《宏观经济学》课程教学资源（英文版）Lecture 2 Answers to Textbook Questions and Problems_Mankiw.pdf_大学文库

CHAPTEr 2 The data of macroeconomics questions for Review 1. GDP measures both the total income of everyone in the economy and the total expendi- ture 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 alter- native, 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 3. The Bureau of labor Statistics classifies each person into one of the following three cat- egories: 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 x 100 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 decreases in real GDP. Okun's law can be summarized by the equation,Ssociated with workers do not. Increases in the unemployment rate are therefore as %△ 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 applications 1. A large number of economic statistics are released regularly. These include the follow Gross Domestic Product-the market value of all final goods and services produced in a The Unemployment Rate the percentage of the civilian labor force who do not have a Corporate Profits-the accounting profits remaining after taxes of all manufacturing corporations. It gives an indication of the general financial health of the corporate sec The Consumer Price Index(CPia measure of the ay 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 alue of goods imported from abroad

Questions for Review 1. 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 = . 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 Applications 1. 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. 5 Number of Unemployed × 100 Labor Force CHAPTER 2 The Data of Macroeconomics

Answers to Textbook Questions and problems 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 rood (the bread) 3. When a woman marries her butler gDP falls by the amount of the butlers salary. This happens because measured total income, and therefore measured GDP, falls by the amount of the butlers loss in salary. If GDP truly measured the value of all goods and ervices, 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 activ ity because the value of some goods and services is left out. Once the butlers 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. government purchases b. investment c. net exports d. consumption 5. Data on parts(a) to(g) can be downloaded from the Bureau of Economic Analysis (www.bea.docgov-followthelinkstoGdpandrelateddata).Mostofthedata(not necessarily the earliest year)can also be found in the Economic Report of the president By dividing each component(a)to(g) by nominal GDP and multiplying by 100, we obtain the following percentages 1950 2000 a. Personal consumption expenditures 63.0% b. Gross private domestic investment 14.1% c. Government consumption purchases 15.9% 22.1% 176% d. Net exports -3.7% e. National defense purchases 6.6% f. State and local purchases 7.1% 12.8% 11.7% g. Import 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 en re (c) The share going to government consumption purchases rose more than 6 percentage points from 1950 to 1975 but has receded somewhat (d)Net exports, which were positive in 1950 and 1975, were substantially negative in (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

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. government purchases b. investment c. net exports d. consumption e. 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 dividing each component (a) to (g) by nominal GDP and multiplying by 100, we obtain the following percentages: 1950 1975 2000 a. Personal consumption expenditures 65.5% 63.0% 68.2% b. Gross private domestic investment 18.4% 14.1% 17.9% c. Government consumption purchases 15.9% 22.1% 17.6% d. Net exports 0.2% 0.8% –3.7% e. National defense purchases 6.7% 6.6% 3.8% f. State and local purchases 7.1% 12.8% 11.7% g. Imports 3.9% 7.5% 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. 6 Answers to Textbook Questions and Problems

6. a. i. Nominal GDP is the total value of goods and services measured at current prices. Therefore, Nominal GDP2000 = (P × Q ) + (P × Q ) = ($50,000 × 100) + ($10 × 500,000) = $5,000,000 + $5,000,000 = $10,000,000. Nominal GDP2010 = (P × Q ) + (P × Q ) = ($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 = (P × Q ) + (P × Q ) = ($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. iii. 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 = . Using the values for Nominal GDP2010 and real GDP2010 calculated above: Implicit Price Deflator2010 = = 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.) iv. 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 = = = = 1.6. Chapter 2 The Data of Macroeconomics 7 2000 cars 2000 cars 2000 bread 2000 bread 2010 cars 2010 cars 2010 bread 2010 bread 2000 cars 2010 cars 2000 bread 2010 bread Nominal GDP2010 Real GDP2010 $15,200,000 $10,000,000 $16,000,000 $10,000,000 ($60,000 × 100) + ($20 × 500,000) ($50,000 × 100) + ($10 × 500,000) ( )( ) ( PQ PQ P Q cars cars bread bread cars c 2010 2000 2010 2000 2000 ×+× × ars bread bread 2000 2000 2000 )( ) + × P Q

