Solution Manual For Macroeconomics Ninth Edition
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Chapter 1 — The Science of Macroeconomics 1 Answers to Textbook Questions and Problems CHAPTER 1 The Science of Macroeconomics Questions for Review 1. Microeconomics is the study of how individual firms and households make decisions, and how they interact with one another. Microeconomic models of firms and households are based on principles of optimization — firms and households do the best they can given the constraints they face. For example, households choose which goods to purchase in order to maximize their utility, whereas firms decide how much to produce in order to maximize profits. In contrast, macroeconomics is the study of the economy as a whole; it focuses on issues such as how total output, total employment, and the overall price level are determined. These economy - wide variables are based on the interaction of many households and many firms; therefore, microeconomics forms the basis for macroeconomics. 2. Economists build models as a means of summarizing the relationships among economic variables. Models are useful because they abstract from the many details in the economy and allow one to focus on the most important economic connections. 3. A market - clearing model is one in which prices adjust to equilibrate supply and demand. Market - clearing models are useful in situations where prices are flexible. Yet in many situations, flexible prices may not be a realistic assumption. For example, labor contracts often set wages for up to three years. Or, firms such as magazine publishers change their prices only every three to four years. Most macroeconomists believe that price flexibility is a reasonable assumption for studying long - run issues. Over the long run, prices respond to changes in demand or supply, even though in the short run they may be slow to adjust. Problems and Applications 1. Monetary policy in the United States and the European Union has been a big topic of conversation in early 2015 . The EU embarked upon a quantitative easing policy in March 2015 in an at tempt to stimulate growth and prevent de flation . There has been some concern that the inflation rate in Europe will turn negative . In the United States , there is continued discussion and speculation concerning when the Federal Reserve might choose to increase the target federal funds rate . Also in the United States, the unemployment rate has declined to about 5.5 percent and this suggests that wages may begin to increase . The Federal Reserve will be watching for wage and price increases as they decide when to increase interest rates. 2. Many philosophers of science believe that the defining characteristic of a science is the use of the scientific method of inquiry to establish stable relationships. Scientists examine data, often provided by controlled experiments, to support or disprove a hypothesis. Economists are more limited in their use of experiments. They cannot conduct controlled experiments on the economy; they must rely on the natural course of developments in the economy to collect data. To the extent that economists use the scientific method of inquiry, that is, developing hypotheses and testing them, economics has the characteristics of a science. 3. We can use a simple variant of the supply - and - demand model for pizza to answer this question. Assume that the quantity of ice cream demanded depends not only on the price of ice cream and income, but also on the price of frozen yogurt: Q d = D ( P IC , P FY , Y ). We expect that demand for ice cream rises when the price of frozen yogurt rises, because ice cream and frozen yogurt are substitutes. That is, when the price of frozen yogurt goes up, I consume less of it and, instead, fulfill more of my frozen dessert urges through the consumption of ice cream.
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Chapter 1 — The Science of Macroeconomics 2 The next part of the model is the supply function for ice cream, Q s = S ( P IC ). Finally, in equilibrium, supply must equal demand, so that Q s = Q d . Y and P FY are the exogenous variables, and Q and P IC are the endogenous variables. Figure 1 - 1 uses this model to show that a fall in the price of frozen yogurt results in an inward shift of the demand curve for ice cream. The new equilibrium has a lower price and quantity of ice cream. 4. The price of haircuts changes rather infrequently. From casual observation, hairstylists tend to charge the same price over a one - or two - year period irrespective of the demand for haircuts or the supply of cutters. A market - clearing model for analyzing the market for haircuts has the unrealistic assumption of flexible prices. Such an assumption is unrealistic in the short run when we observe that prices are inflexible. Over the long run, however, the price of haircuts does tend to adjust; a market - clearing model is therefore appropriate.
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Chapter 2 — The Data of Macroeconomics 3 Answers to Textbook Questions and Problems CHAPTER 2 The Data of Macroeconomics Questions for Review 1. GDP measures the total income earned from the production of the new final goods and services in the economy, and it measures the total expenditures on the new final goods and services produced in the economy. GDP can measure two things at once because the total expenditures on the new final goods and services by the buyers must be equal to the income earned by the sellers of the new final goods and services. 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 four components of GDP are consumption, investment, government purchases, and net exports . The consumption category of GDP consists of household expenditures on new final goods and services, such as the purchase of a new television . The investment category of GDP consists of business fixed investment, residential fixed investment, and inventory investment . When a business buys new equipment this counts as investment . Government purchases consists of purchases of new final goods and services by federal, state, and local governments, such as payments for new military equipment . Net exports measures the value of goods and services sold to other countries minus the value of goods and services foreigners sell us . When the U.S. sells corn to foreign countries , it counts in the net export category of GDP. 3 . The consumer price index (CPI) 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. The GDP deflator is the ratio of nominal GDP to real GDP in a given year. The GDP deflator measures the prices of all goods and services produced, whereas the CPI only measures prices of goods and services bought by consumers. The GDP deflator includes only domestically produced goods, whereas the CPI includes domestic and foreign goods bought by consumers. Finally, the CPI is a Laspeyres index that assigns fixed weights to the prices of different goods, whereas the GDP deflator is a Paasche index that assigns changing weights to the prices of different goods. In practice, the two price indices tend to move together and do not often diverge. 4 . The CPI measures the price of a fixed basket of goods relative to the price of the same basket in the base year . The PCE deflator is the ratio of nominal consumer spending to real consumer spending . The CPI and the PCE deflator are similar in that they both only include the prices of goods purchased by consumers, and they both include the price of imported goods as well as domestically produced goods . The two measures differ because the CPI measures the change in the price of a fixed basket whereas the goods measured by the PCE deflator change from year to year depending on what consumers are purchasing in that particular year. 5 . The Bureau of Labor Statistics (BLS) 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 Labor Force ´ 100 . Note that the labor force is the number of people employed plus the number of people unemployed. 6 . Every month, the B ureau of Labor Statistics undertakes two surveys to measure employment. First, the BLS surveys about 60,000 households and thereby obtains an estimate of the share of people who say they are working. The BLS multiplies this share by an estimate of the population to estimate the number of people working. Second, the BLS surveys about 160,000 business establishments and asks how many people they employ. Each survey is imperfect; so the two measures of employment are not identical.
