable
income is higher, so consumer confidence might be positively
related to disposable income. However, consumer confidence
should depend on expectations about the future, rather than on
current variables per se. Hence, there are reasons to think
changes in consumer confidence might not always track changes in
disposable income.
b. There appears to be positive relationship between the
variables, but it is not tight.
c. Personal disposable income increased at an annual rate of 11.5%
in 2001:III and at an
annual rate of 11.6% in 2002:I. Consumer confidence fell in
2001:III but rose in 2002:I. The events of September 11, as well
as the ongoing recession, probably played a role in the consumer
confidence numbers for 2001:III.
cHAPTER 17
Quick Check
1. a. False.
b. False.
c. False.
d. True/Uncertain. Consumers can rely on forecasts by others, but
somebody has to do it.
e. False.
f. True.
g. False.
2. a. Higher real stock prices led to an increase real wealth
directly, which would tend to increase consumption. Moreover,
the hype about the New Economy, combined with increasing stock
prices, may have led to favorable expectations about future
labor income, which would also tend to increase consumption.
b. Subsequent declines in the stock market decreased wealth and may
have led consumers to revise (downward) expectations about future
labor income, effects that would tend to reduce consumption.
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. In 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.
4. Rational expectations may be unrealistic, but it does not imply that
every consumer has perfect knowledge of the economy. It implies that
consumers use the best available information—models, data, and
techniques—to assess the future and make decisions. Moreover,
consumers do not have to work out the implications of economic models
for the future by themselves. They can rely on the predictions of
experts on television or in the newspapers. Essentially, rational
expectations rules out systematic mistakes on the part of consumers.
Thus, although rational expectations may not literally be true, it
seems a reasonable benchmark for policy analysis.
5. The answers below ignore any effect on capital accumulation and
output in the long run. Assume the tax cut policy in the future is
temporary, so we need only worry about future short-run effects.
a. The effect on current output is ambiguous. The tax cut in the
future will lead to a boom. Output and the real interest rate
will increase. The increase in expected future output tends to
shift the IS curve to the right; the increase in the expected
future real interest rate tends to shift the IS curve to the
left. Finally, the fall in expected future taxes tends to
increase expected future after-tax income (for any given level
of income). This effect tends to shift the IS curve to the
right.
b. This means that the Fed will increase the interest rate in the
future (shift the LM curve to the left in the future). The
expected interest rate will increase more, which tends to to
shift the IS curve to the left, but there is still the effect of
lower expected taxes on current consumption. The effect today
on output is still ambiguous, but more likely to be negative
than in part (a).
c. Future output will be higher, the future interest rate will not
increase, and future taxes will be lower. The IS curve
definitely shifts to the right in the current period, and
current output increases.
Dig Deeper
6. a-b. See the discussion in the text.
c. The gesture seemed to indicate that the Fed supported deficit
reduction, and was willing to conduct expansionary monetary
policy in the future to offset the direct negative effects on
output from spending cuts and tax increases. A belief that the
Fed was willing to act in this way would tend to increase
expected future output (relative to the case where the Fed did
nothing) and to reduce expected future interest rates. Both of
these effects would tend to increase output in the short-run.
7. a. Future interest rates will tend to rise. Future output will
tend to fall. Both effects shift the IS curve to the left in
the present. Current output and the current interest rate
fall. The yield curve gets steeper on the day of the
announcement.
b. No.
c. Compared to original expectations, the nominee is expected to
follow a more expansionary monetary policy. The yield curve
will get flatter on the day of the announcement.
Explore Further
8. a. The interest rate will increase in the short run, and increase
even further in the medium run. The yield curve will get
steeper.
b. The spread increased over the period.
5-Year Yield minus 3-Month Yield
August 2002: 1.64%
January 2003: 1.86%
August 2003: 2.4%
January 2004: 2.22%
Chapter 18
Quick Check
1. a. True.
b. False.
c. False.
d. False.
e. False.
f. The statement should read: "Given the definition of the
exchange rate adopted in this chapter, if the dollar is the
domestic currency and the euro the foreign currency, a nominal
exchange rate of 1.10 means that one dollar is worth 1.1 euros."
This statement is True.
g. False.
