Download Answers to Text Questions and Problems Chapter 22 Answers to

Answers to Text Questions and Problems
Chapter 22
Answers to Review Questions
3.
In general, producers of durable goods are affected most by recessions while producers of
nondurables (like food) and services are affected least. Automobiles are durable goods, so the
automobile producer would probably see its profits reduced the most, while the barbershop
(which provides a service) will see the smallest decline in profit. Boots and shoes are “semidurable”, since a pair of shoes may last for several years and people can put off purchases of
these for a while if necessary. Thus the boot manufacturer’s losses are likely to fall in between
those of the other two firms.
4.
The natural unemployment rate is the sum of structural and frictional unemployment and
excludes cyclical unemployment. Hence, the natural unemployment rate by definition should not
be affected by a recession. Also by definition, the cyclical unemployment rate rises in recession.
Inflation tends to decline in the period following a recession. Finally, poll ratings of presidents
tend to be strongly correlated with the state of the economy, so a recession will probably reduce
a president’s popularity.
5.
Potential output, or potential GDP, is the maximum sustainable amount of output (real GDP) that
an economy can produce. Because inputs can be used at greater than normal rates for a time
(for example, workers can work overtime and machines can be used at night or on weekends), it
is possible for the economy to produce an amount exceeding potential output.
7.
False. When output equals potential output, the unemployment rate equals the natural
unemployment rate. Cyclical unemployment is zero when output equals potential output, but
frictional and structural unemployment still exist.
Answers to Problems
3.
NOTE: this is different than in the galley proofs. We decided to extend the data to 2007.
The data from the problem along with the output gap, the type of gap and the growth rate of
real GDP are given in the table below:
Year Real GDP Potential GDP Output gap Type of gap Growth rate of real GDP
1999 $9,470
$9,248
2.4%
expansionary
2000 $9,817
$9,590
2.4%
expansionary
3.7%
2001 $9,891
$9,927
-0.4%
recessionary
0.8%
2002 $10,049
$10,227
-1.7%
recessionary
1.6%
2003 $10,301
$10,501
-1.9%
recessionary
2.5%
2004 $10,676
$10,777
-0.9%
recessionary
3.6%
2005 $11,003
$11,068
-0.6%
recessionary
3.1%
2006 $11,319
$11,372
-0.5%
recessionary
2.9%
2007 $11,567
$11,687
-1.0%
recessionary
2.2%
The growth rate of GDP slowed to 0.8% in 2001; growth accelerated from 2002 to 2004,
corresponding to the official dating of the recession. Note, however, that a recessionary gap
continued throughout the 2001-2007 period, meaning that despite the resumption of normal
growth rates the economy never caught up with potential after the 2001 recession.
5.
Working with Okun’s law:
a.
In 2010, real GDP is 2% below potential GDP, so cyclical unemployment is 1%. Since the
actual unemployment rate is 6%, the natural rate must be 5%.
b.
In 2011, the natural rate equals the actual rate, so cyclical unemployment equals zero.
Okun’s law implies that the output gap is therefore zero, and potential output equals
the actual output level of 8,100.
c.
In 2012, cyclical unemployment equals 4% - 4.5% = -0.5%, so by Okun’s Law the output
is gap is 1%. This implies that real GDP is 1% larger than potential GDP, so real GDP
must equal 8,282 (= (1.01)(8200)).
d.
In 2013, the output gap is 2% since real GDP is 2% above potential GDP. Using Okun’s
law, this implies that cyclical unemployment is –1%. Since the natural unemployment
rate is 5%, actual unemployment is 4%.
Chapter 23
Answers to Review Questions
1. The key assumption of the basic Keynesian model is that in the short run, firms meet demand at
pre-set prices. The fact that firms produce to meet demand implies that changes in demand
affect output in the short run.
2. There are many possible examples. Goods that are standardized and are bought and sold in
large quantities, such as wheat or other commodities, tend to have rapidly adjusting prices since
the benefits of setting up active auction markets for such goods usually exceeds the costs.
Goods such as dresses or skirts, which are not standardized (they vary in size, color, style) and
which are usually sold in retail stores one by one, tend to have prices that are changed less
frequently.
