22
Gordon • Macroeconomics, Eleventh Edition
„
Answers to Questions in Textbook
1. Movements in endogenous variables are explained by the theory; movements in exogenous variables
are not. Here and throughout the book, Gordon makes no distinction between exogenous variables
and parameters. Both are determined outside the model and fixed for each period of analysis. Both,
however, may be variables for purposes of problems and exercises. Thus, although the marginal
propensity to consume is treated as a fixed parameter throughout the chapter, the end-of-chapter
problems contain examples where MPC takes a different value.
Endogenous
Exogenous
Consumption
Net exports
GDP
Tax revenue
Disposable income
Saving
Foreign trade surplus (deficit)
Government budget surplus (deficit)
Autonomous taxes
Marginal propensity to consume
Exports
Price level
Interest rate
Investment
2. We distinguish between the two types of consumption for two reasons. First, each type of spending
is determined by a different cause: induced consumption is determined by the level of disposable
income and the marginal propensity to consume, while autonomous consumption is determined by
factors other than income. Second, changes in autonomous consumption cause a multiplier effect in
the economy, but changes in induced consumption do not.
3. The decline in the real personal saving rate from the late 1980s through the 1990s was due to the
stock market boom that started in 1982 and ended in 2000. Stock prices rose tenfold over that period,
resulting in a sharp increase in household wealth. That increase allowed consumers to increase
consumption expenditures relative to disposable income.
Between 2001 and 2003, monetary policymakers sharply reduced interest rates, resulting in lower
mortgage payments for many households. Those enabled consumers to maintain or increase their
consumption expenditures relative to disposable income following 2000’s stock market collapse.
4. Businesses reduce production during a recession primarily because of falling demand for their
goods and services. One of the first indications businesses get that demand has fallen is that they
have more unsold goods in inventories than they would like. That is, businesses see an unintended
rise in inventories, which causes them to reduce output. On the other hand, once businesses become
confident that the economy is on the rebound, then they will start to build up inventories in
anticipation of higher sales.
5. Positive unintended inventory investment results if income is greater than planned expenditure and
businesses’ inventories build up. To avoid the costs of financing and storing unwanted inventories,
businesses cut production, which causes income to fall. Negative unintended inventory investment
occurs if income is less than planned expenditure and businesses’ inventories shrink. To meet current
sales and replenish inventories, businesses raise production, causing income to rise.
6. Answer: a. The impact of a change in investment will be greater the larger the marginal propensity
to consume. Although the initial impact of the change in autonomous investment is the same in any
case, the larger the MPC, the greater will be the secondary effects on consumer spending.
Chapter 3
Spending, Income, and Interest Rates
23
7. Expansionary fiscal policy would include increasing government spending or decreasing taxes. In
each case, the size of the deficit would increase. If the budget were initially in surplus, however, the
same policy choice would decrease the surplus.
8. The IS curve is downward sloping because a fall in the interest rate results in a rise in consumption
and planned investment, the two interest rate sensitive components of autonomous planned spending.
That increase in planned spending results in a rise in income as businesses increase output in
response to the greater demand for goods and services. Income continues to rise until the commodity
market is once again in equilibrium. Note that the higher level of income takes place at a lower
interest rate, which is shown graphically as a movement down the IS curve. A shift of the IS curve
takes place when autonomous planned spending changes due to something other than a change in the
interest rate. For example, suppose that there is a change in fiscal policy which reduces autonomous
planned spending. That decrease causes a fall in income as business firms cut output in response to
the lower demand for goods and services. Income continues to fall until the commodity market is
once again in equilibrium. Note that the lower level of income takes place at the same interest rate,
which is shown graphically as a shift left of the IS curve.
9. a.