2. Domestic Country Balance of Payments ($)
Current Account
Exports 25
Imports 100
Trade Balance -75 (=25-100)
Investment Income Received 0
Investment Income Paid 15
Net Investment Income -15
(=0-15)
Net Transfers Received -25
Current Account Balance -115 (=-75-15-
25)
Capital Account
Increase in Foreign Holdings of Domestic Assets 80 (=65+15)
Increase in Domestic Holdings of Foreign Assets -50
Net Increase in Foreign Holdings 130 (=80-(-50))
Statistical Discrepancy -15 (=115-
130)
Foreign Country Balance of Payments ($)
Current Account
Exports 100
Imports 25
Trade Balance 75 (=100-25)
Investment Income Received 15
Investment Income Paid 0
Net Investment Income 15
(=15-0)
Net Transfers Received 25
Current Account Balance 115
(=75+15+25)
Capital Account
Increase in Foreign Holdings of Domestic Assets -50
Increase in Domestic Holdings of Foreign Assets 80 (=65+15)
Net Increase in Foreign Holdings -130 (=-50-80)
Statistical Discrepancy 15 (=130-
115)
3. a. The nominal return on the U.S. bond is 10,000/(9615.38)–1=4%.
The nominal return on the German bond is 6%.
b. Uncovered interest parity implies that the expected exchange
rate is given by
E(1+i*)/(1+i)=0.75(1.06)/(1.04)=0.76 Euro/$.
c. If you expect the dollar to depreciate, purchase the German
bond, since it pays a higher interest rate and you expect a
capital gain on the currency.
d. The dollar depreciates by 4%, so the total return on the German
bond (in $) is
6% + 4% =10%. Investing in the U.S. bond would have produced a
4% return.
e. The uncovered interest parity condition is about equality of
expected returns, not equality
of actual returns.
Dig Deeper
4. a. GDP is 15 in each economy. Consumers will spend 5 on each
good.
b. Each country has a zero trade balance. Country A exports
clothes to Country B, Country
B exports cars to Country C, and Country C exports computers to
Country A.
c. No country will have a zero trade balance with any other
country.
d. There is no reason to expect that the United States will have
balanced trade with any particular country, even if the United
States eliminates its overall trade deficit.
5. a. The relative price of domestic goods falls. Relative demand
for domestic goods rises. The domestic unemployment rate falls
in the short run.
b. The price of foreign goods in terms of domestic currency is
P*/E. A nominal depreciation (a fall in E) increases the price
of foreign goods in terms of domestic currency. Therefore, a
nominal depreciation tends to increase the CPI.
c. The real wage falls.
d. Essentially, a nominal depreciation stimulates output by
reducing the domestic real wage, which leads to an increase in
domestic employment.
Explore Further
6. a. Considering the evidence through May 2008, the yen appreciated
from mid-1985 to mid-1995, depreciated until mid-1998,
appreciated through the end of 1999, depreciated through the end
of 2001, appreciated through 2004, depreciated through mid-2007,
and then began to appreciate. From a broader perspective,
between the January 1979 and May 2008, the yen appreciated by
90%. The yen reached its strongest value against the dollar in
mid-1995.
b. Depreciation of the yen.
c. The yen appreciated from the end of 2001 to the end of 2004, and
again after mid-2007, . This did not help the Japanese
recovery.
7. a. The sum of world current account balances should be zero. In
2007, the sum was positive, which implies literally that the
world as a whole was borrowing. Obviously, this cannot have
been true.
b. In 2007, the United States was the world's biggest borrower by
far. The rest of the advanced economies as a whole were
lenders, although the Euro area as a borrower. The economies of
the Middle East and developing economies in Asia were other
large lenders; the economies of central and eastern Europe were
large borrowers.
c. In 2007, the saving of the advanced economies other than the
Untied States amounted to only 24% of U.S. borrowing. So, the
United States was borrowing heavily from all regions of the
world.
d. The projections in the April 2008 World Economic Outlook
suggested no qualitative change in the answers to parts (a)
through (c).
8. a. World saving essentially equals world investment, as it must
logically.
b. In 2007. U.S. saving was 13.6% of GDP, but U.S. investment was
18.8% of GDP. The United States financed the difference by
borrowing from abroad. The April 2008 World Economic Outlook
projected a gap of similar magnitude for the next two years.
Chapter 19
Quick Check
1. a. False.
b. False. An increase in the budget deficit will lead to an
increase in the trade deficit, but we can't conclude that from
the national income accounting identity. We have to use our
model to make that prediction.
c. False.
d. True.
e. False. Econometric evidence suggests that a real depreciation
does not lead to an immediate improvement in the trade balance.
Typically, the trade balance improves six to twelve months after
a real depreciation. only after six to twelve months between
only after six to twelve months.
f. True.
g. False.
