SOLUTION MANUAL
, MANKIW WORTH
PUBLISHERS’
MACROECONOMICS
SOLUTIONS
CHAPTERS COVERED:
3 National Income
5 Inflation
8 Economic Growth I
9 Economic Growth II
10 Economic Fluctuations Business Cycles
11 Aggregate Demand I: Building ISLM model
12 Aggregate Demand II: applying ISLM model
14 Aggregate Supply and Phillips Curve
15 Dynamic Model of AD and AS
16 Consumption theories
17 Investment Theories
18 Stabilization Policy and Perspectives
,CHAPTER 3 National Income: Where It Comes From
and Where It Goes
Questions for Review
1. The factors of production and the production technology determine the amount of out-
put an economy can produce. The factors of production are the inputs used to produce
goods and services: the most important factors are capital and labor. The production
technology determines how much output can be produced from any given amounts of
these inputs. An increase in one of the factors of production or an improvement in tech-
nology leads to an increase in the economy’s output.
2. When a firm decides how much of a factor of production to hire or demand, it considers how
this decision affects profits. For example, hiring an extra unit of labor increases output and
therefore increases revenue; the firm compares this additional revenue to the additional
cost from the higher wage bill. The additional revenue the firm receives depends on the
marginal product of labor (MPL) and the price of the good produced (P). An additional unit
of labor produces MPL units of additional output, which sells for P dollars per unit.
Therefore, the additional revenue to the firm is P × MPL. The cost of hiring the additional
unit of labor is the wage W. Thus, this hiring decision has the following effect on profits:
ΔProfit = ΔRevenue – ΔCost
= (P × MPL) – W.
If the additional revenue, P × MPL, exceeds the cost (W) of hiring the additional unit of
labor, then profit increases. The firm will hire labor until it is no longer profitable to do
so—that is, until the MPL falls to the point where the change in profit is zero. In the
equation above, the firm hires labor until Δprofit = 0, which is when (P × MPL) = W.
This condition can be rewritten as:
MPL = W/P.
Therefore, a competitive profit-maximizing firm hires labor until the marginal product
of labor equals the real wage. The same logic applies to the firm’s decision regarding
how much capital to hire: the firm will hire capital until the marginal product of capital
equals the real rental price.
3. A production function has constant returns to scale if an equal percentage increase in
all factors of production causes an increase in output of the same percentage. For exam-
ple, if a firm increases its use of capital and labor by 50 percent, and output increases
by 50 percent, then the production function has constant returns to scale.
If the production function has constant returns to scale, then total income (or
equivalently, total output) in an economy of competitive profit-maximizing firms is
divided between the return to labor, MPL × L, and the return to capital, MPK × K. That
is, under constant returns to scale, economic profit is zero.
4. A Cobb–Douglas production function function has the form F(K,L) = AKαL1–α. The text
showed that the parameter α gives capital’s share of income. (Since income equals out-
put for the overall economy, it is also capital’s share of output.) So if capital earns one-
fourth of total income, then a = 0.25. Hence, F(K,L) = AK0.25L0.75.
5. Consumption depends positively on disposable income—the amount of income after all
taxes have been paid. The higher disposable income is, the greater consumption is.
The quantity of investment goods demanded depends negatively on the real inter-
est rate. For an investment to be profitable, its return must be greater than its cost.
Because the real interest rate measures the cost of funds, a higher real interest rate
makes it more costly to invest, so the demand for investment goods falls.
11
, 12 Answers to Textbook Questions and Problems
6. Government purchases are a measure of the dollar value of goods and services pur-
chased directly by the government. For example, the government buys missiles and
tanks, builds roads, and provides services such as air traffic control. All of these activi-
ties are part of GDP. Transfer payments are government payments to individuals that
are not in exchange for goods or services. They are the opposite of taxes: taxes reduce
household disposable income, whereas transfer payments increase it. Examples of
transfer payments include Social Security payments to the elderly, unemployment
insurance, and veterans’ benefits.
7. Consumption, investment, and government purchases determine demand for the econo-
my’s output, whereas the factors of production and the production function determine
the supply of output. The real interest rate adjusts to ensure that the demand for the
economy’s goods equals the supply. At the equilibrium interest rate, the demand for
goods and services equals the supply.