Answers to Textbook Questions and problems This calculation shows that the price of goods purchased in 2010 increased by 6 percent compared to the prices these goods would have sold for in 2000. The CPI for 2000, the base year, equals 1.0 b. The implicit price deflator is a Paasche index because it is computed with a chang ing 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 prices rose by 60 percent from what they were in the year 200( ich indicates that ear 2000. From(5. a iv. the CPI for the year 2010 If prices of all goods rose by, say, 50 percent, then one could say unam- biguously 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, making bread relatively more expensive As the discrepancy between the CPi and the implicit price deflator illus- trates, the change in the price level depends on how the goods' prices are weight- ed. 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 pur- chased 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. c. 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 CPl, 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 7. a. The consumer price index uses the consumption bundle in year l to figure out how much weight to put on the price of a given good Qm)+(Ppen×x ($2×10)+($1×0) ($1×10)+($2×0) According to the cpl, prices have doubled. Nominal spending is the total value of output produced in each year. In year 1 and 2, Abby buys 10 apples for $1 each, so her nominal spending remains con- stant at $10. For example Nominal Spending =(Pred xQ2ed)+( 82×0)+($1×10)

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. b. 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, making 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. c. 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. 7. a. 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: CPI2 = = = 2. According to the CPI, prices have doubled. b. 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 × Q ) + (P × Q ) = ($2 × 0) + ($1 × 10) = $10. 8 Answers to Textbook Questions and Problems ($2 × 10) + ($1 × 0) ($1 × 10) + ($2 × 0) 2 red 2 red 2 green 2 green ( )( ) ( )( PQ P Q PQ P Q red red green green red red green gre 21 2 1 11 1 ×+ × ×+ × en 1 )

Chapter 2 The Data of Macroeconomics 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=(PHd×Q2d)+(Plen×Qen) =($1×0)+($2×10) Hence, abby s real spending rises from $10 to $20 d. The implicit price deflator is calculated by dividing Abby's nominal spending in year 2 by her real spending that year: Implicit Price Deflator, =Nominal Spending Real Spendi $10 Thus, the implicit price deflator suggests that prices have fallen by half. The rea prices prevailing in year 1. From this perspective green apples appear very val son for this is that the deflator estimates how much abby values her apples usin able. In year 2, when Abby consumes 10 green apples, it appears that her con sumption 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 CPl, however the cost of living has doubled. This because the CPi only takes into account the fact that the red apple price has dou bled; 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 defla- or estimates the cost of living has halved. Thus, the CPl, a Laspeyres index, over states the increase in the cost of living and the deflator, a Paasche index, under- states it. This chapter of the text discusses the difference between Laspeyres and Paasche indices in more detail 8. a. 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 work ers 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) b. Real GDP rises because the original capital and labor in farm production now pro- duce 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 con- sume more wheat, then farmers and farmland can be shifted to producing other goods that society values.) c. 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) e. 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

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 × Q ) + (P × Q ) = ($1 × 0) + ($2 × 10) = $20. Hence, Abby’s real spending rises from $10 to $20. d. The implicit price deflator is calculated by dividing Abby’s nominal spending in year 2 by her real spending that year: Implicit Price Deflator2 = = = 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. 8. a. 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). b. 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.) c. Real GDP falls because with fewer workers on the job, firms produce less. This accurately reflects a fall in economic well-being. d. 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). e. 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 Chapter 2 The Data of Macroeconomics 9 1 red 2 red 1 green 2 green Nominal Spending2 Real Spending2 $10 $20