2. a. There is a real appreciation over time. Over time, the trade
balance worsens.
b. The currency depreciates at the rate of (-(*.
3. a. The share of Japanese spending on U.S. goods relative to U.S.
GDP is
(0.06)(0.11)=0.7%.
b. U.S. GDP falls by 2(.05)(.007)=0.07%.
c. U.S. GDP falls by 2(.05)(0.11)=1.1%.
d. This is an overstatement. The numbers above indicated that even
if U.S. exports fall by 5%, the effect is to reduce GDP growth
by 1.1%.
4. Answers follow the model in the text.
Dig Deeper
5. a. The ZZ and NX lines shift up. Domestic output and domestic net
exports increase.
b. Domestic investment will increase because output increases.
Assuming taxes are fixed, there is no effect on the deficit.
c. NX=S-I+T-G. Since the budget deficit is unchanged, and I and NX
increase, S must increase.
d. Except for G and (for our purposes) T, the other variables in
equation (19.5) are endogenous. An exogenous shock such as an
increase in foreign output can affect all of the endogenous
variables simultaneously.
6. a. There must be a real depreciation.
b. Y=C+I+G+NX. If NX rises while Y remains constant, C+I+G must
fall. The government can reduce G or increase T, which will
reduce C.
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 less 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 m1(Y= m1/(1-c1-d1+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 additional unit of income on domestic
goods than smaller economies do.
e. (Y (NX
small economy (m1=0.5) 1.1 0.6
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.
8. a. It is convenient to wait to substitute for G until the last
step.
Y = C + I + G + X – IM = 10 + 0.8(Y - 10) + 10+G + 0.3Y*- 0.3Y
Y = [1/(1 - .8 + .3)](12 + G + 0.3Y*) = 2(12 + G + 0.3Y*) = 44
+ 0.6Y*
When foreign output is fixed, the multiplier is 2 (=1/(1-
0.8+0.3)). The closed economy multiplier is 5 (=1/(1-0.8)). In
the open economy, some of an increase in autonomous demand falls
on foreign goods, so the multiplier is smaller.
b. Since the countries are identical, Y=Y*=110. Taking into
account the endogeneity of foreign income, the multiplier equals
[1/(1-0.8 -0.3*0.6 +0.3)]=3.125. The multiplier is higher than
the open economy multiplier in part (a) because it takes into
account the fact that an increase in domestic income leads to an
increase in foreign income (as a result of an increase in
domestic imports of foreign goods). The increase in foreign
income leads to an increase in domestic exports.
c. If Y=125, then Y*=44+0.6(125)=119. Using these two facts and
the equation Y=2(12+G+0.3Y*) yields
125=24+2G+0.6(119), which implies G=14.8. In the domestic
economy, NX=0.3(119)-0.3(125)=-1.8 and T-G=10-14.8=-4.8. In the
foreign economy, NX*=1.8 and T*-G*=0.
d. If Y=Y*=125, then 125=24+2G+0.6(125), which implies G=G*=13. In
both countries, net exports are zero, but the budget deficit is
3.
e. In part, fiscal coordination is difficult to achieve because of
the benefits of doing nothing and waiting for another economy to
undertake a fiscal expansion, as indicated from part (c).
Explore Further
8. a. NX=National Saving - I.
b. As a % of GDP, gross private domestic investment was 3.6
percentage points higher in 2006 than in 1981. Net exports were
5.7 percentage points lower. Therefore, the national income
identity implies that national saving fell by 3.6–5.7 = 2.1
percentage points relative to GDP.
c. Change in Investment Change in NX
(% of GDP) (% of GDP)
1981-1990 -0.7% -0.9%
1990-2000 5.1% -3.1%
2000-2004 -0.7% -1.7%
Only in the 1990s was the fall in NX matched by an increase in
investment.
d. Yes. An increase in investment leads to more capital
accumulation and more output in
the future, and therefore to a greater ability to repay foreign
debt.
Chapter 20
Quick Check
1. a. False.
b. True.
c. True.
d. True.
e. Uncertain. If expected appreciation of the yen is greater than
or equal to the interest rate in other countries, than foreign
investors will hold yen bonds.
f. False. The money stock will change in response to shocks
(including policy shocks) so that the home interest rate equals
the foreign interest rate.
2. The appropriate mix is a monetary expansion to lessen the value of
the currency (and thereby to improve the trade balance) and a fiscal
contraction to prevent output from increasing.
3. a. Consumption increases because output increases. Investment
increases because output increases and the interest rate falls.
b. A monetary expansion has an ambiguous effect on net exports.