3. Planned aggregate expenditure (PAE) is total planned spending on final goods and services. It
consists of consumption spending, investment spending, and government purchases of goods
and services, and net exports (exports less imports).
Changes in output are cause changes in the income received by producers, which in turn affects
consumption spending through the consumption function. Since consumption is a component
of PAE, changes in output lead to changes in PAE.
4. Planned spending includes planned additions to inventories to firms. When firms’ actual sales
differ from planned sales, the resulting additions to inventory will differ from what was planned,
and actual spending will differ from planned spending. For example, suppose a firm planned to
produce 100 units, sell 90 units to the public, and add 10 units to its inventory. But in fact the
firm sells only 80 units and thus must add 20 units to inventory. The firm’s planned inventory
investment (a component of investment and thus total spending) was 10 units, but its actual
inventory investment was 20 units. So the firm’s actual investment spending (inclusive of
inventory investment) is greater than it planned. On the other hand, if the firm sold all 100
units, it would add nothing to inventory, and its actual investment (including inventory
investment) would be less than planned.
5. Figure 23.2 shows a consumption function. Consumption (C), is on the vertical axis and
disposable income (Y – T), is on the horizontal axis.
a. A movement from left to right along the consumption function shows that consumption
increases as disposable income increases.
b. A parallel shift upward of the consumption function indicates that people are consuming
more at any given level of disposable income. This implies that some factor other than a
change in disposable income is stimulating consumption.
6. Figure 23.4 shows the Keynesian cross diagram. The 45-degree line captures the definition of
short-run equilibrium output, Y = PAE; this implies that short-run equilibrium output must lie on
this line. The flatter line, the expenditure line, shows how planned aggregate expenditure
depends on output. Because increased output raises disposable income, which in turn increases
consumption and planned aggregate expenditure, the expenditure line is upward sloping.
Autonomous expenditure is given by the intercept of the expenditure line, the marginal
propensity to consume equals the slope of the expenditure line, and short-run equilibrium
output is the point on the horizontal axis corresponding to the intersection of the expenditure
line and the Y = PAE line. To find induced expenditure, draw a horizontal line from the
intersection of Y = PAE and the expenditure line to the vertical axis. The difference between the
resulting point on the vertical axis (which equals actual output) and the intercept of the
expenditure line (which equals autonomous expenditure) equals induced expenditure.
7. The two factors cited in the text as causes of the 2001 recession were a fall in consumer
confidence and a credit crunch. A fall in consumer confidence reduces consumers’ willingness
to spend at each level of disposable income (a fall in C ). A credit crunch reduces planned
investment, I . Each of these leads to a reduction in autonomous expenditure. Graphically, a
decline in autonomous expenditure shifts the expenditure line downward and lowers short-run
equilibrium output. (See Figure 23.5 for an illustration.)
8. The multiplier tells us the effect of a one-unit increase in autonomous expenditure on short-run
equilibrium output. The multiplier is greater than one because a one-unit increase in
autonomous expenditure directly increases output by one unit and increases producers’
incomes by one unit. The increase in income leads to further spending on the part of producers,
which raises income of other producers and increases their spending. This multiple-round
process of spending and income creation leads to a final increase in output that is greater than
the one-unit initial impact.
9. The increase in government purchases raises autonomous expenditure by 50 units. The tax cut
raises disposable income by 50 units, which also stimulates planned aggregate expenditure by
increasing consumption spending. However, the tax cut raises autonomous expenditure by only
50 units times the marginal propensity to consume (mpc); since the mpc is less than one, the tax
cut will increase autonomous expenditure by less than 50 units. Thus the increase in
government purchases will have the greater impact on planned aggregate expenditure.
10. First, government spending and taxing decisions may affect potential output as well as planned
aggregate expenditure. What the government spends its money on, as well as the incentive
effects of changes in tax and transfer programs, need to be factored in when evaluating the
effects of fiscal policy. The type of spending may affect long-run growth of potential output, as
well as how tax policies affect labor supply decisions and investment decisions. Second, changes
in government spending and taxing can affect the government’s budget deficit, which in turn
may affect long-run investment in capital goods and the growth of potential output. For
example, an expansionary fiscal policy may boost planned aggregate expenditure in the short
run, leading to increased output and employment, but it may also raise real interest rates if it
reduces national saving (by increasing the government’s budget deficit without an offsetting
increase in private saving). The increased interest rates may reduce capital investment and
long-run growth of output. Third, fiscal policy is relatively inflexible, with long legislative
processes reducing the government’s ability to quickly respond to output gaps. The delays in
implementation may stem from the legislative process itself (budget recommendations are first
presented to Congress by the President, then are often debated for months before finally
becoming law, and may take effect months after this) or from political wrangling over spending
and taxing priorities.
