曼昆经济学原理第五版习题英文答案

Answers.to.Textbook.Questions.and.Problems

CHAPTER

2

The Data of Macroeconomics

Questions for Review1. GDP measures both the total income of everyone in the economy and the total expenditure on the economy’s output of goods and services. GDP can measure two things at once because both are really the same thing: for an economy as a whole, income must equal expenditure. As the circular flow diagram in the text illustrates, these are alternative, equivalent ways of measuring the flow of dollars in the economy. 2. The consumer price index measures the overall level of prices in the economy. It tells us the price of a fixed basket of goods relative to the price of the same basket in the base year. 3. The Bureau of Labor Statistics classifies each person into one of the following three categories: employed, unemployed, or not in the labor force. The unemployment rate, which is the percentage of the labor force that is unemployed, is computed as follows: Unemployment Rate= Number of Unemployed× 100 Labor Force .

Note that the labor force is the number of people employed plus the number of people unemployed. 4. Okun’s law refers to the negative relationship that exists between unemployment and real GDP. Employed workers help produce goods and services whereas unemployed workers do not. Increases in the unemployment rate are therefore associated with decreases in real GDP. Okun’s law can be summarized by the equation:% Real GDP= 3%– 2× ( Unemployment Rate). That is, if unemployment does not change, the growth rate of real GDP is 3 percent. For every percentage-point change in unemployment (for example, a fall from 6 percent to 5 percent, or an increase from 6 percent to 7 percent), output changes by 2 percent in the opposite direction.

Problems and Applications1. A large number of economic statistics are released regularly. These include the following: Gross Domestic Product—the market value of all final goods and services produced in a year. The Unemployment Rate—the percentage of the civilian labor force who do not have a job. Corporate Profits—the accounting profits remaining after taxes of all manufacturing corporations. It gives an indication of the general financial health of the corporate sector. The Consumer Price Index (CPI)—a measure of the average price that consumers pay for the goods they buy; changes in the CPI are a measure of inflation. The Trade Balance—the difference between the value of goods exported abroad and the value of goods imported from abroad.

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2. Value added by each person is the value of the good produced minus the amount the person paid for the materials necessary to make the good. Therefore, the value added by the farmer is$1.00 ($1– 0=$1). The value added by the miller is$2: she sells the flour to the baker for$3 but paid$1 for the flour. The value added by the baker is$3: she sells the bread to the engineer for$6 but paid the miller$3 for the flour. GDP is the total

value added, or$1+$2+$3=$6. Note that GDP equals the value of the final good (the bread). 3. When a woman marries her butler, GDP falls by the amount of the butler’s salary. This happens because measured total income, and therefore measured GDP, falls by the amount of the butler’s loss in salary. If GDP truly measured the value of all goods and services, then the marriage would not affect GDP since the total amount of economic activity is unchanged. Actual GDP, however, is an imperfect measure of economic activity because the value of some goods and services is left out. Once the butler’s work becomes part of his household chores, his services are no longer counted in GDP. As this example illustrates, GDP does not include the value of any output produced in the home. Similarly, GDP does not include other goods and services, such as the imputed rent on durable goods (e.g., cars and refrigerators) and any illegal trade. 4. a. b. c. d. e. government purchases investment net exports consumption investment

5. Data on parts (a) to (g) can be downloaded from the Bureau of Economic Analysis (www.bea.doc.gov—follow the links to GDP and related data). Most of the data (not necessarily the earliest year) can also be found in the Economic Report of the President. By piding each component (a) to (g) by nominal GDP and multiplying by 100, we obtain the following percentages:1950a. b. c. d. e. f. g. Personal consumption expenditures Gross private domestic investment Government consumption purchases Net exports National defense purchases State and local purchases Imports 65.5% 18.4% 15.9% 0.2% 6.7% 7.1% 3.9%

197563.0% 14.1% 22.1% 0.8% 6.6% 12.8% 7.5%

200068.2% 17.9% 17.6%–3.7% 3.8% 11.7% 14.9%

(Note: These data were downloaded February 5, 2002 from the BEA web site.) Among other things, we observe the following trends in the economy over the period 1950–2000: (a) Personal consumption expenditures have been around two-thirds of GDP, although the share increased about 5 percentage points between 1975 and 2000. (b) The share of GDP going to gross private domestic investment fell from 1950 to 1975 but then rebounded. (c) The share going to government consumption purchases rose more than 6 percentage points from 1950 to 1975 but has receded somewhat since then. (d) Net exports, which were positive in 1950 and 1975, were substantially negative in 2000. (e) The share going to national defense purchases fell from 1975 to 2000. (f) The share going to state and local purchases rose from 1950 to 1975. (g) Imports have grown rapidly relative to GDP.