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Chapter 2 — The Data of Macroeconomics 4 Problems and Applications 1 . From the main bea. gov Web page click on the interactive data tab at the top, select GDP, begin using t he data, section 1, and then table 1.1.1 . Real GDP grew at a rate of 2.2 percent in quarter 4 of 2014 . When compared to growth rates of − 2.1 percent , 4.6 percent , and 5 percent for the first three quarte rs of 2014 , t he rate of 2.2 percent was slightly below average . From the main bls.gov Web page select the data tools tab, then top picks . Check the box for the unemployment rate and retrieve the data . The unemployment rate in March 2015 was 5.5 percent , which was about equal to the natural rate of unemployment, or the long run average rate . From the main bls.gov page, select the economic releases tab, then inflation and prices . Access the report for the CPI . In February 2015, the inflation rate for all items was 0 percent , and if food and e nergy were excluded the rate was 1.7 percent . The inflation rate was below average and below the Federal Reserve’s target of 2 percent . 2. Value added by each person is equal to the value of the good produced minus the amount the person paid for the materials needed 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 GDP measures total income, and therefore GDP, falls by the amount of the butler’s loss i n salary. If GDP truly measures 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. 4. a. The airplane sold to the U.S. Air Force counts as government purchases because the Air Force is part of the government. b. The airplane sold to American Airlines counts as investment because it is a capital good sold to a private firm. c. The airplane sold to Air France counts as an export because it is sold to a foreigner. d. The airplane sold to Amelia Earhart counts as consumption because it is sold to a private individual. e. The airplane built to be sold next year counts as investment. In particular, the airplane is counted as inventory investment, which is where goods that are produced in one year and sold in another year are counted. 5. Data on parts (a) to ( f ) can be downloaded from the Bureau of Economic Analysis . Go to the bea.gov W ebsite, click on the interactive data tab at the top, select GDP, begin using the data, section 1, and then table 1.1.5 . Choose the “ modify the data ” option to select the years you in which you are interested . By dividing each component (a) to ( f ) by nominal GDP and multiplying by 100, we obtain the following percentages: 1950 1980 201 4 a. Personal consumption expenditures 6 4 . 0 % 6 1 . 3 % 68 . 5 % b. Gross private domestic inve stment 18. 8 % 1 8 . 5 % 1 6 . 4 % c. G overnment consumption purchases 1 6 .9 % 20. 6 % 1 8 . 2 % d. Net exports 0.2 % – 0.5 % 3. 1 % e. National defense purchases 7 . 6 % 6. 3 % 4 . 4 % f . Imports 3.9 % 10. 3 % 1 6 . 5 % (Note: The above data w as downloaded April 3 , 201 5 , from the BEA Web site.) Among other things, we observe the following trends in the economy over the period 1950 – 201 5 : a. Personal consumption expenditures have been around two - thirds of GDP between 1980 and 20 15 . b. The share of GDP going to gross private domestic investment remained fairly steady.
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Chapter 2 — The Data of Macroeconomics 5 c. The share going to government consumption purchases rose sharply from 1950 to 1980. d. Net exports, which were positive in 1950, have been negative since that time. e . The share going to national defense purchases has fallen . f . Imports have grown rapidly relative to GDP. 6. a . GDP measures the value of the final goods and services produced, or $1,000,000. b . NNP is equal to GNP minus depreciation . In this example, GDP is eq ual to GNP because there are no foreign transactions . Therefore, NNP is equal to $875,000. c . National income is equal to NNP, or $875,000. d . Employee compensation is equal to $600,000. e . Proprietor s ’ income measures the income of the owner , and is equal to 150,000. f . Corporate profit is equal to corporate taxes plus dividends plus retained earnings, or $275,000. Retained earnings is calculated as sales minus wages minus dividends minus depreciation minus corporate tax, or $75,000. g . Personal income is equal to employee compensation plus dividends, or $750,000. h . Disposable personal income is personal income minus taxes, or $ 550,000. 7 . a. i. Nominal GDP is the total value of goods and services measured at current prices. Therefore, Nominal GDP 20 1 0 = P hotdogs 2010 ´ Q hotdogs 2010 ( ) + P burgers 2010 ´ Q burgers 2010 ( ) = ($ 2 2 00) + ($ 3 2 00) = $ 4 00 + $ 6 00 = $1 , 000. Nominal GDP 201 5 = P hotdogs 2015 ´ Q hotdogs 2015 ( ) + P burgers 2015 ´ Q burgers 2015 ( ) = ($ 4 2 5 0) + ($ 4 5 00) = $ 1, 000 + $ 2 ,000 = $ 3 ,000. ii. Real GDP is the total value of goods and services measured at constant prices. Therefore, to calculate real GDP in 201 5 (with base year 20 1 0), multiply the quantities purchased in the year 201 5 by the 20 1 0 prices: Real GDP 201 5 = P 2010 hotdogs ´ Q 2015 hotdogs ( ) + P 2010 burgers ´ Q 2015 burgers ( ) = ($ 2 2 5 0) + ($ 3 5 00) = $ 5 00 + $ 1 , 5 00 = $ 2 ,000. Real GDP for 20 1 0 is calculated by multiplying the quantities in 20 1 0 by the prices in 20 1 0. Since the base year is 20 1 0, real GDP 20 1 0 equals nominal GDP 20 1 0 , which is $10 , 00 . Hence, real GDP increased between 20 1 0 and 201 5 . 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 Deflator 201 5 = Nominal GDP 2010 Real GDP 2010 = 1 Using the values for Nominal GDP 201 5 and real GDP 201 5 calculated above: Implicit Price Deflator 201 5 = $3 , 000 $2 , 000
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Chapter 2 — The Data of Macroeconomics 6 = 1.50 . This calculation reveals that prices of the goods produced in the year 201 5 increased by 5 0 percent compared to the prices that the goods in the economy sold for in 20 1 0. (Because 20 1 0 is the base year, the value for the implicit price deflator for the year 20 1 0 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 20 1 0, the CPI in 201 5 is measuring the cost of the basket in 20 15 relative to the cost in 2010 . The CPI 201 5 is calculated as follows: CPI 2015 = ( P 2015 hotdogs ´ Q 2010 hotdogs ) + ( P 2015 burgers ´ Q 2010 burgers ) ( P 2010 hotdogs ´ Q 2010 hotdogs ) + ( P 2010 burgers ´ Q 2010 burgers ) = $16,000,000 $10,000,000 = 1.6. This calculation shows that the price of goods purchased in 201 5 increased by 60 percent compared to the prices these goods would have sold for in 20 1 0. The CPI for 20 1 0, 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 ( 7 .a.iii), the implicit price deflator for the year 201 5 is 1.5 0 , which indicates that prices rose by 5 0 percent from what they were in the year 20 1 0. From ( 7 .a.iv.), the CPI for the year 201 5 is 1.6, which indicates that prices rose by 60 percent from what they were in the year 20 1 0. If prices of all goods rose by, for example, 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 hot dogs rose by 10 20 percent; the price of hamburgers rose by 33.33 percent, making hamburgers relatively less 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 20 1 0. The implicit price deflator weights the price of goods by the quantities purchased in the year 201 5 . Since the quantity of the two goods wa s the same in 2010, the CPI is placing equal weight on the two price changes . In 2015, the quantity of hamburgers was twice as large as hot dogs, so there is twice as much weight placed on the hamburger price relative to the hot dog price . For this reason, the CPI shows a larger inflation rate – more weight is placed on the good with the larger price increase. 8 . 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: CPI 2 = $2 ´ 10 ( ) + $1 ´ 0 ( ) $1 ´ 10 ( ) + $2 ´ 0 ( ) = P 2 red ´ Q 1 red ( ) + P 2 green ´ Q 1 green ( ) P 1 red ´ Q 1 red ( ) + P 1 green ´ Q 1 green ( ) = 2. According to the CPI, prices have doubled.