Answers to Problems
1. Acme’s planned investment in every case is $1,500,000 (its planned expenditure on new
equipment plus zero planned increase in inventories). The key to this problem is to find the
amount of unplanned inventory investment Acme makes then add this to their planned
investment to find Acme’s actual investment.
a. If Acme sells $3,850,000 worth of goods, it has unplanned inventory investment of
$150,000 and total actual investment of $1,650,000.
b. If Acme sells $4,000,000 worth of goods as it planned, its actual investment of
$1,500,000 equals its planned investment.
c. If Acme sells $4,200,000 worth of goods it must draw down $200,000 worth of goods
from its existing inventory, implying that inventory investment is negative $200,000.
Acme’s actual investment in this case is $1,500,000 - $200,000 = $1,300,000.
Output equals short-run equilibrium output in case b, where planned spending and
actual spending are equal.
2. Working with the consumption function:
a. Disposable income (before-tax income less taxes paid) and consumption are as follows:
Before-tax
income ($)
Taxes paid ($)
Disposable
income ($)
Consumption
($)
25,000
27,000
28,000
30,000
3,000
3,500
3,700
4,000
22,000
23,500
24,300
26,000
20,000
21,350
22,070
23,600
Graph:
24,000
23,500
Consumption
23,000
22,500
22,000
21,500
21,000
20,500
20,000
19,500
21,000
22,000
23,000
24,000
25,000
26,000
27,000
Disposable income
The marginal propensity to consume is the increase in consumption caused by a one
dollar increase in disposable income. In this case, when disposable income increases by
from 22,000 to 23,500, a rise of 1500, consumption rises by 1350. The mpc is therefore
1350/1500 = 0.9. We can confirm this by checking the other points on the consumption
function. For example, when disposable income rises by another 800 (24,300 – 23,500),
consumption rises by 720 (22,070 – 21,350), which is (0.9)(800). Similarly, if disposable
income rises by yet another 1700 (26,000 – 24,300), consumption rises by 1,530 (=
(0.9)(1700)). We can also find the intercept of the consumption function, C . Since the
mpc is 0.9, we know the consumption function can be expressed as
C = C + (0.9)(Y − T) . To find C , plug into the equation any of the numerical
combinations of consumption and disposable income given above. For example, if we
set C = 20,000 and Y – T = 22,000, we get 20,000 = C + (0.9)(22,000) , which implies
C = 200. So the consumption function for the Simpsons is C = 200 + (0.9)(Y − T ) .
b. From the consumption function derived in part a, setting Y = 32,000 and T = 5,000, C =
200 + (0.9)(27,000) = 24,500.
c. The consumption function shifts upward by 1000 at each level of disposable income
(that is, the vertical intercept, C , rises from 200 to 1200.) The mpc is unaffected
because the increase in consumption is the same at each level of disposable income.
This implies that the graph makes a parallel upward shift and the slope, equal to the
mpc, does not change.
3. Working with planned aggregate expenditure and its components:
a. Begin with the definition of PAE:
PAE = C + Ip + G + NX
Next, substitute the components of PAE that are given in the problem:
PAE = [1800 + (0.6)(Y – 1500)] + 900 + 1500 + 100
Collecting terms, we have:
PAE = 3400 + 0.6Y
b. Autonomous expenditure is 3400 and induced expenditure is 0.6Y.
4. Finding short-run equilibrium output in the basic Keynesian model:
a. Numerical determination of short-run equilibrium output: see the table below:
Output
(Y)
8200
8300
8400
8500
8600
8700
8800
8900
9000
Planned aggregate
expenditure (PAE)
8320
8380
8440
8500
8560
8620
8680
8740
8800
Y - PAE
-120
-80
-40
0
40
80
120
160
200
Y = PAE?