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Chapter 2

The Data of Macroeconomics

7

6. a.

i.

Nominal GDP is the total value of goods and services measured at current prices. Therefore, Nominal GDP2000= (P 2000× Q 2000 )+ (P cars cars2000 bread

×Q

2000 bread

)

Nominal GDP2010

= ($50,000× 100)+ ($10× 500,000)=$5,000,000+$5,000,000=$10,000,000. 2010 2010= (P 2010× Q 2010 )+ (P bread× Q bread ) cars cars= ($60,

000× 120)+ ($20× 400,000)=$7,200,000+$8,000,000=$15,200,000.

ii.

Real GDP is the total value of goods and services measured at constant prices. Therefore, to calculate real GDP in 2010 (with base year 2000), multiply the quantities purchased in the year 2010 by the 2000 prices: Real GDP2010= (P2000 cars

× Q 2010 )+ (P cars

2000 bread

×Q

2010 bread

)

= ($50,000× 120)+ ($10× 400,000)=$6,000,000+$4,000,000=$10,000,000. Real GDP for 2000 is calculated by multiplying the quantities in 2000 by the prices in 2000. Since the base year is 2000, real GDP2000 equals nominal GDP2000, which is$10,000,000. Hence, real GDP stayed the same between 2000 and 2010. The implicit price deflator for GDP compares the current prices of all goods and services produced to the prices of the same goods and services in a base year. It is calculated as follows: Implicit Price Deflator2010= Nominal GDP2010 Real GDP2010 .

iii.

Using the values for Nominal GDP2010 and real GDP2010 calculated above:$10,000,000= 1.52. This calculation reveals that prices of the goods produced in the year 2010 increased by 52 percent compared to the prices that the goods in the economy sold for in 2000. (Because 2000 is the base year, the value for the implicit price deflator for the year 2000 is 1.0 because nominal and real GDP are the same for the base year.) The consumer price index (CPI) measures the level of prices in the economy. The CPI is called a fixed-weight index because it uses a fixed basket of goods over time to weight prices. If the base year is 2000, the CPI in 2010 is an average of prices in 2010, but weighted by the composition of goods produced in 2000. The CPI2010 is calculated as follows: CPI2010=2010 2000 2010 2000 (Pcars× Qcars )+ (Pbread× Qbread ) 2000 2000 2000 (Pcars× Qc2000 )+ (Pbread× Qbread ) ars

Implicit Price Deflator2010=

$15,200,000

iv.

==

($60,000× 100)+ ($20× 500,000) ($50,000× 100)+ ($10× 500,000)$16,000,000

$10,000,000= 1.6.

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b.

c.

This calculation shows that the price of goods purchased in 2010 increased by 60 percent compared to the prices these goods would have sold for in 2000. The CPI for 2000, the base year, equals 1.0. The implicit price deflator is a Paasche index because it is computed with a changing basket of goods; the CPI is a Laspeyres index because it is computed with a fixed basket of goods. From (5.a.iii), the implicit price deflator for the year 2010 is 1.52, which indicates that prices rose by 52 percent from what they were in the year 2000. From (5.a.iv.), the CPI for the year 2010 is 1.6, which indicates that prices rose by 60 percent from what they were in the year 2000. If prices of all goods rose by, say, 50 percent, then one could say unambiguously that the price level rose by 50 percent. Yet, in our example, relative prices have changed. The price of cars rose by 20 percent; the price of bread rose by 100 percent, ma