The nominal depreciation tends to increase net exports, but the
increase in output tends to reduce net exports.
4. a. The IS curve shifts right, because net exports tend to
increase. Domestic output increases.
b. The IS curve shifts right, because the increase in i* tends to
create a depreciation of the domestic currency and therefore an
increase in net exports. Domestic output increases. The
interest parity line also shifts up.
c. A foreign fiscal expansion is likely to increase Y* and to
increase i*. A foreign monetary expansion is likely to increase
Y* and to reduce i*.
d. A foreign fiscal expansion is likely to increase home output.
A foreign monetary expansion has an ambiguous effect on home
output. The increase in Y* tends to increase home output, but
the fall in i* tends to reduce home output.
Dig Deeper
5. a. An increase in Y* shifts the IS curve to the right. The
incipient rise in the home interest rate creates a monetary
expansion as the home central bank purchases foreign exchange to
prevent the domestic currency from appreciating. So, the LM
curve shifts right. Output and net exports increase.
b. The interest parity line shifts up, and the LM curve shifts left
as the central bank sells foreign exchange to prevent the
domestic currency from depreciating. Output falls, which leads
to an increase in net exports.
c. A fiscal expansion in the Leader country, which increases Y* and
i*, reduces domestic output, if the effect of Y* on domestic
output is small. A monetary expansion in the Leader country,
which increases Y* and reduces i*, increases domestic output.
6. a. The IS curve shifts to the left. Output falls, the interest
rate falls, and the currency depreciates. The currency
depreciation tends to increase output by increasing net exports.
Therefore, the exchange rate movement dampens the effect of the
fall in business confidence.
b. The IS curve shifts left and the LM curve shifts left (because
the money supply falls) as the central bank sells foreign
exchange to prevent the domestic currency from appreciating.
The fall in output is greater than in part (a).
c. When the exchange rate is flexible, movements of the exchange
rate tend to dampen the output effects of IS shocks. The
currency depreciates when the IS curve shifts left and
appreciates when the IS curve shifts right.
Explore Further
7. a. Et=Eet+1(1+it+x)/(1+i*t+1)
b. The IS curve slopes down as before, but with the result in part
(a) substituted for the nominal exchange rate in the NX
function.
c. The IS curve shifts right, because the fall in the expected
exchange rate creates a depreciation (which leads to an increase
in net exports) at the original interest rate. The interest
parity line shifts left. Output increases, net exports
increase, and the currency depreciates.
d. An increase in x tends to increase the value of the domestic
currency and therefore to shift the IS curve to the left.
According the assumption of the problem, the IS curve returns to
its original position. As a result, the combined effect of the
increase in the expected exchange rate and the increase in x is
no change in output. Since there is no change in output, there
is no change in net exports or the exchange rate. The increase
in x shifts the interest parity line to the right, back to its
original position.
e. Yes and yes.
8. a-b. According to data in The Economist on May 22, 2008, the dollar
was expected to appreciate against the pound, the euro, and the
renminbi; to depreciate by 1% against the Canadian dollar over
10 years; and to depreciate by 20% over the yen over 10 years.
c. If significant real depreciation of the dollar is required, the
results of part (b) imply that U.S. inflation needs to be
consistently lower than foreign inflation by a substantial
margin. For example, if real depreciation of 20% against the
euro is required over a 10-year horizon, U.S. inflation must be
2 percentage points lower than European inflation every year.
If the dollar appreciates against the euro, as forecast by
uncovered interest parity, U.S. inflation would have to be even
lower than European inflation to achieve the needed real
depreciation. Differences in annual inflation of this size seem
unlikely to happen for an entire decade.
d. Perhaps the relatively strong demand for dollar assets,
irrespective of the interest rate or expected depreciation, has
slowed the depreciation of the dollar that might have been
expected to result from the enormous U.S. current account
deficit.
Chapter 21
Quick Check
1. a. True. Britain returned to the gold standard at too appreciated
a parity.
b. True.
c. False.
d. False.
e. False.
2. b. The AD curve shifts right in the short run. The AS curve
shifts left in the medium run. In the medium run, output is
unchanged, but the price level is higher.
c. Consumption is unchanged in the medium run.
d. The real exchange rate appreciates, since the price level
rises. As a result of the real appreciation, net exports fall
in the medium run.
e. The domestic interest rate equals the foreign interest rate,
i*. The nominal interest rate is unaffected by government
spending. Since expected inflation is constant, the real
interest rate is also unaffected. Investment is unchanged in
the medium run.
f. In a closed economy, an increase in government spending reduces
investment in the medium run.
g. The statement is true. Under fixed exchange rates, the
interest rate is tied to the foreign interest rate. Since the
interest rate does not change, there is no mechanism for
government spending to crowd out investment.