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Chapter 2 — The Data of Macroeconomics 7 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 Spending 2 = P 2 red ´ Q 2 red ( ) + P 2 green ´ Q 2 green ( ) = ($2 0) + ($1 10) = $10. 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 Spending 2 = P 1 red ´ Q 2 red ( ) + P 1 green ´ Q 2 green ( ) = ($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 Deflator 2 = Nominal Spending 2 Real Spending 2 = $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 fell. 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 been cut in half. Thus, the CPI, a Laspeyres index, overstates the increase in the cost of living and the deflator, a Paasche index, understates it. 9. a . The labor force includes full time workers, part time workers, those who run their o wn business, and those who do not have a job but are looking for a job . The labor force consists of 70 people . The working age population consists of the labor force plus those not in the labor force . The 10 discouraged workers and the 10 retired people are not in the labor force, but assuming they are capable of working, they are part of the adult population . The adult population consists of 90 people, so the labor force participation rate is equal to 70/90 or 77.8 percent . b . The number of unemployed workers is equal to 10 , so the unemployment rate is 10/70 or 14.3 percent .
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Chapter 2 — The Data of Macroeconomics 8 c . The household survey estimates total employment by asking a sample of households about their employment status . The household survey would report 60 people employed . The establishment survey estimates total employment by asking a sample of businesses to report how many workers they are employing . In this case the establishment survey would report 55 people employed . The 5 people with 2 jobs would be counted twice, and the 10 people who run their own business would not be counted. 10 . As Senator Robert Kennedy pointed out, GDP is an imperfect m easure of economic performance or well - being. In addition to the left - out items that Kennedy cited, GDP also ignores 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 and cleaning; and the value of goods produced and sold in illegal activities, such as the drug trade. These imperfections in the measurement of GDP do not necessarily reduce its usefulness. As long as these measurement problems stay constant over time, then GDP is useful in comparing economic activity from year to year. Moreover, a large GDP allows us to afford better medical care for our children, newer books for their education, and more toys for their play. Finally, countries with higher levels of GDP tend to have higher levels of life expectancy, better access to clean water and sanitation, and higher levels of education. GDP is therefore a useful measure for comparing the level of growth and development across countries. 11 . a. Real GDP falls because Disney World 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 World falls (the income side of the national accounts), and people’s consumption of Disney World 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 mea sured output but more clean air. C lean air is not traded in markets and, thus, does not show up in measured GDP, but is nevertheless a good that people value. f. Real GDP rises because the high school students go from an activity in which they are not producing market goods and services to one in which they are. Economic well - being, however, may decrease. In ideal national accounts, attending school would show up as investment because it presumably increases the future productivity of the worker. Actual national accounts do not measure this type of investment. Note also that future GDP may be lower than it would be if the students stayed in school, since the future work force will be less educated. g. 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 because but unmeasured production of child - rearing services rises. The well - being of the average person may very well rise if we assume the fathers and the children enjoy the extra time they are spending together.
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Chapter 3 — Natio nal Income: Where It Comes From and Where It Goes 9 Answers to Textbook Questions and Problems 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 output 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 technology 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 i s no longer profitable to do so — that is, u ntil the MPL falls to the point where the change in profit is zero. In the equation abov e, the firm hires labor until ΔP rofit = 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 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. A Cobb – Douglas production function has the form F ( K,L ) = AK α L 1 – α . The text showed that the parameter α gives capital’s share of income. So if capital earns one - fourth of total income, then = 0.25. Hence, F ( K,L ) = AK 0.25 L 0.75 . 5. Consumption depends positively on disposable income — i.e. the amount of income after all taxes have been paid. H igher disposable income means higher consumption. 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.
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Chapter 3 — Natio nal Income: Where It Comes From and Where It Goes 10 6. Government purchases are a measure of the value of goods and services purchased 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 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. 7. 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. 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 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. 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 = 100 0.5 100 0.5 = 100. b. According to the text, the formulas for the marginal product of labor and the marginal product of capital (land) are: MPL = (1 – α ) AK α L – α . MPK = α AK α – 1 L 1 – α .