king bread relatively more expensive. As the discrepancy between the CPI and the implicit price deflator illustrates, the change in the price level depends on how the goods’ prices are weighted. The CPI weights the price of goods by the quantities purchased in the year 2000. The implicit price deflator weights the price of goods by the quantities purchased in the year 2010. The quantity of bread consumed was higher in 2000 than in 2010, so the CPI places a higher weight on bread. Since the price of bread increased relatively more than the price of cars, the CPI shows a larger increase in the price level. There is no clear-cut answer to this question. Ideally, one wants a measure of the price level that accurately captures the cost of living. As a good becomes relatively more expensive, people buy less of it and more of other goods. In this example, consumers bought less bread and more cars. An index with fixed weights, such as the CPI, overestimates the change in the cost of living because it does not take into account that people can substitute less expensive goods for the ones that become more expensive. On the other hand, an index with changing weights, such as the GDP deflator, underestimates the change in the cost of living because it does not take into account that these induced substitutions make people less well off. The consumer price index uses the consumption bundle in year 1 to figure out how much weight to put on the price of a given good: CPI22 1 2 1 (Pred× Qred )+ (Pgreen× Qgreen )

7. a.

= (P 1× Q1 )+ (P 1× Q1 ) red red green green=

($2× 10)+ ($1× 0) ($1× 10)+ ($2× 0)

= 2. b. According to the CPI, prices have doubled. Nominal spending is the total value of output produced in each year. In year 1 and year 2, Abby buys 10 apples for$1 each, so her nominal spending remains constant at$10. For example, Nominal Spending2= (P 2× Q 2 red red

)+ (P 2× Q 2 ) green green

= ($2× 0)+ ($1× 10)=$10.

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Chapter 2

The Data of Macroeconomics

9

c.

Real spending is the total value of output produced in each year valued at the prices prevailing in year 1. In year 1, the base year, her real spending equals her nominal spending of$10. In year 2, she consumes 10 green apples that are each valued at their year 1 price of$2, so her real spending is$20. That is, Real Spending2= (P 1× Q 2 red red

)+ (P 1× Q 2 ) green green

= ($1× 0)+ ($2× 10)=$20. Hence, Abby’s real spending rises from$10 to$20. d. The implicit price deflator is calculated by piding Abby’s nominal spending in year 2 by her real spending that year: Implicit Price Deflator2= Nominal Spending2 Real Spending2$10=$20= 0.5. Thus, the implicit price deflator suggests that prices have fallen by half. The reason for this is that the deflator estimates how much Abby values her apples using prices prevailing in year 1. From this perspective green apples appear very valuable. In year 2, when Abby consumes 10 green apples, it

appears that her consumption has increased because the deflator values green apples more highly than red apples. The only way she could still be spending$10 on a higher consumption bundle is if the price of the good she was consuming feel. e. If Abby thinks of red apples and green apples as perfect substitutes, then the cost of living in this economy has not changed—in either year it costs$10 to consume 10 apples. According to the CPI, however, the cost of living has doubled. This is because the CPI only takes into account the fact that the red apple price has doubled; the CPI ignores the fall in the price of green apples because they were not in the consumption bundle in year 1. In contrast to the CPI, the implicit price deflator estimates the cost of living has halved. Thus, the CPI, a Laspeyres index, overstates the increase in the cost of living and the deflator, a Paasche index, understates it. This chapter of the text discusses the difference between Laspeyres and Paasche indices in more detail. Real GDP falls because Disney does not produce any services while it is closed. This corresponds to a decrease in economic well-being because the income of workers and shareholders of Disney falls (the income side of the national accounts), and people’s consumption of Disney falls (the expenditure side of the national accounts). Real GDP rises because the original capital and labor in farm production now produce more wheat. This corresponds to an increase in the economic well-being of society, since people can now consume more wheat. (If people do not want to consume more wheat, then farmers and farmland can be shifted to producing other goods that society values.) Real GDP falls because with fewer workers on the job, firms produce less. This accurately reflects a fall in economic well-being. Real GDP falls because the firms that lay off workers produce less. This decreases economic well-being because workers’ incomes fall (the income side), and there are fewer goods for people to buy (the expenditure side). Real GDP is likely to fall, as firms shift toward production methods that produce fewer goods but emit less pollution. Economic well-being, however, may rise. The economy now produces less measured output but more clean air; clean air is not

8. a.

b.

c. d.

e.