3. a. The home real interest rate equals the foreign real interest
rate minus expected real appreciation of the home currency.
When the home currency is expected to appreciate in real terms,
foreign bonds must offer a real interest rate higher than the
home real interest rate to compensate international portfolio
investors for the expected loss in the real value of the foreign
currency. When the home currency is expected to depreciate in
real terms, home bonds must pay a real interest rate higher than
the foreign real interest rate.
b. According to uncovered interest parity, 10%=6%-expected nominal
appreciation, which implies that expected nominal appreciation
equals -4% per year. In other words, expected depreciation is
4% per year.
c. According to real interest parity, 10%-6%=(6%-3%) - expected
real appreciation, which implies that expected real appreciation
equals -1% per year. Therefore, expected real depreciation is
1% per year.
d. You would purchase the domestic bond because the foreign bond
will pay less interest than the domestic bond, and the domestic
currency is expected to gain in value relative to the foreign
currency.
4. a. The expected exchange rate is (E. The home interest rate is
i*.
b. The expected exchange rate is less than(E. The home interest
rate is greater than i*.
c. The domestic interest rate returns to i*, because expected
depreciation is zero.
d. Devaluation per se does not lead to higher interest rates.
Fear of devaluation does.
Dig Deeper
5. a. The price level rises by 10%.
b. The real exchange rate is EP/P*. If P rises by 10%, E falls by
10%. There is a 10% depreciation of the currency in nominal
terms.
c. Eet+n falls by 10%.
d. E falls by 10%.
e. E falls by more than 10%. By interest parity, i-i* equals
expected depreciation. If i falls
below i* in the short run, then there is expected appreciation.
This can only happen if E falls by more than 10% in the short
run. So, E falls by more in the short run than it does in the
medium run.
6. a. Eet+1 falls.
b. The UIP curve shifts up. The domestic interest rate must
increase to maintain the fixed exchange rate.
c. The money supply falls as the central bank sells foreign
exchange to buy its own currency. The LM curve shifts left.
d. Output falls and the interest rate rises. The government might
choose to abandon the fixed exchange rate to avoid the fall in
output, even if initially the government had no intention of
devaluing. Self-fulfilling crises are possible.
7. a. The domestic interest rate equals the foreign interest rate
before and after the devaluation.
b. The expected exchange rate falls to(E(. The UIP curve shifts
up.
c. The IS curve shifts right, because the devaluation tends to
increase net exports. The interest rate would increase with no
change in the money supply.
d. The money supply must increase. The LM curve shifts right.
e. Output increases.
f. Fear of further devaluation will increase the expected exchange
rate above (E( and increase the interest rate above i*. These
effects will tend to reduce the increase in output. If the
initial devaluation creates a strong enough fear of further
devaluation, the devaluation could lead to a fall in output.
Explore Further
8. The answer is given in the comments after part (c). The exchange
rate is many times more variable than the interest rate differential.
Chapter 22
Quick Check
1. a. False.
b. True.
c. Uncertain/False. Even though the unemployment rate declined, it
remained high until World War II. Traditional Phillips curve
analysis suggests that deflation should have continued.
Something more is needed to explain the end of deflation. The
text explores several possible explanations.
d. True.
e. False.
2. a. The central bank could increase M and shift the LM curve to the
right.
b. Since the unemployment rate is above the natural rate, P>Pe.
As a result, Pe falls, the AS curve shifts down, and P falls.
In the IS-LM diagram, the fall in P implies an increase in M/P,
so the LM curve shifts right.
c. Expected inflation is likely to fall. The fall in expected
inflation tends to increase the real interest rate and shift IS
to the left. Output moves further away from the natural level.
d. No. If the Fed does nothing, the economy may not return to the
natural level of output, if the effect of the fall in expected
inflation is strong enough.
3. b. P falls and M/P rises, so the LM curve shifts right. The
adjustment mechanism does not work when the nominal interest
rate equals zero. As the LM curve shifts right, output does not
change.
c. Monetary policy is ineffective. An increase in M shifts the LM
curve to the right, which does not lead to an increase in output
when the nominal interest rate equals zero.
d. Yes. An increase in G or a reduction in T would shift the IS
curve to the right. As a result, output would increase.
e. This is not wise advice. If the economy is in a liquidity
trap, the central bank cannot restore output to its natural
level.