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Chapter 3 — Natio nal Income: Where It Comes From and Where It Goes 11 In this problem, α is 0.5 and A is 1. Substitute in the given values for labor and land to find the marginal product of labor is 0.5 and marginal product of capital (land) is 0.5. We know that the real wage equals the marginal product of labor and the real rental price of land equals the marginal product of capital (land). c. Labor’s share of the output is given by the marginal product of labor times the quantity of labor, or 50. d. The new level of output is 70.71. e. The new wage is 0.71. The new rental price of land is 0.35. f. Labor now receives 35.36 . 3. 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 output increases by less than double , then the production function has decreasing returns to scale. 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 the amount of capital and labor increases the output by more than double , then the production function has increasing returns to scale. This may happen if specialization of labor becomes greater as the population grows. For example, if only 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. But if many workers build a car, then each one can specialize in a particular task and become more productive . 4. a. A Cobb – Douglas production function has the form Y = AK α L 1 – α . The text showed that the marginal products for the Cobb – Douglas production function are: MPL = (1 – α ) Y/L . MPK = α Y/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 = α Y/K . Rewriting this: ( W/P ) L = MPL L = (1 – α ) Y . ( R/P ) K = MPK K = α Y . 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 of α = 0.3, then the above formulas indicate that labor receives 70 percent of total output (or income ) and capital receives 30 percent of total output (or income). 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 α L 1 – α .
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Chapter 3 — Natio nal Income: Where It Comes From and Where It Goes 12 Let Y 1 equal the initial value of output and Y 2 equal final output. We know that α = 0.3. We also know that labor L increases by 10 percent: Y 1 = AK 0.3 L 0.7 . Y 2 = AK 0.3 (1.1 L ) 0.7 . 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, divide Y 2 by Y 1 : Y 2 Y 1 = AK 0.3 1.1 L ( ) 0.7 AK 0.3 L 0.7 = 1.1 ( ) 0.7 = 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 = α AK α – 1 L 1 – α . We know that α = 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 let ( 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 = 0.3 AK – 0.7 L 0.7 . ( R/P ) 2 = 0.3 AK – 0.7 (1.1 L ) 0.7 . The rental price increases by the ratio R / P ( ) 2 R / P ( ) 1 = 0.3 AK - 0.7 1.1 L ( ) 0.7 0.3 AK - 0.7 L 0.7 = 1.1 ( ) 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 α L – α . We know that α = 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 let ( 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 0.3 L – 0.3 . ( W/P ) 2 = (1 – 0.3) AK 0.3 (1.1 L ) – 0.3 . To calculate the percentage change in the real wage, divide ( W/P ) 2 by ( W/P ) 1 :
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Chapter 3 — Natio nal Income: Where It Comes From and Where It Goes 13 W / P ( ) 2 W / P ( ) 1 = 1 - 0.3 ( ) AK 0.3 1.1 L ( ) - 0.3 1 - 0.3 ( ) AK 0.3 L - 0.3 = 1.1 ( ) - 0.3 = 0.972 That is, the real wage falls by 2.8 percent. c. We can use the same logic as in part (b) to set Y 1 = AK 0.3 L 0.7 . Y 2 = A (1.1 K ) 0.3 L 0.7 . Therefore, we have: Y 2 Y 1 = A 1.1 K ( ) 0.3 L 0.7 AK 0.3 L 0.7 = 1.1 ( ) 0.3 = 1.029 This equation shows that output increases by about 3 percent. Notice that α < 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 in part (b) for the change in the real rental price of capital: R / P ( ) 2 R / P ( ) 1 = 0.3 A 1.1 K ( ) - 0.7 L 0.7 0.3 AK - 0.7 L 0.7 = 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. Finally, the change in the real wage is: W / P ( ) 2 W / P ( ) 1 = 0.7 A 1.1 K ( ) 0.3 L - 0.3 0.7 AK 0.3 L - 0.3 = 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.) d. Using the same formula, we find that the change in output is: Y 2 Y 1 = 1.1 A ( ) K 0.3 L 0.7 AK 0.3 L 0.7 = 1.1
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Chapter 3 — Natio nal Income: Where It Comes From and Where It Goes 14 This equation shows that output increases by 10 percent. Similarly, the rental price of capital and the real wage also increase by 10 percent: R / P ( ) 2 R / P ( ) 1 = 0.3 1.1 A ( ) K - 0.7 L 0.7 0.3 AK - 0.7 L 0.7 = 1.1 W / P ( ) 2 W / P ( ) 1 = 0.7 1.1 A ( ) K 0.3 L - 0.3 0.7 AK 0.3 L - 0.3 = 1.1 5. Labor income is defined as W P ´ L = WL P Labor’s share of income is defined as WL P æ è ç ç ö ø ÷ ÷ / Y = WL PY For example, i f t his ratio is about constant at a value of 0.7, then the value of W / P = 0.7 * Y / L . This means that the real wage is roughly proportional to labor productivity. Hence, any trend in labor productivity must be matched by an equal trend in real wages. O therwise, labor’s share would deviate from 0.7. Thus, the first fact (a constant labor share) implies the second fact (the trend in real wages closely tracks the trend in labor productivity) . 6. a. Nominal wages are measured as dollars per hour worked . Prices are measured as dollars per unit produced (either a haircut or a unit of farm output) . Marginal productivity is measured as units of output produced per hour worked. b . According to the neoclassical theory, technical progress that increases the marginal product of farmers causes their real wage to rise . The real wage for farmers is measured as units of farm output per hour worke d . The real wage is W / P F , and this is equal to ($/ hour worke d )/($/unit of farm output). c. If the marginal productivity of barbers is unchanged, then their real wage is unchanged. The real wage for barbers is measured as haircuts per hour worke d . The real wage is W / P B , and this is equal to ($/ hour worke d )/($/haircut). d . If workers can move freely between being farmers and being barbers, then they must be paid the same wage W in each sector. e . 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. We know that W / P = MPL so that W = P MPL . This means that P F MPL F = P H MPL B , given that the nominal wages are the same. Since the marginal product of labor for barbers has not changed and the marginal product of labor for farmers has risen, the price of a haircut must have risen relative to the price of the farm output. If we express this in growth rate terms, then the growth of the farm price + the growth of the marginal product of the farm labor = the growth of the haircut price. f . The farmers and the barbers are equally well off after the technological progress in farming, given