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f.

g.traded in markets and, thus, does not show up in measured GDP, but is neverthe-less a good that people value.Real GDP rises because the high-school students go from an activity in which theyare not producing market goods and services to one in which they are. Economicwell-being, however, may decrease. In ideal national accounts, attending schoolwould show up as investment because it presumably increases the future produc-tivity of the worker. Actual national accounts do not measure this type of invest-ment. Note also that future GDP may be lower than it would be if the studentsstayed in school, since the future work force will be less educated.Measured real GDP falls because fathers spend less time producing market goods

and services. The actual production of goods and services need not have fallen,however. Measured production (what the fathers are paid to do) falls, but unmea-sured production of child-rearing services rises.

9.As Senator Robert Kennedy pointed out, GDP is an imperfect measure of economic per-formance or well-being. In addition to the left-out items that Kennedy cited, GDP alsoignores the imputed rent on durable goods such as cars, refrigerators, and lawnmowers;many services and products produced as part of household activity, such as cooking andcleaning; and the value of goods produced and sold in illegal activities, such as the drugtrade. These imperfections in the measurement of GDP do not necessarily reduce itsusefulness. As long as these measurement problems stay constant over time, then GDPis useful in comparing economic activity from year to year. Moreover, a large GDPallows us to afford better medical care for our children, newer books for their education,

and more toys for their play.

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services such as air traffic control. All of these activities are part of GDP. Transfer payments are government payments to inpiduals 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. 6. Consumption, investment, and government purchases determine demand for the economy’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. 7. When the government increases taxes, disposable income falls, and therefore consumption falls as well. The decrease in consumption equals the amount that taxes increase multiplied 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 factors 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 fa

ll in the real interest rate.

Problems and Applications1. a. According to the neoclassical theory of distribution, the real wage equals the marginal 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. 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. 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.

b.

c.

2. A production function has decreasing returns to scale if an equal percentage increase in all factors of production leads to a smaller percentage increase in output. For example, if we double the amounts of capital and labor, and output less than doubles, then the production function has decreasing returns to capital and labor. This may happen if there is a fixed factor such as land in the production function, and this fixed factor becomes scarce as the economy grows larger. A production function has increasing returns to scale if an equal percentage increase in all factors of production leads to a larger percentage increase in output. For example, if doubling inputs of capital and labor more than doubles output, then the production function has increasing returns to scale. This may happen if specialization of labor becomes greater as population grows. For example, if one worker builds a car, then it takes him a long time because he has to learn many different skills, and he must constantly change tasks and tools; all of this is fairly slow. But if many workers build a car, then each one can specialize in a particular task and become very fast at it. 3. a. b. According to the neoclassical theory, technical progress that increases the marginal product of farmers causes their real wage to rise. The real wage in (a) is measured in terms of farm goods. That is, if the nominal wage is in dollars, then the real wage is W/PF, where PF is the dollar price of farm goods.

Answers.to.Textbook.Questions.and.Problems

c.

d.

e.

f.

g.If the marginal productivity of barbers is unchanged, then their real wage isunchanged.The real wage in (c) is measured in terms of haircuts. That is, if the nominal wageis in dollars, then the real wage is W/PH, where PH is the dollar price of a hair-cut.If workers can move freely between being farmers and being barbers, then theymust be paid the same wage W in each sector.If the nominal wage W is the same in both sectors, but the real wage in terms offarm goods is greater than the real wage in terms of haircuts, then the price ofhaircuts must have risen relative to the price of farm goods.Both groups benefit from technological progress in farming.

4.The effect of a government tax increase of $100 billion on (a) public saving, (b) private

saving, and (c) national saving can be analyzed by using the following relationships:

National Saving = [Private Saving] + [Public Saving]

= [Y– T– C(Y– T)] + [T– G]

= Y– C(Y– T) – G.

Public Saving—The tax increase causes a 1-for-1 increase in public saving. T

increases by $100 billion and, therefore, public saving increases by $100 billion.

Private Saving—The increase in taxes decreases disposable income, Y– T, by

$100 billion. Since the marginal propensity to consume (MPC) is 0.6, consumption

falls by 0.6 ×$100 billion, or $60 billion. Hence,

Private Saving = – $100b– 0.6 ( – $100b) = – $40b.