Dig Deeper
4. a. Short-term unemployment has a greater effect on wages. The
long-term unemployed may not be searching for employment and may
not be very employable.
b. u=[.05/1.05(1-0.5()]
c. If (=0, 0.4, 0.8, the natural rate =4.8%, 6.0%, 7.9%.
Intuitively, if the weight on long-term unemployed were zero
instead of 0.5, the wage-setting and price-setting equations
would determine the natural short-term rate of unemployment.
The long-term unemployed would simply increase the aggregate
unemployment rate. Thus, as the proportion of long-term
unemployed increased, the natural rate of unemployment would
increase. The same kind of reasoning applies here, but the
effect is less strong because the weight on long-term unemployed
in the wage-setting equation is not zero.
In terms of the logic of the labor market, the long-term
unemployed put less downward pressure on wages than the short-
term unemployed. So, increasing the proportion of long-term
unemployed tends to increase the real wage. Effectively, this
implies that the labor supply curve (the wage-setting equation)
shifts up. If the labor demand curve were downward-sloping,
employment would fall as the real wage rose since workers would
be less attractive to firms. In this problem, labor demand
(the price-setting equation) is flat at a fixed real wage, which
implies that all of the adjustment from an increase in the
proportion of long-term unemployment takes the form of less
employment (and a higher unemployment rate) and none of the
adjustment takes the form of a higher real wage.
5. a. Higher unemployment implies lower wages given expected prices.
This implies lower prices given expected prices. Equivalently,
it implies lower inflation given expected inflation, which here
equals past inflation.
b. (t - πt-1 = - ((uS + uL – un)
c. πt - πt-1 = - ((uS – un)
d. πt - πt-1 = - ([(1 - ()ut – un]
e. The curve will shift to up, so that any unemployment rate is
associated with a greater increase in the inflation rate.
f. More overall unemployment is needed to achieve the same decrease
in inflation. The cost of disinflation increases.
g. An increase in the proportion of long-term unemployed tends to
imply a larger increase in inflation. In the Great Depression,
perhaps the long-term unemployed did not exert much pressure on
wages and prices, so deflation ended despite high unemployment.
Explore Further
6. Answers will vary depending upon when the question is answered.
Chapter 23
Quick Check
1. a. True.
b. False.
c. False.
d. False/Uncertain. Incomes policies may be part of a successful
stabilization program in
some cases, but they don't seem in general to be a prerequisite
for stabilization.
e. False.
f. False.
2. a. If money growth = 25%, 50%, 75%, seignorage=162.5, 325, 487.5.
b. In the medium run, if money growth = 25%, 50%, 75%,
seignorage=162.5, 200, 112.5. The fall in real money balances
associated with higher ongoing inflation reduces the potential
for seignorage. Part (a) did not allow for this effect.
3. a. This policy would reduce the effect of inflation on real tax
revenues.
b. This policy would reduce the effect of inflation on real tax
revenues.
c. This policy would decrease the effect of inflation on real tax
revenues, but would also have other effects. The income tax can
tax the rich at a higher rate than the poor, but the sales tax
rate is the same for rich and poor.
Dig Deeper
4. a. The end to the crisis depends on shifting the composition of
taxes away from the inflation tax and toward other taxes.
Workers are already paying the inflation tax.
b. The central bank must make a credible commitment that it will no
longer automatically monetize the government debt. Although a
currency board would do this, it is a drastic and perhaps
unnecessary step.
c. Price controls may help, but price controls without other policy
changes only cause distortions and are a recipe for failure.
d. A recession is not needed, but it may happen. Although nominal
rigidities are less important during hyperinflations—a fact that
implies that the sacrifice ratio is small—the issue of
credibility remains. Unless firms and workers believe in the
stabilization program, a severe recession may be the result.
e. The statement has two components: (i) there is an ongoing
fiscal deficit that the government is unable or unwilling to
finance from nonmonetary sources, and (ii) the central bank is
willing to monetize the debt. The order in which these issues
are resolved ultimately depends on the political realities. The
fiscal authority could eliminate the deficits. If it does not
do so, the central bank could commit not to monetize government
debt. However, this could drive the government into default on
its bonds.
5. seignorage=(Y/P)(0.9- M/M)( M/M)
Seignorage is maximized when M/M=45%.