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Chapter 3 — Natio nal Income: Where It Comes From and Where It Goes 15 the assumption that labor is freely mobile between the two sectors and both types of people consume the same basket of goods . Given that the nominal wage ends u p equal for each type of worker and that they pay the same prices for final goo ds, they are equally well off in terms of what they can buy with their nominal income. The real wage is a measure of how many units of output are produced per worker . Technological progress in farming increased the units of farm output produced per hour worked . Movement of labor between sectors then equalized the nominal wage. 7. a. The marginal product of labor ( MPL ) is found by differentiating the production function with respect to labor: MPL = dY dL = 1 3 K 1/3 H 1/3 L - 2/3 An increase in human capital will increase the marginal product of labor because more human capital makes all the existing labor more productive. b. The marginal product of human capital ( MPH ) is found by differentiating the production function with respect to human capital: MPH = dY dH = 1 3 K 1/3 L 1/3 H - 2/3 An increase in human capital will decrease the marginal product of human capital because there are diminishing returns. c. 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 divided by the total amount of output to compute the labor share: Labor Share = ( 1 3 K 1/3 H 1/3 L - 2/3 ) L K 1/3 H 1/3 L 1/3 = 1 3 We can use the same logic to find the human capital share: Human Capital Share = ( 1 3 K 1/3 L 1/3 H - 2/3 ) H K 1/3 H 1/3 L 1/3 = 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. d. The ratio of the skilled wage to the unskilled wage is:
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Chapter 3 — Natio nal Income: Where It Comes From and Where It Goes 16 W skilled W unskilled = MPL + MPH MPL = 1 3 K 1/3 L - 2/3 H 1/3 + 1 3 K 1/3 L 1/3 H - 2/3 1 3 K 1/3 L - 2/3 H 1/3 = 1 + L H Notice that the 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. e. If more college s provide scholarships , it will increase H , and 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. 8. 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, ΔPrivate Saving = – $100 b – 0.6 ( – $100 b ) = – $40 b . 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 side of this equation is national saving, so the equation just says that national saving equals investment. Since national saving increases by $60 billion, investment must also increase by $60 billion. How does this increase in investment take place? We know that investment depends on the
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Chapter 3 — Natio nal Income: Where It Comes From and Where It Goes 17 real interest rate. For investment to rise, the real interest rate must fall. Figure 3 - 1 illustrates saving and investment as a function of the real interest rate. 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. 9. 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 illustrates 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. 10. a. Private saving is the amount of disposable income, Y – T , that is not consumed: S private = Y – T – C = 8 ,000 – 2 ,000 – [ 1,00 0 + (2/3) ( 8 ,000 – 2 ,000)] = 1,00 0. Public saving is the amount of taxes the government has left over after it makes its purchases:
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Chapter 3 — Natio nal Income: Where It Comes From and Where It Goes 18 S public = T – G = 2 ,000 – 2 , 5 00 = – 50 0. National saving is the sum of private saving and public saving: S national = S private + S public = 1,00 0 + ( 50 0 ) = 5 0 0. b. The equilibrium interest rate is the value of r that clears the market for loanable funds. We already know that national saving is 50 0, so we just need to set it equal to investment: S national = I 5 0 0 = 1, 2 00 – 10 0 r Solving this equation for r , we find: r = 0.07 or 7 %. c. When the government increases its spending, private saving remains the same as before (notice that G does not appear in the S private equation above) while government saving decreases. Putting the new G into the equations above: S private = 1,00 0 S public = T – G = 2 ,000 – 2 , 00 0 = 0. Thus, S national = S private + S public = 1,00 0 + (0) = 1,0 00. d. Once again the equilibrium interest rate clears the market for loanable funds: S national = I 1,0 00 = 1, 2 00 – 10 0 r Solving this equation for r , we find: r = 0.02 or 2 %. 11. To determine the effect on investment of an equal increase in both taxes and government 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 Y is fixed by the factors of production. We also know that the change in consumption equals the marginal propensity to consume ( MPC ) times the change in disposable income. This tells us that ΔNational Saving = { – Δ T – [ MPC ( – Δ T )] } + [Δ T – Δ G ] = [ – Δ T + ( MPC Δ T )] + 0
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Chapter 3 — Natio nal Income: Where It Comes From and Where It Goes 19 = ( MPC – 1) Δ T . The above expression tells us that the impact on national 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 will shift to the left in Figure 3 - 3. The real interest rate rises, and investment falls. 12. a. The demand curve for business investment shifts out to the right because the subsidy increases the number of profitable investment opportunities for any given interest rate. The demand curve for residential investment remains unchanged. b. The total demand curve for investment in the economy shifts out to the right since it represents the sum of business investment, which shifts out to the right, and residential investment, which is unchanged. As a result the real interest rate rises as in Figure 3 - 4. 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 movement along the curve), whereas the rightward shift of the business investment curve leads business investment to rise by an equal amount. Figure 3 - 5 shows this change. Note that I 1 B + I 1 R + I 2 B + I 2 R = S .
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Chapter 3 — Natio nal Income: Where It Comes From and Where It Goes 20 13. In this chapter, we concluded that an increase in government expenditures reduces national saving and raises the interest rate . The increase in government expenditure therefore crowds out investment by the full amount of the increase. Similarly, a tax cut increases disposable income and hence consumption . T his increase in consumption translates into a fall in national saving, and the increase in consumption crowds out investment by the full amount of the increase . If consumption depends on the interest rate, then saving will also depend on it. 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. 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 tha t government purchases rises by. T his 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 investment is crowded out by government purchases .