The decline in sales of American agricultural exports reduces net exports. Therefore,
autonomous planned spending decreases at a given interest rate. The reduction results in a
fall in equilibrium income at a given interest rate, which is shown graphically as a shift left
of the IS curve.
b. The collapse in consumer confidence reduces consumption. Therefore, autonomous planned
spending decreases at a given interest rate. The reduction results in a fall in equilibrium income
at a given interest rate, which is shown graphically as a shift left of the IS curve.
c. The decline in the personal savings rate is accompanied by a rise in consumption. Therefore,
autonomous planned spending increases at a given interest rate. The increase leads to a rise in
equilibrium income at a given interest rate, which is shown graphically as a shift right of the
IS curve.
d. The collapse in business confidence reduces planned investment. Therefore, autonomous
planned spending decreases at a given interest rate. The reduction results in a fall in equilibrium
income at a given interest rate, which is shown graphically as a shift left of the IS curve.
10. Since a demand shock is a significant change in desired spending by consumers, business firms, the
government, or foreigners, a demand shock causes a change in autonomous planned spending at a
given interest rate. That change in autonomous planned spending results in a change in equilibrium
income, given the interest rate, and is shown graphically as a shift in the IS curve. Thus the
hypothesis that the increased stability of the U.S. economy since 1985 is due to smaller and less
important demand shocks can be interpreted to mean that shifts of the IS curve have become smaller.
11. C = a + c(Y − T) = a + cY − c(Ta + tY) = a − cTa + c(1 − t)Y.
S = −a + s(Y − T) = −a + sY − s(Ta + tY) = −a − sTa + s(1 − t)Y.
12. Answer: b. The greater the MPC, the smaller is the marginal leakage rate. Therefore, the impact of
a change in investment will be greater the smaller the marginal leakage rate. It will take more rounds
of spending and saving to generate the necessary increase in leakages to match the initial change in
autonomous spending.
13. The marginal leakage rate in this case is s + nx, so the balanced budget multiplier is s/(s + nx), which
is less than one.
24
Gordon • Macroeconomics, Eleventh Edition
„
Answers to Problems in Textbook
1.
a. Consumption equals 1,400 + 0.6(10,000 − 1,750) = 1,400 + 4,950 = 6,350.
b. Saving equals disposable income minus consumption, which equals 8,250 − 6,350 = 1,900.
c. The level of planned investment equals 1,800. To compute the level of actual investment, I,
remember that income and expenditures (E) are always equal, and since net exports equal zero
in this problem, E = C + I + G, so that I = Y − C − G or I = 10,000 − 6,350 − 1950 = 1,700. Since
unintended inventory investment, Iu = I − IP, Iu = 1,700 − 1,800 = −100.
d. Leakages equal saving plus taxes = 1,900 + 1,750 = 3,650. Injections equal investment plus
government = 1,700 + 1,950 = 3,650. So both leakages and injections equal 3,650.
e. Since planned expenditure exceeds income, the economy is not in equilibrium. In this economy,
the equilibrium level of income equals Ap /s, where s is the marginal propensity to save.
Autonomous planned spending, Ap, equals Ca − cT + Ip + G = 1,400 − 0.6(1,700) + 1,800 +
1,950 = 4,100. The marginal propensity to save equals 1 − c = 1 − 0.6 = 0.4. Therefore, the
equilibrium level of income equals 4,100/0.4 = 10,250.
f. At the equilibrium level of income, there is a government deficit of 200 billion since taxes equal
1,750 and government spending on goods and services equals 1,950.
2.
a. The marginal propensity to save, s, equals 1 − c = 1 − .6 = .4.
b. Autonomous planned spending, Ap, equals Ca − cTa + Ip + G + NX = 1,500 − 10r −.6(1,800) +
2,400 − 50r + 2,000 − 200 = 4,620 − 60r. Therefore, at an interest rate equal to 5, autonomous
planned spending equals 4,620 − 60(5) = 4,320.
c. Since the marginal propensity to save equals .4 and the equilibrium level of income equals Ap /s,
the equilibrium level of income equals 4,320/.4 = 10,800, given the interest rate equals 5.
d. Since autonomous consumption changes by four percent of any change in household wealth and
the decline in the housing market in 2006–07 and drop in the stock market in the summer of
2007 reduces household wealth by 750 billion dollars, the decrease in autonomous consumption
that results from the decline in household wealth equals .04(750) = 30 billion.