chaPteR 3 National Income Where it comes from and where|tG。es questions for Review 1. Factors of production and the production technology determine the amount of output an economy can produce. 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 technology leads to 2. When a firm decides how much of a factor of production to hire, 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 addition al 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 addi tional unit of labor produces MPL units of additional output, which sells for P dollars Therefore, the additional revenue to the firm is P x MPL. The cost of hiring the addi- tional unit of labor is the wage w. Thus, this hiring decision has the following effect on △ Profit=△ Revenue-△Cost =(P×MPL)-W If the additional revenue, Px 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 Aprofit=0, which is when(Px 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 firms decision to hire capi- tal: the firm will hire capital until the marginal product of capital equals the real capi- a production function has constant returns if an equal percentage increase in all factors of production causes an increase in t of the same percentage. For exam- ple, if a firm increases its use of capital and 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 XL, and the return to capital, MPK K. That is, under constant returns to scale, economic profit is zero 4. 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 gher real interest rate makes it more costly to invest, so the demand for investment goods fall 5. Government purchases are those goods and services purchased directly by the govern ment. For example, the government buys missiles and tanks, builds roads, and provides

Questions for Review 1. Factors of production and the production technology determine the amount of output an economy can produce. 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 technology leads to an increase in the economy’s output. 2. When a firm decides how much of a factor of production to hire, 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. 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: ∆Profit = ∆Revenue – ∆Cost = (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 ∆profit = 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 to hire capital: 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 example, 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. 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 interest 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. 5. Government purchases are those goods and services purchased directly by the government. For example, the government buys missiles and tanks, builds roads, and provides 11 CHAPTER 3 National Income: Where It Comes From and Where It Goes

Answers to Textbook questions and Problems services such as air traffic control. All of these activities are part of GDP. Transfer pay ments 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 hereas 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 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 goods and services equals the supply 7. When the government increases taxes, disposable income falls, and therefore consump tion 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 fixed by the fact gative effect of the tax increase on consumption. Because output chases 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. 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. 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 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 pro- luction function has increasing returns to scale. This may happen if specialization 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. According to the neoclassical theory, technical progress that increases the margin al product of farmers causes their real wage to rise. b. 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

services such as air traffic control. All of these activities 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. 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 fall in the real interest rate. Problems and Applications 1. 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. 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. 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. 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. According to the neoclassical theory, technical progress that increases the marginal product of farmers causes their real wage to rise. b. 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. 12 Answers to Textbook Questions and Problems

Chapter 3 National Income: Where It Comes From and Where It Goes c. If the marginal productivity of barbers is unchanged, then their real wage is unchanged d. The real wage in(c)is measured in terms of haircuts. That is, if the nominal wage is in dollars, then the real wage is W/PH, where PH is the dollar price of a hair cut e. If workers can move freely between being farmers and being barbers then they must be paid the same wage w in each sector. f. If the nominal wage w is the same in both sectors but the real wage in terms of farm goods is greater than the real wage in terms of haircuts, then the price of haircuts must have risen relative to the price of farm goods g. 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 relationship National Saving =[Private Saving]+[Public Saving] TY-T-c(Y-T)+IT-GI Y-C(Y-T)-G a. Public Saving-The tax increase causes a l-for-l increase in public saving. T increases by $100 billion and, therefore, public saving increases by $100 billion b. 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 x $100 billion, or $60 billion. Hence APrivate Saving=-$1006-06(-$1006)=-$406 Private saving falls $40 billion c. 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 savin 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 neither G nor Y changes, national saving thus rises by $60 billion d. 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-⑦)-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

c. If the marginal productivity of barbers is unchanged, then their real wage is unchanged. d. The real wage in (c) is measured in terms of haircuts. That is, if the nominal wage is in dollars, then the real wage is W/PH, where PH is the dollar price of a haircut. e. If workers can move freely between being farmers and being barbers, then they must be paid the same wage W in each sector. f. If the nominal wage W is the same in both sectors, but the real wage in terms of farm goods is greater than the real wage in terms of haircuts, then the price of haircuts must have risen relative to the price of farm goods. g. 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. a. 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. b. 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. c. National Saving—Because national saving is the sum of private and public saving, 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 billion. Since neither G nor Y changes, national saving thus rises by $60 billion. d. 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. Chapter 3 National Income: Where It Comes From and Where It Goes 13