Explore Further
6. Answers may vary depending upon when the website is accessed, but it
is clear that a fall in oil
prices would tend to increase the budget deficit in Venezuala. This
would create the possibility
of a hyperinflation if the government is unwilling or unable to
finance itself and the central bank finances the deficit through money
creation.
Chapter 24
Quick Check
1. a. False.
b. True/Uncertain.
c. False.
d. False.
e. True.
f. Uncertain. It may be wise for a government to commit not to
negotiate with hostage takers as a means to deter hijackings,
even recognizing that after a hijacking has taken place, there
is a strong incentive to negotiate. However, the phrase "under
no circumstances" is categorical. There may some circumstances
under which a government might wish to violate its commitment.
This statement, of course, illustrates the difficulty of
precommitment. Can a government really commit not to negotiate,
no matter what the circumstances, even if these circumstances
may not have been imagined at the time the commitment was made?
g. False.
2. a. Inflation will increase in the fourth year.
b. The President should aim for high unemployment early in the
administration, to reduce
inflation before the fourth year.
c. The policies are not likely to achieve the desired the increase
in output desired in the fourth year. Since people are forward-
looking, expected inflation fourth year will account for the
intentions of policymakers. If inflation equals expected
inflation, unemployment equals the natural rate.
3. Answers will vary, but there is some discussion of this issue in the
text.
4. New Zealand wants to eliminate fears that the central bank might try
to reduce unemployment
below the natural rate with expansionary monetary policy and higher
inflation. See Chapter 25
for a discussion of inflation targeting.
Dig Deeper
5. a. (et=0.5((D + (R)
b. The unemployment rate will be less than the natural rate.
Inflation will be higher than
expected.
c. The unemployment rate will be greater than the natural rate.
Inflation will be lower than
expected.
d. The results fit the evidence in Table 24-1 if one looks at the
first two years of each administration, and not just the first
year.
e. The unemployment will equal the natural rate, because π = πe,
and there will be high inflation.
6. The payoffs should be symmetrical, as written below. The table
presented in the text leads to the same equilibrium, however.
" " "Welfare Cuts "
" " "Yes "No "
"Defense "Yes "(R=1, D=1) "(R=-2, D=3) "
"cuts " " " "
" "No "(R=3, D=-2) "(R=-1, D=-1) "
a. If the Republicans cut military spending, the Democrats get 1
if they cut welfare, but 3 if they do not. So their best
response is to vote against welfare cuts. The Republicans will
get –2 in this case.
b. If the Republicans do not cut military spending, the Democrats
get –2 if they cut welfare, but –1 if they do not. So their
best response is not to cut welfare. The Republicans will get
–1 in this case.
c. Given the answers above, the Republicans will not cut military
spending, and the Democrats will not cut welfare. The two
parties are locked in a bad equilibrium. They could make a
deal: both vote for cuts. If they do, they will both be better
off.
Explore Further
7. Answers will vary.
Chapter 25
Quick Check
1. a. False.
b. False.
c. False.
d. False/Uncertain. Evidence suggests that people have money
illusion, when would seem
to imply that inflation would distort decision making.
e. False.
f. True. The capital gains tax is not indexed to inflation.
2. a. Demand for M1 falls while demand for M2 is unchanged. People
shift funds from savings accounts to time deposits.
b. Demand for M1 increases as people transfer funds from money
market funds to checking accounts. Demand for M2 remains
unchanged.
c. There is a shift in the composition of M1 (and consequently M2)
as people hold more currency and make fewer trips to the bank
while holding smaller checking account balances.
d. The demand for M2 increases as the benefit of holding
government securities falls.
3. a. i. r=4%-0%=4%; ii. r=14%-10%=4%
b. i. r=4%(1-0.25)-0%=3%; ii. r=14%(1-0.25)-10%=10.5%-10%=0.5%
c. Given the deductibility of nominal mortgage interest payments,
inflation is good for homeowners in the United States.
4. a. The unemployment rate will remain equal to the natural rate.
b. It is unlikely that the central bank will be able to hit its
target every period. There will be surprises, and there are
lags and uncertainty in policymaking.
c. Changes in the natural rate will make it more difficult for the
Fed to hits its target. It will be harder to distinguish
changes in the actual rate of unemployment from changes in the
natural rate of unemployment.
Dig Deeper
5. Discussion question.
6. b. The IS curve slopes down, and the MP relation slopes up.
c. An increase in government spending shifts the IS curve right,
so output and the real interest rate rise.
d. The MP relation shifts up. Output falls and the real interest
rate increases.