No
No
No
YES
No
No
No
No
No
Y = PAE when output and PAE are equal to 8500, so Y = 8500 is the level of short-run
equilibrium output.
b. From problem 3, we know that PAE = 3400 + 0.6Y. To find short-run equilibrium output
we use the condition that defines short-run equilibrium output, Y = PAE:
Y = PAE
Y = 3400 + 0.6Y
0.4Y = 3400
Y = 8500
The result is the same as we found in part a.
c. From problem 3 we know that full employment output (Y*) is 9000, so the output gap, Y
– Y*, equals 8500 - 9000 = -500. As a percentage of full employment, the gap is 500/9000 = -5.6%. By Okun’s Law, cyclical unemployment is minus one times one-half
of the output gap, or 2.8%. Since the natural rate is 4%, the actual unemployment rate
is 4% + 2.8% = 6.8%.
5. Calculating the effects of changes in autonomous expenditure on short-run equilibrium output:
a. An increase in government purchases of 100 causes autonomous expenditure to rise
from 3400 to 3500. Equilibrium output is found by setting Y = PAE:
Y = PAE
Y = 3500 + 0.6Y
0.4Y = 3500
Y = 8750
b. A decrease in tax collections of 100 causes autonomous expenditure to rise from 3400
to 3460. (Remember: the 100 unit decrease in T is multiplied by the mpc of 0.6 since
the decrease in taxes affects consumption via disposable income.) Equilibrium output
is found by setting Y = PAE:
Y = PAE
Y = 3460 + 0.6Y
0.4Y = 3460
Y = 8650
c. A decrease in planned investment of 100 causes autonomous expenditure to fall from
3400 to 3300. Equilibrium output is found by setting Y = PAE:
Y = PAE
Y = 3300 + 0.6Y
0.4Y = 3300
Y = 8250
All three examples demonstrate that the multiplier, equal to the change in output per 1unit change in autonomous aggregate demand, is 2.5 for this economy. (For example, in
part a, the 100 unit increase in government spending led to a 250 unit increase in shortrun equilibrium output.) We can verify this also by the formula for the multiplier,
1
1
1
=
= 2.5
1 − mpc . In this economy, mpc = 0.6, so the multiplier is 1 − 0.6 0.4
6. Using the multiplier to calculate changes in short-run equilibrium output:
1
a. The multiplier is given by 1 − mpc , where mpc is the marginal propensity to consume.
1
1
=
=4
In this economy, mpc = 0.75, so the multiplier is 1 − 0.75 0.25
. Therefore, the
recessionary gap will be four times the size of the fall in planned investment.
b. To restore equilibrium at full employment, overall autonomous spending must increase
to its previous level, so the increase in government spending required to close the
recessionary gap will be just equal to the fall in planned investment. With a multiplier of
4, the change in output will be four times the change in government spending, offsetting
the drop in output caused by the fall in planned investment.
c. Again, to restore equilibrium at full employment, overall autonomous spending must
increase to its previous level, but since consumers only spend 0.75 of any increase in
disposable income, the reduction in taxes must be larger than the fall in planned
investment. (If taxes were reduced by the amount of the change in planned investment,
autonomous spending would increase by only 75% of this change, leaving the economy
with a recessionary gap.) Taxes therefore need to be reduced so that the resulting
increase in autonomous consumer spending just equal the fall in planned investment.
Mathematically, this implies the following:
(0.75)(change in taxes) = -(change in planned investment)
Dividing both sides by 0.75, we have
change in taxes = -(1.33)(change in planned investment)
That is, taxes must be reduced by an amount that is 33% greater than the decline in
planned investment that occurred. For example, if planned investment fell by $100
million, then taxes must be reduced by $133 million. With an increase of $133 in
income, consumers will then spend 0.75 of this increase, leading to an increase in
autonomous consumption of (approximately) $100 million.
d. If the government increases government spending and taxes by the same amount, the
result will be an increase in autonomous spending because the increase in government
spending contributes fully to an increase in autonomous spending, while the decrease in
taxes will only reduce autonomous consumer spending by 0.75 of the tax increase.
Thus, for every dollar increase in government spending matched by a dollar increase in
taxes (preserving the balanced budget), autonomous spending will increase by $0.25.