Private saving falls $40 billion.

National Saving—Because national saving is the sum of private and public sav-

ing, we can conclude that the $100 billion tax increase leads to a $60 billion

increase in national saving.

Another way to see this is by using the third equation for national saving

expressed above, that national saving equals Y– C(Y– T) – G. The $100 billion

tax increase reduces disposable income and causes consumption to fall by $60 bil-

lion. Since neitherGnor Ychanges, national saving thus rises by $60 billion.

Investment—To determine the effect of the tax increase on investment, recall the

national accounts identity:

Y= C(Y– T) + I(r) + G.

Rearranging, we find

Y– C(Y– T) – G= I(r).

The left-hand side of this equation is national saving, so the equation just says the

national saving equals investment. Since national saving increases by $60 billion,

investment must also increase by $60 billion.a.b.c.d.

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Answers to Textbook Questions and Problems

How does this increase in investment take place? We know that investment depends on the real interest rate. For investment to rise, the real interest rate must fall. Figure 3–1 graphs saving and investment as a function of the real interest rate.r S1 S2 FiguFigure 3–1 re 3–1

Real interest rate

r1

r2 I (r)

I, S Investment, Saving

The tax increase causes national saving to rise, so the supply curve for loanable funds shifts to the right. The equilibrium real interest rate falls, and investment rises. 5. If consumers increase the amount that they consume today, then private saving and, therefore, national saving will fall. We know this from the definition of national saving: National Saving=[Private Saving]+[Public Saving]=[Y– T– C(Y– T)]+[T– G]. An increase in consumption decreases private saving, so national saving falls. Figure 3–2 graphs saving and investment as a function of the real interest rate. If national saving decreases, the supply curve for loanable funds shifts to the left, thereby raising the real interest rate and reducing investment.

r

S2

S1

Figure 3–2 Figure 3–2

Real interest rate

r1

r2 I (r)

I, S Investment, Saving

Answers.to.Textbook.Questions.and.Problems

6.a.Private saving is the amount of disposable income, Y – T, that is not consumed:

Sprivate= Y – T – C

= 5,000 – 1,000 – (250 + 0.75(5,000 – 1,000))

= 750.

Public saving is the amount of taxes the government has left over after it

makes its purchases:

Spublic= T – G

= 1,000 – 1,000

= 0.

Total saving is the sum of private saving and public saving:

S= Sprivate+ Spublic

= 750 + 0

= 750.

b.The equilibrium interest rate is the value of rthat clears the market for loanable

funds. We already know that national saving is 750, so we just need to set it equal

to investment:

S= I

750= 1,000 – 50r

Solving this equation for r, we find:

r= 5%.

c.When the government increases its spending, private saving remains the same as

before (notice that Gdoes not appear in the Sprivateabove) while government saving

decreases. Putting the new Ginto the equations above:

Sprivate= 750

Spublic= T – G

= 1,000 – 1,250

= –250.

Thus,

S= Sprivate+ Spublic

= 750 + (–250)

= 500.

d.Once again the equilibrium interest rate clears the market for loanable funds:

S= I

500= 1,000 – 50r

Solving this equation for r, we find:

r= 10%.

7.To determine the effect on investment of an equal increase in both taxes and govern-

ment spending, consider the national income accounts identity for national saving:

National Saving = [Private Saving] + [Public Saving]

= [Y– T– C(Y– T)] + [T– G].

We know that Yis fixed by the factors of production. We also know that the change inconsumption equals the marginal propensity to consume (MPC) times the change indisposable income. This tells us that

National Saving = [– T– (MPC×( – T))] + [ T– G]= [– T+ (MPC× T)] + 0

= (MPC– 1) T

.