7. a. The MP relation shifts up. Output falls and the real interest
rate increases.
b. Since Y
level.
c. The MP relation shifts down. Output increases and the real
interest rate falls.
d. Since Y>Yn, (e rises. Inflation tends to move away from its
target level. A value of a<1
makes no sense as part of the policy rule, because inflation
would tend to move away from its target
Explore Further
8. Answers will depend upon current Fed policy.
Chapter 26
Quick Check
1. a. True.
b. False.
c. Uncertain.
d. False.
e. False.
f. False
g. False
2. a. Interest payments are 10% of GDP, so the primary surplus is 10%-
4%=6%.
b. Real interest payments are (10%-7%)*100%=3% of GDP. So the
inflation-adjusted surplus is 6%-3%=3%.
c. Assume that last period unemployment was at the natural rate, so
there has been a two percentage point increase in the
unemployment rate over the last period. By Okun's law (with a
normal growth rate of 3%), output growth is lower by two
percentage points. So, output is roughly two percent lower than
it would have been. Using the rule of thumb in the text, the
surplus is lower by 0.5*2%=1%. So the cyclically-adjusted,
inflation- adjusted surplus is 2%.
d. The change in the debt to GDP ratio = (3%-2%)*100% - 3% = -2%.
The debt to GDP ratio falls by 2% a year.
e. In 10 years, the debt to GDP ratio will be 80%.
3. a. The new interest rate is 10%+0.5*20%=20%. So assuming that
expected depreciation was previously zero, the domestic interest
rate increases from 10% to 20%.
b. The real interest rate increases from 3% to 13%. The high real
interest rate is likely to decrease growth.
c. The official deficit increases from 4% to 14% of GDP. The
inflation-adjusted deficit increases from –3% (a surplus) to 7%
(a deficit).
d. The change in the debt ratio = (13%-(-2%))*100%-3%=12%. It
goes up very quickly.
e. In this example, the worries were self-fulfilling.
4. First, even a temporary deficit leads to an increase in the national
debt, and therefore to higher interest payments. This, in turn,
implies continued deficits, higher taxes, or lower government spending
in the future. Second, the evidence does not support the Ricardian
equivalence proposition. Third, if Ricardian equivalence did hold,
then government spending would have the same effect on output
regardless of whether it was financed by bonds (i.e., with a deficit)
taxes. Thus, a deficit, per se, would not be needed to stimulate
output. Fourth, war-time economies are already low-unemployment
economies. There is no need for further stimulation by using deficits
rather than tax finance. The only correct part of the statement is
the first sentence. A deficit can be preferable to higher taxes
during a war, but not for the reasons stated here.
Dig Deeper
5. Discussion question. Also see the box on Social Security in Chapter
11 (p. 215).
6. If financial market participants discount future dividends at the
rate of interest on government bonds, then this economy will exhibit
Ricardian equivalence. If there is a risk-premium applied to stocks,
then this economy will not exhibit Ricardian equivalence.
To see why, let τt be the dividend tax rate at time t and consider the
pre-dividend stock price under a fixed sequence of expected dividends.
$Qt = $Dt(1 - τt) + $Det+1(1 -τt+1)/(1 + i1t)+ . . .
= [$Dt + $Det+1/(1 + i1t)+ . . .] - [$Dtτt +
$Det+1τt+1/(1 + i1t) + . . .]
The second term in brackets is the present discounted value of tax
receipts for the government. To finance a given expenditure policy,
the government must keep the PDV of tax receipts constant. Thus, for
a given sequence of expected dividends, the timing of dividend taxes
will not affect the stock price, consumption or investment. As a
result, this economy will exhibit Ricardian equivalence. Note that,
ex post, dividends will vary from their expected values, so taxes may
be adjusted in the future. This new information could affect stock
prices. In addition, note that the level of dividend taxes – the PDV
of tax receipts – could affect stock prices.
If stocks are assessed a risk premium (θ), however, so that they are
discounted at rate i + θ, then the timing of dividend taxes will
matter, because the government budget constraint will incorporate a
different discount rate than the stock market price. As an example,
suppose that i=0 forever but θ is positive. In this case, the
government can assess taxes at any time with no consequence, but
shifting taxes to the future will be favorable to holders of stocks.
Since future dividends are uncertain, so are future tax payments –
they might not have to be made if dividends turn out to be low. In
this scenario, shifting taxes to the future would tend to increase the
current stock price, and thus increase consumption and investment (if
firms are liquidity constrained). So, Ricardian equivalence is
violated.