To restore equilibrium in the economy, recall that overall autonomous spending must
increase to its original level prior to the fall in investment spending. As a result, to move
the economy to full employment, the government must increase spending (and taxes)
by four times the fall in autonomous investment spending. The resulting increase in
autonomous spending will just offset the fall in investment spending, restoring the
original level of overall autonomous spending in the economy and increasing output
back to the full employment level.
7. Working with the basic Keynesian model:
a. To find planned aggregate expenditures (PAE), begin with the definition of PAE:
PAE = C + Ip + G + NX
Next, substitute the components of PAE that are given in the problem:
PAE = [40 + (0.8)(Y – 150)] + 70 + 120 + 10
Collecting terms, we have:
PAE = 120 + 0.8Y
b. The table below illustrates the level planned aggregate expenditure (PAE) for various
output levels:
Output (Y)
550
560
570
580
590
600
610
620
630
640
Planned aggregate
expenditure (PAE)
560
568
576
584
592
600
608
616
624
632
Y - PAE
-10
-8
-6
-4
-2
0
2
4
6
8
Short-run equilibrium output is 600 since this is the level of output at which Y = PAE.
c. Since Y*=580, there is an expansionary output gap of 20. To eliminate the output gap,
autonomous spending needs to be reduced or taxes raised. In the former case, with a
multiplier of 5, government spending needs to be reduced by 4; this will lead to a
decrease of 4 × 5 = 20 in output. In the latter case, overall autonomous spending needs
to be reduced by 4; with an mpc of .8, an increase in taxes by 5 will lead to a reduction
in autonomous spending of .8 × 5 = 4, which in turn will lead to reduction in output of
20, given the multiplier of 5.
d. In the case where Y*=630, there is a recessionary gap of 30. To eliminate this output
gap, autonomous spending needs to be increased or taxes reduced. In the former case,
with a multiplier of 5, government spending needs to increase by 6; this will lead to an
increase of 6 × 5 = 30 in output. In the latter case, overall autonomous spending needs
to be increased by 6; with an mpc of .8, a reduction in taxes by 7.5 will lead to an
increase in autonomous spending of .8 × 7.5 = 6, which in turn will lead to an increase in
output of 30, given the multiplier of 5.
e. Graph:
650
640
630
Y = PAE
620
Planned aggregate
expenditure (PAE)
Potential GDP = 580
610
Potential GDP = 630
600
590
580
570
560
550
540
540
550
560
570
580
590
600
610
620
630
640
650
8. Working with the basic Keynesian model:
a. To find planned aggregate expenditures (PAE), begin with the definition of PAE:
PAE = C + Ip + G + NX
Next, substitute the components of PAE that are given in the problem:
PAE = [3,000 + (0.5)(Y – 2000)] + 1,500 + 2,500 + 200
Collecting terms, we have:
PAE = 6200 + 0.5Y
•
•
Autonomous expenditure is 6200.
1
The multiplier is given by 1 − mpc , where mpc is the marginal propensity to consume. In
1
1
1
=
=
=2
this economy, mpc = 0.5 so the multiplier is 1 − mpc 1 − 0.5 0.5
.
•
Short-run equilibrium output can be determined from a table showing the relationship
between planned aggregate expenditure (PAE) or algebraically. In table form,
Output (Y)
12,000
12,100
12,200
12,300
12,400
12,500
12,600
12,700
Planned aggregate
expenditure (PAE)
12,200
12,250
12,300
12,350
12,400
12,450
12,500
12,550
Y - PAE
-200
-150
-100
-50
0
50
100
150
Equilibrium occurs at Y=12,400, i.e. where Y = PAE. Algebraically, equilibrium output is
found by setting Y = PAE:
Y = PAE
Y = 6200 + 0.5Y
0.5Y = 6200
Y = 12400
•
If Y* = 12,000, then there is an expansionary output gap of 400 in this economy. To
eliminate this output gap, given the multiplier of 2, autonomous expenditure needs to be
reduced by 200.