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Answers to Textbook Questions and Problems

The above expression tells us that the impact on saving of an equal increase in T and G depends on the size of the marginal propensity to consume. The closer the MPC is to 1, the smaller is the fall in saving. For example, if the MPC equals 1, then the fall in consumption equals the rise in government purchases, so national saving[Y– C(Y– T)– G] is unchanged. The closer the MPC is to 0 (and therefore the larger is the amount saved rather than spent for a one-dollar change in disposable income), the greater is the impact on saving. Because we assume that the MPC is less than 1, we expect that national saving falls in response to an equal increase in taxes and government spending. The reduction in saving means that the supply of loanable funds curve shifts to the left in Figure 3–3. The real interest rate rises, and investment falls.r S2 S1 Figure 3–2 Figure 3–3

Real interest rate

r2

r1 I (r)

I, S Investment, Saving

8. a.

b.

The demand curve for business investment shifts out because the subsidy increases the number of profitable investment opportunities for any given interest rate. The demand curve f

or residential investment remains unchanged. The total demand curve for investment in the economy shifts out since it represents the sum of business investment, which shifts out, and residential investment, which is unchanged. As a result the real interest rate rises as in Figure 3–4.

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Chapter 3

National Income: Where It Comes From and Where It Goes

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r S

Figure3–4 4 Figure 3–

Real interest rate

B

1. An increase in desired investment . . .

A 2. . . . raises the interest rate. Investment, Saving

I2

I1 I, S

c.

The total quantity of investment does not change because it is constrained by the inelastic supply of savings. The investment tax credit leads to a rise in business investment, but an offsetting fall in residential investment. That is, the higher interest rate means that residential investment falls (a shift along the curve), whereas the outward shift of the business investment curve leads business investment to rise by an equal amount. Figure 3–5 shows this change. Note thatB R I1B+ I1R= I2+ I2= S

Figure 3–5r r

r2 r1

r2 r1

B I1

B I2

R I1

R I2

Business Business Investment investment

Residential Residential Investment investment

9. In this chapter, we concluded that an increase in government expenditures reduces national saving and raises the interest rate; it therefore crowds out investment by the full amount of the increase in government expenditure. Similarly, a tax cut increases disposable income and hence consumption; this increase in consumption translates into a fall in national saving—again, it crowds out investment.

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If consumption depends on the interest rate, then these conclusions about fiscal policy are modified somewhat. If consumption depends on the interest rate, then so does saving. The higher the interest rate, the greater the return to saving. Hence, it seems reasonable to think that an increase in the interest rate might increase saving and reduce consumption. Figure 3–6 shows saving as an increasing function of the interest rate.

r

S(r)

Figure 3–6 Figure 3–6

Real interest rate

S Saving

Consider what happens when government purchases increase. At any given level of the interest rate, national saving falls by the change in government purchases, as shown in Figure 3–7. The figure shows that if the saving function slopes upward, investment falls by less than the amount that government purchases rise; this happens because consumption falls and saving increases in response to the higher interest rate. Hence, the more responsive consumption is to the interest rate, the less government purchases crowd out investment.

r

S2(r)

S1(r)

FiFigure–7 gure 3 3–7

Real interest rate

r1 r G

I(r)

I1

I

I, S

Investment, Saving

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Chapter 3

National Income: Where It Comes From and Where It Goes

19

More Problems and Applications to Chapter 31. a. A Cobb–Douglas production function has the form Y= AK L . In the appendix w

e showed that the marginal products for the Cobb–Douglas production function are: MPL= (1–α)Y/L. MPK=αY/K. Competitive profit-maximizing firms hire labor until its marginal product equals the real wage, and hire capital until its marginal product equals the real rental rate. Using these facts and the above marginal products for the Cobb–Douglas production function, we find: W/P= MPL= (1–α)Y/L. R/P= MPK=αY/K. Rewriting this: (W/P)L= MPL× L= (1–α)Y. (R/P)K= MPK× K=αY. Note that the terms (W/P)L and (R/P)K are the wage bill and total return to capital, respectively. Given that the value ofα= 0.3, then the above formulas indicate that labor receives 70 percent of total output, which is (1– 0.3), and capital receives 30 percent of total output. b. To determine what happens to total output when the labor force increases by 10 percent, consider the formula for the Cobb–Douglas production function: Y= AK L . Let Y1 equal the initial value of output and Y2 equal final output. We know thatα= 0.3. We also know that labor L increases by 10 percent: Y1= AK L . Y2= AK (1.1L) . Note that we multiplied L by 1.1 to reflect the 10-percent increase in the labor force. To calculate the percentage change in output, pide Y2 by Y1:0.3 0.7 Y2 (1.1L)= AK 0.3 0.7 Y1 AK L 0.3 0.7 0.3 0.7α 1–αα 1–α