e. Since the decrease in autonomous consumption that results from the decline in household wealth
equals 30 billion, autonomous planned spending decreases by that amount as well. Therefore,
the new amount of autonomous planned spending equals 4,320 − 30 = 4,290. Therefore, the new
equilibrium level of income equals 4,290/.4 = 10,725, given the interest rate equals 5.
f. The multiplier, k, equals ΔY/ΔAp = (10,725 − 10,800)/(4,290 − 4,320) = (−75)/(−30) = 2.5.
g. Since the multiplier equals 2.5 and income must increase by 75 billion to restore income to its
initial equilibrium level of 10,800, fiscal or monetary policymakers must take actions that
increase autonomous planned spending by 30 billion in order to restore equilibrium income
to 10,800.
i. If fiscal policymakers increase government spending, G, and there are no changes in either
taxes or the interest rate, then ΔAp = 30 = ΔG. Therefore, fiscal policymakers must increase
government spending by 30 billion to restore equilibrium income to 10,800, given no
changes in taxes or the interest rate.
ii. If fiscal policymakers decrease taxes, Ta, and there are no changes in either government
spending or the interest rate, then ΔAp = 30 = −cΔTa = −.6ΔTa. Therefore, 30/(−.6) = −50 =
ΔTa. Therefore, fiscal policymakers must cut taxes by 50 billion to restore equilibrium
income to 10,800, given no changes in government spending or the interest rate.
Chapter 3
Spending, Income, and Interest Rates
25
iii. If fiscal policymakers increase government spending and taxes, then given no change in
the interest rate, ΔAp = ΔG − .6ΔTa = 30. Furthermore, since fiscal policymakers at the
same time don’t change the government budget balance, then ΔG = ΔTa, so that ΔAp =
ΔG − .6ΔG = 30 or .4ΔG = 30 or ΔG = 75. Therefore, fiscal policymakers increase both
government spending and taxes by 75 billion to restore equilibrium income to 10,800, given
no changes in the government budget balance or the interest rate.
iv. The parameter on the interest rate in the equation for autonomous planned spending
indicates that autonomous planned spending increases by 60 billion for every one
percentage point drop in the interest rate. Therefore, since autonomous planned spending
must increase by 30 billion to restore equilibrium income to 10,800, monetary policymakers
must reduce the interest rate by one-half of a percentage point to restore equilibrium income
to 10,800, given no changes in government spending or the interest rate.
3.
a. The marginal propensity to save equals 1 − c = 1 − .6 = .4.
b. The equation for autonomous planned spending, Ap, equals 1,500 − 20r − .6(1,750) + 2,450 −
60r + 1,980 − 200 = 4,680 − 80r. When the interest rate equals 0, autonomous planned spending
equals 4,680. When the interest rate equals 2, autonomous planned spending equals 4,680 −
80(2) = 4,520. When the interest rate equals 4, autonomous planned spending equals 4,680 −
80(4) = 4,360, and when it equals 6, autonomous planned spending equals 4,680 − 80(6) =
4,200.
c. The equilibrium level of income equals Ap /s. At an interest rate of 0, the equilibrium level of
income equals 4,680/.4 = 11,700. At an interest rate of 2, the equilibrium level of income equals
4,520/.4 = 11,300. At an interest rate of 4, the equilibrium level of income equals 4,360/.4 =
10,900, and at an interest rate of 6, it equals 4,200/.4 = 10,500. Your graph of the IS curve has
the label of real income on the horizontal axis and the label of interest rate on the vertical axis.
The four points on your IS curve are: (11,700, 0); (11,300, 2); (10,900, 4); and (10,500, 6).
d. The decrease in government spending of 160 billion decreases autonomous planned spending
by the same amount at each interest rate. Therefore, when the interest rate equals 0,
autonomous planned spending equals 4,680 − 160 = 4,520. When the interest rate
equals 2, autonomous planned spending equals 4,520 − 160 = 4,360. When the interest
rate equals 4, autonomous planned spending equals 4,360 − 160 = 4,200, and when it equals 6,
autonomous planned spending equals 4,200 − 160 = 4,040.