9. The role of net exports in recessions and expansions:
a. We can find equilibrium output either using a table or using algebra. We present the
algebraic solution here. Begin by finding planned aggregate expenditure (PAE):
PAE = C + Ip + G + NX
PAE = [40 + (0.8)(Y – 150)] + 70 + 120 + 0
PAE = 110 + 0.8Y
Short-run equilibrium output is found where Y = PAE:
Y = PAE
Y = 110 + 0.8Y
0.2Y = 110
Y = 550
b. Planned aggregate expenditures will then be given by
PAE = C + Ip + G + NX
PAE = [40 + (0.8)(Y – 150)] + 70 + 120 + 100
PAE = 210 + 0.8Y
Short-run equilibrium output is found where Y = PAE:
Y = PAE
Y = 210 + 0.8Y
0.2Y = 210
Y = 1050
Short-run equilibrium output now 500 higher than the original equilibrium. This is what
we would expect, since the multiplier for this economy is 5 (5 times the change in
autonomous expenditure = (5)(100) = 500 = change in equilibrium output level.)
c. Planned aggregate expenditures will then be given by
PAE = C + Ip + G + NX
PAE = [40 + (0.8)(Y – 150)] + 70 + 120 - 100
PAE = 10 + 0.8Y
Short-run equilibrium output is found where Y = PAE:
Y = PAE
Y = 10 + 0.8Y
0.2Y = 10
Y = 50
Short-run equilibrium output now 500 lower than the original equilibrium. Again, this is
what we would expect, since the multiplier for this economy is 5 (5 times the change in
autonomous expenditure = (5)(-100) = -500 = change in equilibrium output level.)
d. Changes in autonomous spending in one country lead to changes in autonomous
spending in other countries through NX. For example, suppose that U.S. consumers
reduce their purchases when domestic income falls because of recession. Consumption
spending (C) includes consumer purchases of both domestically produced goods and
imported goods. (Remember: this is why NX is in PAE: we need to subtract out
imported goods from PAE and add in foreign purchases of domestic goods so that PAE
only includes purchases of domestic goods.) So, as U.S. imports decline, this causes
exports from other countries to the U.S. to decline as well. This causes autonomous
expenditure in other countries to fall, causing their short-run equilibrium output levels
to fall as well. Thus, a recession in the U.S. is spread to the rest of the world via changes
in NX. The same reasoning works in the case of an expansion as well.
10. Automatic stabilizers and equilibrium output:
a. We can solve for short-run equilibrium output in the usual way, except that we will keep
the equations in their general algebraic form (as in the Appendix to Chapter 23.) The
first step is to find the relationship of aggregate demand to output:
PAE = C + I p + G + NX
PAE = C + (mpc)(Y − T ) + I + G + NX
PAE = C + (mpc)(Y − tY) + I + G + NX
PAE = C + I + G + NX + (mpc)(1 − t )Y
Notice that, in this model, autonomous expenditure is C + I + G + NX and induced
expenditure is (mpc)(1 - t)Y.
Short-run equilibrium output is found where Y = PAE:
Y = PAE
Y = C + I + G + NX + (mpc)(1 − t )Y
Y([1 − (mpc)(1 − t )] = C + I + G + NX
1
( C + I + G + NX )
Y=
1 − (mpc)(1 − t )
The last line above gives an algebraic expression for short-run equilibrium output in the
model in which taxes are proportional to output.
b. From the expression for short-run equilibrium output in part a, we can see that a one
unit increase in autonomous expenditure, C + I + G + NX , raises output by
1
1
1 − (mpc)(1 − t ) units, so 1 − (mpc)(1 − t ) is the multiplier. This multiplier is smaller
1
than the standard multiplier, 1 − mpc , as can be verified algebraically or by trying
numerical values for mpc and t.
c. As we showed in part a, short-run equilibrium output equals the multiplier times
autonomous expenditure. For given fluctuations in autonomous aggregate demand, the
smaller is the multiplier, the less output will fluctuate. So changes in the economy that
reduce the multiplier, such as taxes that are proportional to output, tend to stabilize
output for given fluctuations in autonomous expenditure.
d. Plugging these values into the expression for output in part a, we get
1
(500 + 1500 + 2000 + 0)
1 − 0.8(1 − 0.25)
1
(4000)
Y=
1 − 0.6
Y = (2.5)(4000) = 10,000
Y=
1
1
1
1
=
=
=
= 2.5
1
(
0
.
8
)(
1
0
.
25
)
1
(
0
.
8
)(
0
.
75
)
1
0
.
6
0
.
4
−
−
−
−
.
The multiplier is