= (1.1)= 1.069. That is, output increases by 6.9 percent. To determine how the increase in the labor force affects the rental price of capital, consider the formula for the real rental price of capital R/P: R/P= MPK=αAK L . We know thatα= 0.3. We also know that labor (L) increases by 10 percent. Let (R/P)1 equal the initial value of the rental price of capital, and (R/P)2 equal the final rental price of capital after the labor force increases by 10 percent. To find (R/P)2, multiply L by 1.1 to reflect the 10-percent increase in the labor force: (R/P)1= 0.3AK (R/P)2= 0.3AK– 0.7α–1 1–α

0.7

L . (1.1L) .0.7

0.7

– 0.7

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Answers to Textbook Questions and Problems

The rental price increases by the ratio (R/P)2 0.3AK (1.1L)=– 0.7 0.7 (R/P)1 0.3AK L= (1.1)0.7– 0.7 0.7

= 1.069. So the rental price increases by 6.9 percent. To determine how the increase in the labor force affects the real wage, consider the formula for the real wage W/P: W/P= MPL= (1–α)AK L . We know thatα= 0.3. We also know that labor (L) increases by 10 percent. Let (W/P)1 equal the initial value of the real wage and (W/P)2 equal the final value of the real wage. To find (W/P)2, multiply L by 1.1 to reflect the 10-percent increase in the labor force: (W/P)1= (1– 0.3)AK L0.3 0.3– 0.3α–α

.– 0.3

(W/P)2= (1– 0.3)AK (1.1L) . To calculate the percentage change in the real wage, pide (W/P) 2 by (W/P)1: (W/P)2 (1 0.3) AK 0.3 (1.1 L) 0.3= (W/P)1 (1 0.3) AK 0.3 L 0.3= (1.1)– 0.3

c.

= 0.972. That is, the real wage falls by 2.8 percent. We can use the same logic as (b) to

set Y1= AK0.3L0.7. Y2= A(1.1K)0.3L0.7. Therefore, we have:0.3 1.7 Y2= A(1.1K) L 0.3 0.7 Y1 AK L

= (1.1)0.3= 1.029. This equation shows that output increases by 2 percent. Notice thatα< 0.5 means that proportional increases to capital will increase output by less than the same proportional increase to labor. Again using the same logic as (b) for the change in the real rental price of capital: (R/P)2 0.3A(1.1K) L=– 0.7 0.7 (R/P)1 0.3AK L= (1.1)–0.7= 0.935. The real rental price of capital falls by 6.5 percent because there are diminishing returns to capital; that is, when capital increases, its marginal product falls.–0.7 0.7

Answers.to.Textbook.Questions.and.Problems

Chapter 3

National Income: Where It Comes From and Where It Goes

21

Finally, the change in the real wage is:–0.7 0.7 (W/P)2 0.7A(1.1K) L=– 0.7 0.7 (W/P)1 0.7AK L (1.1)0.3= 1.029. Hence, real wages increase by 2.9 percent because the added capital increases the marginal productivity of the existing workers. (Notice that the wage and output have both increased by the same amount, leaving the labor share unchanged—a feature of Cobb–Douglas technologies.) Using the same formula, we find that the change in output is: 0.3 0.7 Y2 (1.1A)K L= 0.3 0.7 Y1 AK L= 1.1. This equation shows that output increases by 10 percent. Similarly, the rental price of capital and the real wage also increase by 10 percent:–0.7 0.7 (R/P)2 0.3(1.1A)K L=– 0.7 0.7 (R/P)1 0.3AK L= 1.1.

d.

2. a.