e. Again, the equilibrium level of income equals Ap /s. At an interest rate of 0, the new equilibrium
level of income equals 4,520/.4 = 11,300. At an interest rate of 2, the new equilibrium level of
income equals 4,360/.4 = 10,900. At an interest rate of 4, the new equilibrium level of income
equals 4,200/.4 = 10,500, and at an interest rate of 6, it now equals 4,040/.4 = 10,100. The four
points on your new IS curve are: (11,300, 0); (10,900, 2); (10,500, 4); and (10,100, 6). Note that
the decrease in autonomous planned spending that results from the decline in government
spending shifts the IS curve left.
f. The increase in government spending of 80 billion increases autonomous planned spending
by the same amount at each interest rate. Therefore, when the interest rate equals 0,
autonomous planned spending equals 4,680 + 80 = 4,760. When the interest rate
equals 2, autonomous planned spending equals 4,520 + 80 = 4,600. When the interest
rate equals 4, autonomous planned spending equals 4,360 + 80 = 4,440, and when it equals 6,
autonomous planned spending equals 4,200 + 80 = 4,280.
g. Again, the equilibrium level of income equals Ap /sw. At an interest rate of 0, the new equilibrium
level of income equals 4,760/.4 = 11,900. At an interest rate of 2, the new equilibrium level of
income equals 4,600/.4 = 11,500. At an interest rate of 4, the new equilibrium level of income
equals 4,440/.4 = 11,100, and at an interest rate of 6, it now equals 4,280/.4 = 10,700. The four
points on your new IS curve are: (11,900, 0); (11,500, 2); (11,100, 4); and (10,700, 6). Note that
the increase in autonomous planned spending that results from the rise in government spending
shifts the IS curve right.
26
Gordon • Macroeconomics, Eleventh Edition
h. Your answer to Part e shows that monetary policymakers will reduce the interest rate to 2 if
they wish to maintain equilibrium level at 10,900, the natural level of real GDP, given the
decline in government spending. Your graph of the IS curve from Part g shows that monetary
policymakers will increase the interest rate to 5 if they wish to maintain equilibrium level at
10,900, the natural level of real GDP, given the rise in government spending.
4.
a.
Ap = 660 − 0.8(200) + 500 + 500 + 300 = 1800.
b. Multiplier = 0.1/(0.2(1 − 0.2) + 0.2 + 0.04) = 2.5.
c. Y = 1800 × 2.5 = 4500.
d. T − G = [200 + 0.2(4500)] − 500 = 600 (surplus); NX = 300 − 0.04(4500) = 120 (surplus).
e. Leakages = S + T = 20 + 1100 = 1120. Injections = I + G + NX = 500 + 500 + 120 = 1120.
f. Since the multiplier is 2.5, the decline in Ap of 150 means a decline in Ep. Y now exceeds Ep and
there is unintended inventory accumulation. Firms lay off workers and Y declines. Ep declines as
well but at a slower rate. Eventually, equilibrium is re-attained at a lower Y.
g. Equilibrium income decreases by 375 from 4500 to 4125.
5.
The marginal propensity to save equals 1 − c = 1 − 0.5 = 0.5. The multiplier, k, equals the
inverse of the marginal propensity to save = 1/0.5 = 2.
b. The equation for autonomous planned spending, Ap, equals Ca − cT + Ip + G + NX = 1,400 −
15r − 0.5(1,600) + 2,350 − 35r + 1,940 − 200 = 4,690 − 50r.
a.
c. The equation for the IS curve equals Y = 2(4,690 − 50r) = 9,380 − 100r.
d. At an interest rate of 0, the equilibrium level of income equals 9,380. At an interest rate of 3,
the equilibrium level of income equals 9,380 − 100(3) = 9,080. At an interest rate of 6, the
equilibrium level of income equals 9,380 − 100(6) = 8,780.
e. The slope of the IS curve, Δr/ΔY, equals (2 − 0)/(9,180 − 9,380) = (4 − 2)/(9,180 − 8,980) =
2/(−200) = −0.01.
f. A rise in consumer confidence causes a rise in consumption expenditures. The new equation for
autonomous planned spending equals 1,440 − 15r − 0.5(1,600) + 2,350 − 35r + 1,940 − 200 =
4,730 − 50r. The new equation for the IS curve equals 2(4,730 − 60r) = 9,460 − 100r.