8. When the government increases taxes, disposable income falls, and therefore consumption
falls as well. The decrease in consumption equals the amount that taxes increase multi-
plied by the marginal propensity to consume (MPC). The higher the MPC is, the greater is
the negative effect of the tax increase on consumption. Because output is fixed by the fac-
tors of production and the production technology, and government purchases have not
changed, the decrease in consumption must be offset by an increase in investment. For
investment to rise, the real interest rate must fall. Therefore, a tax increase leads to a
decrease in consumption, an increase in investment, and a fall in the real interest rate.
Problems and Applications
1. a. According to the neoclassical theory of distribution, the real wage equals the mar-
ginal product of labor. Because of diminishing returns to labor, an increase in the
labor force causes the marginal product of labor to fall. Hence, the real wage falls.
Given a Cobb–Douglas production function, the increase in the labor force
will increase the marginal product of capital and will increase the real rental price
of capital. With more workers, the capital will be used more intensively and will
be more productive.
b. The real rental price equals the marginal product of capital. If an earthquake
destroys some of the capital stock (yet miraculously does not kill anyone and lower
the labor force), the marginal product of capital rises and, hence, the real rental
price rises.
Given a Cobb–Douglas production function, the decrease in the capital stock
will decrease the marginal product of labor and will decrease the real wage. With
less capital, each worker becomes less productive.
c. If a technological advance improves the production function, this is likely to
increase the marginal products of both capital and labor. Hence, the real wage
and the real rental price both increase.
d. High inflation that doubles the nominal wage and the price level will have no
impact on the real wage. Similarly, high inflation that doubles the nominal rental
price of capital and the price level will have no impact on the real rental price of
capital.
2. a. To find the amount of output produced, substitute the given values for labor and
land into the production function:
Y = 1000.51000.5 = 100.
b. According to the text, the formulas for the marginal product of labor and the mar-
ginal product of capital (land) are:
MPL = (1 – α)AKαL–α
MPK = αAKα – 1L1 – α
, MANKIW WORTH
PUBLISHERS’
MACROECONOMICS
SOLUTIONS
CHAPTERS COVERED:
3 National Income
5 Inflation
8 Economic Growth I
9 Economic Growth II
10 Economic Fluctuations Business Cycles
11 Aggregate Demand I: Building ISLM model
12 Aggregate Demand II: applying ISLM model
14 Aggregate Supply and Phillips Curve
15 Dynamic Model of AD and AS
16 Consumption theories
17 Investment Theories
18 Stabilization Policy and Perspectives
,CHAPTER 3 National Income: Where It Comes From
and Where It Goes
Questions for Review
1. The factors of production and the production technology determine the amount of out-
put an economy can produce. The factors of production are the inputs used to produce
goods and services: the most important factors are capital and labor. The production
technology determines how much output can be produced from any given amounts of
these inputs. An increase in one of the factors of production or an improvement in tech-
nology leads to an increase in the economy’s output.
2. When a firm decides how much of a factor of production to hire or demand, it considers how
this decision affects profits. For example, hiring an extra unit of labor increases output and
therefore increases revenue; the firm compares this additional revenue to the additional
cost from the higher wage bill. The additional revenue the firm receives depends on the
marginal product of labor (MPL) and the price of the good produced (P). An additional unit
of labor produces MPL units of additional output, which sells for P dollars per unit.
Therefore, the additional revenue to the firm is P × MPL. The cost of hiring the additional
unit of labor is the wage W. Thus, this hiring decision has the following effect on profits:
ΔProfit = ΔRevenue – ΔCost
= (P × MPL) – W.
If the additional revenue, P × MPL, exceeds the cost (W) of hiring the additional unit of
labor, then profit increases. The firm will hire labor until it is no longer profitable to do
so—that is, until the MPL falls to the point where the change in profit is zero. In the
equation above, the firm hires labor until Δprofit = 0, which is when (P × MPL) = W.
This condition can be rewritten as:
MPL = W/P.