(W/P)2 0.7(1.1A)K L= 0.3– 0.3 (W/P)1 0.7AK L= 1.1. The marginal product of labor MPL is found by differentiating the production function with respect to labor: dY dL 1 1/3 1/3–2/3= K H L . 3 This equation is increasing in human capital because more human capital makes all the existing labor more productive. The marginal product of human capital MPH is found by differentiating the production function with respect to human capital: MPL= dY dH 1 1/3 1/3–2/3= K L H . 3 This equation is decreasing in human capital because there are diminishing returns. The labor share of output is the proportion of output that goes to labor. The total amount of output that goes to labor is the real wage (which, under perfect competition, equals the marginal product of labor) times the quantity of labor. This quantity is pided by the total amount of output to compute the labor share: MPH= Labor Share= ( 1 K 1 3 H1 3 L-2 3 ) L 3 K 1 3 H1 3 L1 3 1= . 3

0.3

–0.3

b.

c.

Answers.to.Textbook.Questions.and.Problems

22

Answers to Textbook Questions and Problems

We can use the same logic to find the human capital share: Human Capital Share=1 ( 3 K1/3L1/3H–2/3) H

K1/3H1/3L1/3

d.

1=, 3 so labor gets one-third of the output, and human capital gets one-third of the output. Since workers own their human capital (we hope!), it will appear that labor gets two-thirds of output. The ratio of the skilled wage to the unskilled wage is: Wskilled MPL+ MPH= Wunskilled MPL=1 1/3–2/3 1/3 3K L H 1 3

+

1 3

K1/3L1/3H–2/3

K1/3L–2/3H1/3

e.

L . H Notice that th

e ratio is always greater than 1 because skilled workers get paid more than unskilled workers. Also, when H increases this ratio falls because the diminishing returns to human capital lower its return, while at the same time increasing the marginal product of unskilled workers. If more college scholarships increase H, then it does lead to a more egalitarian society. The policy lowers the returns to education, decreasing the gap between the wages of more and less educated workers. More importantly, the policy even raises the absolute wage of unskilled workers because their marginal product rises when the number of skilled workers rises.=1+

Answers.to.Textbook.Questions.and.Problems

CHAPTER

4

Money and Inflation

Questions for Review1. Money has three functions: it is a store of value, a unit of account, and a medium of exchange. As a store of value, money provides a way to transfer purchasing power from the present to the future. As a unit of account, money provides the terms in which prices are quoted and debts are recorded. As a medium of exchange, money is what we use to buy goods and services. 2. Fiat money is established as money by the government but has no intrinsic value. For example, a U.S. dollar bill is fiat money. Commodity money is money that is based on a commodity with some intrinsic value. Gold, when used as money, is an example of commodity money. 3. In many countries, a central bank controls the money supply. In the United States, the central bank is the Federal Reserve—often called the Fed. The control of the money supply is called monetary policy. The primary way that the Fed controls the money supply is through open-market operations, which involve the purchase or sale of government bonds. To increase the money supply, the Fed uses dollars to buy government bonds from the public, putting more dollars into the hands of the public. To decrease the money supply, the Fed sells some of its government bonds, taking dollars out of the hands of the public. 4. The quantity equation is an identity that expresses the link between the number of transactions that people make and how much money they hold. We write it as Money× Velocity= Price× Transactions M× V= P× T. The right-hand side of the quantity equation tells us about the total number of transactions that occur during a given period of time, say, a year. T represents the total number of times that any two inpiduals exchange goods or services for money. P represents the price of a typical transaction. Hence, the product P× T represents the number of dollars exchanged in a year. The left-hand side of the quantity equation tells us about the money used to make these transactions. M represents the quantity of money in the economy. V represents the transactions velocity of money—the rate at which money circulates in the economy. Because the number of transactions is difficult to measure, economists usually use a slightly different version of the quantity equation, in which the total output of the economy

Y replaces the number of transactions T: Money× Velocity= Price× Output M× V= P× Y. P now represents the price of one unit of output, so that P× Y is the dollar value of output—nominal GDP. V represents the income velocity of money—the number of times a dollar bill becomes a part of someone’s income. 5. If we assume that velocity in the quantity equation is constant, then we can view the quantity equation as a theory of nominal GDP. The quantity equation with fixed velocity states that MV= PY. If velocity V is constant, then a change in the quantity of money (M) causes a proportionate change in nominal GDP (PY). If we assume further that output is fixed by the factors of production and the production technology, then we can conclude that the 23

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