g. At an interest rate of 0, the equilibrium level of income equals 9,460. At an interest rate of 3,
the equilibrium level of income equals 9,460 − 100(3) = 9,160. At an interest rate of 6, the
equilibrium level of income equals 9,460 − 100(6) = 8,860.
h. Since equilibrium income increases at each of the three interest rates, the IS curve shifted to
the right when autonomous consumption rises. The horizontal shift of the IS curve equals the
change in equilibrium income at a given interest rate (80), and since the change in equilibrium
income equals the multiplier times the change in autonomous planned spending, the horizontal
shift of the IS curve equals the multiplier times the change in autonomous planned spending
(2 times 40).
6.
The new value of marginal propensity to save equals 1 − 0.6 = 0.4. The new multiplier, k, equals
the inverse of the new marginal propensity to save = 1/0.4 = 2.5.
b. The equation for the new autonomous planned spending equals 1,400 − 15r − 0.6(1,600) +
2,350 − 35r + 1,940 − 200 = 4,530 − 50r.
a.
c. The equation for the new IS curve equals Y = 2.5(4,530 − 50r) = 11,325 − 125r.
d. At an interest rate of 0, the equilibrium level of income equals 11,325. At an interest rate of 3
the equilibrium level of income equals 11,325 − 125(3) = 10,950. At an interest rate of 6, the
equilibrium level of income equals 11,325 − 125(4) = 10,575.
Chapter 3
Spending, Income, and Interest Rates
27
The slope of the new IS curve equals Δr/ΔY = (2 − 0)/(11,075 − 11.325) = (4 − 2)/
(10,825 − 11,075) = 2/(−250) = −0.008.
f. The equation for the new autonomous planned spending equals, 1,400 − 15r − 0.6(1,600) +
2,350 − 45r + 1,940 − 200 = 4,530 − 60r.
g. The equation for the new IS curve equals Y = 2.5(4,530 − 60r) = 11,325 − 150r.
h. At an interest rate of 0, the equilibrium level of income equals 11,325. At an interest rate of 3,
the equilibrium level of income equals 11,325 − 150(3) = 10,875. At an interest rate of 6, the
equilibrium level of income equals 11,325 − 150(6) = 10,425.
i. The slope of the new IS curve equals Δr/ΔY = (2 − 0)/(11,025 − 11,325) = (4 − 2)/
(10,725 − 11,025) = 2/(−300) = −0.0067.
j. As the multiplier increases from 2 to 2.5, the IS curve becomes flatter as the slope decreases
from −0.01 to −0.008 and the decrease in income for a two percentage point rise in the interest
rate increases from 200 billion to 250 billion. Similarly, the IS curve becomes flatter as the
responsiveness of planned spending to the interest rate increases from a 50 billion to a 60 billion
dollar decrease in autonomous planned spending for every one percentage point rise in the
interest rate.
e.
7.
a.
b.
c.
d.
e.
The marginal propensity to save equals 1 − 0.85 = 0.15. The marginal leakage rate equals
0.15(1 − 0.2) + 0.2 + 0.08 = 0.4. The multiplier, k, equals the inverse of the marginal leakage
rate = 1/0.4 = 2.5.
The equation for autonomous planned spending, Ap, equals Ca − cTa + Ip + G + NXa = 225 −
10r − 0.85(100) + 1,610 − 30r + 1,650 + 700 = 4,100 − 40r.
The equation for the IS curve equals Y = 2.5(4,100 − 40r) = 10,250 − 100r.
At an interest rate of 3, the equilibrium level of income equals 9,950.
Taxes at the equilibrium level of income equal 100 + 0.2(9,950) = 2,090.
Consumption at the equilibrium level of income, given r = 3, equals 225 − 10(3) + 0.85(9,950 −
2,090) = 6,876. So saving equals 9,950 − 2,090 − 6,876 = 984. So leakages equal 984 + 2,090 =
3,074. Injections equal investment plus government plus net exports = 1,610 − 30(3) + 1,650 +
700 − 0.08(9,950) = 3,074. So both leakages and injections equal 3,074.