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Chapter 3 — Natio nal Income: Where It Comes From and Where It Goes 21 14. a. Figure 3 - 8 shows the case where the demand for loanable funds is stable but the supply of funds (the saving schedule) fluctuates perhaps reflecting temporary shocks to income, changes in government spending, or changes in consumer confidence. In this case, when interest rates fall, investment rises; when interest rates rise, investment falls. We would expect a negative correlation between investment and interest rates. b. Figure 3 - 9 shows the case where the supply of loanable funds (saving) is stable, whereas the demand for loanable funds fluctuates, perhaps reflecting changes in firms’ expectations about the marginal product of capital. We would now find a positive correlation between investment and the interest rate — when demand for funds rises, it pushes up the interest rate, so we observe that investment and the real interest rate increase at the same time. c. If both curves shift, we might generate a scatter plot as in Figure 3 - 10, where the economy fluctuates among points A, B, C, and D. Depending on how often the economy is at each of these points, we might find little clear relationship between investment and interest rates. d. Situation (c) seems fairly reasonable — as both the supply of and demand for loanable funds fluctuate over time in response to changes in the economy.
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Chapter 4 — The Monetary System: What It Is and How It Works 22 Answers to Textbook Questions and Problems CHAPTER 4 The Monetary System: What It Is and How It Works Questions for Review 1. 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. Open market operations are the purchase and sale of government bonds by the Federal Reserve. If the Fed buys government bonds from the public, then the dollars it pays for the bonds increase the monetary base and thus the money supply. If the Fed sells government bonds to the public, then the dollars paid to the Fed for the bonds decrease the monetary base and thus the money supply. 4. In a system of fractional - reserve banking, banks create money because they ordinarily keep only a fraction of their deposits in reserve. They use the rest of their deposits to make loans. The easiest way to see how this creates money is to consider the bank balance sheets shown in Figure 4 - 1. A. Balance Sheet – Firstbank Money Supply = $1,000 Assets Liabilities_______ Reserves $1,000 Deposits $1,000 B. Balance Sheet – Firstbank Money Supply = $1,800 Assets Liabilities_______ Reserves $200 Deposits $1,000 Loans $800 C. Balance Sheet – Secondbank Money Supply = $2,400 Assets Liabilities_______ Reserves $160 Deposits $800 Loans $640 Suppose that people deposit $1,000 into Firstbank, as in Figure 4 - 1(A). Although the money supply is still $1,000, it is now in the form of demand deposits rather than currency. If the bank holds 100 percent of these deposits in reserve, then the bank has no influence on the money supply. Yet under a system of fractional - reserve banking, the bank need not keep all of its deposits in reserve; it must have enough reserves on hand so that reserves are available whenever depositors want to make withdrawals, but it makes loans with the rest of its deposits. If Firstbank has a reserve – deposit ratio of 20 percent, then it keeps $200 of the $1,000 in reserve and lends out the remaining $800. Figure 4 - 1(B) shows the balance sheet of Firstbank after $800 in loans have been made. By making these loans, Firstbank increases the money supply by $800. There are still $1,000 in demand deposits, but now borrowers also hold an additional $800 in currency. The total money supply equals $1,800. Money creation does not stop with Firstbank. If the borrowers deposit their $800 of currency in Secondbank, then Secondbank can use these deposits to make loans. If Secondbank also has a reserve – deposit ratio of 20 percent, then it keeps $160 of the $800 in reserves and lends out the remaining $640. By lending out this money, Secondbank increases the money supply by $640, as in Figure 4 - 1(C). The total money supply is now $2,440.
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Chapter 4 — The Monetary System: What It Is and How It Works 23 This process of money creation continues with each deposit and subsequent loans made. The text demonstrated that each dollar of reserves generates ($1/ rr ) of money, where rr is the reserve – deposit ratio. In this example, rr = 0.20, so the $1,000 originally deposited in Firstbank generates $5,000 of money. 5. The Fed influences the money supply through open - market operations, reserve requirements, and the discount rate. Open - market operations are the purchases and sales of government bonds by the Fed. If the Fed buys government bonds, the dollars it pays for the bonds increase the monetary base and, therefore, the money supply. If the Fed sells government bonds, the dollars it receives for the bonds reduce the monetary base and therefore the money supply. Reserve requirements are regulations imposed by the Fed that require banks to maintain a minimum reserve – deposit ratio. A decrease in the reserve requirements lowers the reserve – deposit ratio, which allows banks to make more loans on a given amount of deposits and, therefore, increases the money multiplier and the money supply. The discount rate is the interest rate that the Fed charges banks to borrow money. Banks borrow from the Fed if their reserves fall below the reserve requirements. A decrease in the discount rate makes it less expensive for banks to borrow reserves. Therefore, banks will be likely to borrow more from the Fed; t his increases the monetary base and therefore the money supply. 6. To understand why a banking crisis might lead to a decrease in the money supply, first consider what determines the money supply. The model of the money supply we developed shows that M = m B . The money supply M depends on the money multiplier m and the monetary base B . The money multiplier can also be expressed in terms of the reserve – deposit ratio rr and the currency – deposit ratio cr . This expression becomes M = B. This equation shows that the money supply depends on the currency – deposit ratio, the reserve – deposit ratio, and the monetary base. A banking crisis that involved a considerable number of bank failures might change the behavior of depositors and bankers and alter the currency – deposit ratio and the reserve – deposit ratio. Suppose that the number of bank failures reduced public confidence in the banking system. People would then prefer to hold their money in currency (and perhaps stuff it in their mattresses) rather than deposit it in banks. This change in the behavior of depositors would cause massive withdrawals of deposits and, therefore, increase the currency – deposit ratio. In addition, the banking crisis would change the behavior of banks. Fearing massive withdrawals of deposits, banks would become more cautious and increase the amount of money they held in reserves, thereby increasing the reserve – deposit ratio. As the preceding formula for the money multiplier indicates, increases in both the currency – deposit ratio and the reserve – deposit ratio result in a decrease in the money multiplier and, therefore, a fall in the money supply. Problems and Applications 1. Money functions as a store of value, a medium of exchange, and a unit of account. a. A credit card can serve as a medium of exchange because it is accepted in exchange for goods and services. A credit card is, arguably, a (negative) store of value because you can accumulate debt with it. A credit card is not a unit of account because, for example, a car does not cost 5 VISA cards. b. A Rembrandt painting is a store of value only. M = cr + 1 ( ) cr + rr ( ) é ë ê ê ù û ú ú B