Therefore, a competitive profit-maximizing firm hires labor until the marginal product
of labor equals the real wage. The same logic applies to the firm’s decision regarding
how much capital to hire: the firm will hire capital until the marginal product of capital
equals the real rental price.
3. A production function has constant returns to scale if an equal percentage increase in
all factors of production causes an increase in output of the same percentage. For exam-
ple, if a firm increases its use of capital and labor by 50 percent, and output increases
by 50 percent, then the production function has constant returns to scale.
If the production function has constant returns to scale, then total income (or
equivalently, total output) in an economy of competitive profit-maximizing firms is
divided between the return to labor, MPL × L, and the return to capital, MPK × K. That
is, under constant returns to scale, economic profit is zero.
4. A Cobb–Douglas production function function has the form F(K,L) = AKαL1–α. The text
showed that the parameter α gives capital’s share of income. (Since income equals out-
put for the overall economy, it is also capital’s share of output.) So if capital earns one-
fourth of total income, then a = 0.25. Hence, F(K,L) = AK0.25L0.75.
5. Consumption depends positively on disposable income—the amount of income after all
taxes have been paid. The higher disposable income is, the greater consumption is.
The quantity of investment goods demanded depends negatively on the real inter-
est rate. For an investment to be profitable, its return must be greater than its cost.
Because the real interest rate measures the cost of funds, a higher real interest rate
makes it more costly to invest, so the demand for investment goods falls.
11
, 12 Answers to Textbook Questions and Problems
6. Government purchases are a measure of the dollar value of goods and services pur-
chased directly by the government. For example, the government buys missiles and
tanks, builds roads, and provides services such as air traffic control. All of these activi-
ties are part of GDP. Transfer payments are government payments to individuals that
are not in exchange for goods or services. They are the opposite of taxes: taxes reduce
household disposable income, whereas transfer payments increase it. Examples of
transfer payments include Social Security payments to the elderly, unemployment
insurance, and veterans’ benefits.
7. Consumption, investment, and government purchases determine demand for the econo-
my’s output, whereas the factors of production and the production function determine
the supply of output. The real interest rate adjusts to ensure that the demand for the
economy’s goods equals the supply. At the equilibrium interest rate, the demand for
goods and services equals the supply.
8. When the government increases taxes, disposable income falls, and therefore consumption
falls as well. The decrease in consumption equals the amount that taxes increase multi-
plied by the marginal propensity to consume (MPC). The higher the MPC is, the greater is
the negative effect of the tax increase on consumption. Because output is fixed by the fac-
tors of production and the production technology, and government purchases have not
changed, the decrease in consumption must be offset by an increase in investment. For
investment to rise, the real interest rate must fall. Therefore, a tax increase leads to a
decrease in consumption, an increase in investment, and a fall in the real interest rate.
Problems and Applications
1. a. According to the neoclassical theory of distribution, the real wage equals the mar-
ginal product of labor. Because of diminishing returns to labor, an increase in the
labor force causes the marginal product of labor to fall. Hence, the real wage falls.
Given a Cobb–Douglas production function, the increase in the labor force
will increase the marginal product of capital and will increase the real rental price
of capital. With more workers, the capital will be used more intensively and will
be more productive.
b. The real rental price equals the marginal product of capital. If an earthquake
destroys some of the capital stock (yet miraculously does not kill anyone and lower
the labor force), the marginal product of capital rises and, hence, the real rental
price rises.
Given a Cobb–Douglas production function, the decrease in the capital stock
will decrease the marginal product of labor and will decrease the real wage. With
less capital, each worker becomes less productive.
c. If a technological advance improves the production function, this is likely to
increase the marginal products of both capital and labor. Hence, the real wage
and the real rental price both increase.
d. High inflation that doubles the nominal wage and the price level will have no
impact on the real wage. Similarly, high inflation that doubles the nominal rental
price of capital and the price level will have no impact on the real rental price of
capital.
2. a. To find the amount of output produced, substitute the given values for labor and
land into the production function:
Y = 1000.51000.5 = 100.
b. According to the text, the formulas for the marginal product of labor and the mar-
ginal product of capital (land) are:
MPL = (1 – α)AKαL–α
MPK = αAKα – 1L1 – α