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Chapter 4 — The Monetary System: What It Is and How It Works 24 c. A subway token, within the subway system, satisfies all three functions of money. Yet outside the subway system, it is not widely used as a unit of account or a medium of exchange, so it is not a form of money. 2. a. When the Fed buys bonds, the dollars that it pays to the public for the bonds increase the monetary base, and this in turn increases the money supply. The money multiplier is not affected, assuming no change in the reserve – deposit ratio or the currency – deposit ratio. b. When the Fed increases the interest rate , it pays banks to hold reserves. T his gives banks an incentive to hold more reserves relative to deposits. The increase in the reserve deposit ratio will decrease the money multiplier. The decline in the money multiplier will lead to a decrease in the money supply. Since banks are holding more reserves (because they are making fewer loans), the monetary base will increase. c. If the Fed reduces its lending to banks through the Term Auction Facility, then the monetary base will decrease, and this in turn will decrease the money supply. The money multiplier is not affected, assuming no change in the reserve – deposit ratio or the currency – deposit ratio. d. If consumers lose confidence in ATMs and prefer to hold more cash, then the currency – deposit ratio will increase, and this will reduce the money multiplier. The money supply will fall because banks have fewer reserves to lend. The monetary base will increase because people are holding more currency, but will decrease because banks are holding fewer reserves. The net effect on the monetary base is zero. e. If the Fed drops newly minted $100 bills from a helicopter, then this will increase the monetary base and the money supply. If any of the currency ends up in the bank, then there will be a further increase in the money supply. If people end up holding more currency relative to deposits, then the money multiplier would fall. 3. a. If all money is held as currency, then the money supply is equal to the monetary base. The money supply will be $1,000. b. If all money is held as deposits, but banks hold 100 percent of deposits on reserve, then there are no loans. The money supply will be $1,000. c. If all money is held as deposits and banks hold 20 percent of deposits on reserve, then the reserve – deposit ratio is 0.20. The currency – deposit ratio is 0, and the money multiplier will be 1/0.2, or 5. The money supply will be $5,000. d. If people hold an equal amount of currency and deposits, then the currency – deposit ratio is 1. The reserve – deposit ratio is 0.2 and the money multiplier is (1 + 1)/(1 + 0.2) = 1.67. The money supply will be $1,666.67. e. The money supply is proportional to the monetary base and is given by M = m B , where M is the money supply, m is the money multiplier, and B is the monetary base. Since m is a constant number defined by the currency – deposit ratio and the reserve – deposit ratio, a 10 - percent increase in the monetary base B will lead to a 10 - percent increase in the money supply M . 4. a . The money supply is equal to currency plus demand deposits or $5,000 . The monetary base is equal to currency plus reserves . If we assume banks are not holding any excess reserves, then reserves must be 25 percent of deposits, or $1,000 . In this case the monetary base is equal to $2,000 . The money multiplier is equal to the money supply divided by the monetary base, or 2.5 . Alternatively, the money multiplier can be calculated using the formula m = (cr+1)/(cr+rr) , where cr is the currency deposit ratio ( 0.25) and rr is the reserve deposit ratio (0.25).
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Chapter 4 — The Monetary System: What It Is and How It Works 25 b . The bank balance sheet is illustrated below . If we assume the bank is not holding any excess reserves then reserves in the bank are 25 percent of deposits, or $1,000 . This means outstanding loans must be $3,000. Table 4 - 1 Assets Liabilities ______ Reserves $1,000 Deposits $4,000 Loans $3,000 c . To increase the money supply the central bank should buy government bonds because this will increase reserves in the banking system, allowing loans, deposits, and the money supply to increase . We know that M=mB , so M = m B . If the central bank wants the money supply to increase by 10 percent then they want the change in the money supply to equal $ 400 . We know the money multiplier is 2.5 so therefore the monetary base must increase by $160, meaning the central bank must buy $160 of government bonds. 5 . a . Given that banks hold one third of their deposits on reserve, the reserve deposit ratio ( rr ) is 1/3 . Given that p eople hold one third of their money in currency and two thirds in deposits, we can express the currency deposit ratio as 𝑐𝑟 = 𝐶𝑢 𝐷 = 1 3 𝑀 2 3 𝑀 = 1 2 . Therefore, t he money multiplier is equal to 𝑚 = 𝑐𝑟 + 1 𝑐𝑟 + 𝑟𝑟 = 1 2 + 1 1 2 + 1 3 = 1 . 8 . The money supply is equal to the monetary base times the money multiplier, or $1,800. b . If people hold half of their money in currency, then currency holdings are equal to deposits , and the currency deposit ratio is equal to 1 . Therefore , the money multiplier is equal to 1.5 , and the money supply is equal to $1,500. c . The central bank wants to increase the money supply by $300 so they will need to buy government bonds . We know M = m B , so therefore $ 300 = 1.5 B , and the central bank will want to buy $200 of government bonds. 6 . The model of the money supply developed in Chapter 4 shows that M = mB . The money supply M depends on the money multiplier m and the monetary base B . The money multiplier can also be expressed in terms of the reserve – deposit ratio rr and the currency – deposit ratio cr . Rewriting the money supply equation: . This equation shows that the money supply depends on the currency – deposit ratio, the reserve – deposit ratio, and the monetary base. To answer parts (a) through (c), we use the values for the money supply, the monetary base, the money multiplier, the reserve – deposit ratio, and the currency – deposit ratio from Table 4 - 2: M = cr + 1 ( ) cr + rr ( ) é ë ê ê ù û ú ú B
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Chapter 4 — The Monetary System: What It Is and How It Works 26 Table 4 - 2 August 1929 March 1933 Money supply 26.5 0 19.0 0 Monetary base 7.1 0 8.4 0 Money multiplier 3.7 0 2.3 0 Reserve – deposit ratio 0.14 0.21 Currency – deposit ratio 0.17 0.41 a. To determine what would happen to the money supply if the currency – deposit ratio had risen but the reserve – deposit ratio had remained the same, we need to recalculate the money multiplier and then plug this value into the money supply equation M = mB . To recalculate the money multiplier, use the 1933 value of the currency – deposit ratio and the 1929 value of the reserve – deposit ratio: m = ( cr 1933 + 1)/( cr 1933 + rr 1929 ) m = (0.41 + 1)/(0.41 + 0.14) m = 2.56. To determine the money supply under these conditions in 1933: M 1933 = mB 1933 . Plugging in the value for m just calculated and the 1933 value for B : M 1933 = 2.56 8.4 M 1933 = 21.504. Therefore, under these circumstances, the money supply would have fallen from its 1929 level of 26.5 to 21.504 in 1933. b. To determine what would have happened to the money supply if the reserve – deposit ratio had risen but the currency – deposit ratio had remained the same, we need to recalculate the money multiplier and then plug this value into the money supply equation M = mB . To recalculate the money multiplier, use the 1933 value of the reserve – deposit ratio and the 1929 value of the currency – deposit ratio: m = ( cr 1929 + 1)/( cr 1929 + rr 1933 ) m = (0.17 + 1)/(0.17 + 0.21) m = 3.09. To determine the money supply under these conditions in 1933: M 1933 = mB 1933 . Plugging in the value for m just calculated and the 1933 value for B : M 1933 = 3.09 8.4 M 1933 = 25.96. Therefore, under these circumstances, the money supply would have fallen from its 1929 level of 26.5 to 25.96 in 1933. c. From the calculations in parts (a) and (b), it is clear that the decline in the currency – deposit ratio was most responsible for the drop in the money multiplier and, t herefore, the money supply.
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Chapter 4 — The Monetary System: What It Is and How It Works 27 7 . a. The introduction of a tax on checks makes people more reluctant to use checking accounts as a means of exchange. Therefore, they hold more cash for transactions purposes, raising the currency – deposit ratio cr . b. The money supply falls because the money multiplier, cr + 1 cr + rr , is decreasing in cr . Intuitively, the higher the currency – deposit ratio, the lower the proportion of the monetary base that is held by banks in the form of reserves and, hence, the less money banks can create. c. The check tax was not a good policy to implement in the middle of the Great Depression because it result ed in a decrease in the money supply as people preferred to pay in currency rather than write a check. Banks had fewer reserves and were able to make fewer loans. 8 . The leverage ratio is the ratio of a bank’s total assets to its bank capital. If the leverage ratio is 2 0, this means that for each dollar of capital contributed by the bank owners, the bank has $ 2 0 of assets, and therefore $ 1 9 of deposits and debts. The balance sheet below has a leverage ratio of 2 0: total assets are $1,200 and capital is $ 60 . Assets Liabilities and Owners ’ Equity __ Reserves $200 Deposits $800 Loans $ 600 Debt $ 34 0 Securities $400 Capital ( o wners ’ e quity) $ 6 0 If the value of the bank’s assets rises by 2 percent and deposits and debt do not change, then owner’s equity will rise by 2 percent of the asset value . Since the sum of the entries on each side of the balance sheet must be the same, a 2 percent rise in the asset value must be balanced by a 2 percent rise in the right - hand - side value. To reduce the bank’s capital to zero, assets must decline in value by $ 60 , which is 5 percent of the current asset value. 9 . a . JPM’s balance sheet is illustrated below . We know reserves are equal to $3,000 because total a s sets must equal total liabilities. Assets Liabilities and Owners ’ Equity _____ Reserves $ 3,0 00 Deposits $14,0 00 Loans $10,0 00 Debt $ 4,00 0 Securities $ 7,0 00 Capital ( o wners ’ e quity) $ 2,00 0 The leverage ratio is the ratio of a bank’s total assets to its bank capital , or 10. b . If the value of the bank’s assets fall by 5 percent due to loan default, and deposits and debt do not change, then the value of owner s ’ equ ity will fall by 5 percent of the asset value . Loans and owner’s equity both fall by $500 . Owner s ’ eq uity (JPM’s capital) fell by 25 percent . Assets Liabilities and Owners ’ Equity _____ Reserves $3,0 00 Deposits $14,0 00 Loans $9,5 00 Debt $ 4,00 0 Securities $7,0 00 Capital ( o wners ’ e quity) $ 1,50 0
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Chapter 5 — Inflation: Its Causes, Effects, and Social Costs 28 Answers to Textbook Questions and Problems CHAPTER 5 Inflation: Its Causes, Effects, and Social Costs Questions for Review 1. 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 Velo city = Price Transactions M V = P T . The right side of the quantity equation tells us about the value of transactions in monetary terms that occur during a given period of time, for example , a year. T represents the total number of transactions. P represents the price of a typical transaction. Hence, the product P T represents the amount of dollars exchanged in a year. The left 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. 2. If we assume that velocity in the quantity equation is constant, then we can view the quantity equation as a theory to study the effect of changes in the money supple ( M ) . 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 such that Y is constant in the equation, then we can conclude that the quantity of money determines the price level. This is called the quantity theory of money. 3. The holders of money pay the inflation tax. As prices rise, the real value of the money that people hold falls — that is, a given amount of money buys fewer goods and services since prices are higher. This loss of real purchasing power is akin to a ‘tax’ on the money held. 4. The Fisher equation expresses the relationship between nominal and real interest rates. It says that the nominal interest rate i equals the real interest rate r plus the inflation rate π: i = r + π. This tells us that the nominal interest rate can change either because the real interest rate changes or the inflation rate changes. The real interest rate is assumed to be unaffected by inflation; as discussed in Chapter 3, it adjusts to equilibrate saving and investment. There is thus a one - to - one relationship between the inflation rate and the nominal interest rate: if inflation increases by 1 percent, then the
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Chapter 5 — Inflation: Its Causes, Effects, and Social Costs 29 nominal interest rate also increases by 1 percent. This one - to - one relationship is called the Fisher effect. If inflation increases from 6 to 8 percent, then the Fisher effect implies that the nominal interest rate increases by 2 percentage points, while the real interest rate remains constant. 5. The costs of expected inflation include the following: a. Shoeleather costs. Higher inflation means higher nominal interest rates, which mean s that people want to hold lower real money balances. If people hold lower money balances, they must make more frequent trips to the bank to withdraw money. There is an element of inconvenience involved, which is referred to as the ‘shoeleather tax’ because colloquially, more trips to the bank to withdraw money results in the wearing out of the shoes. b. Menu costs. Higher inflation induces firms to change their posted prices more often. This may be costly if they must reprint their menus and catalogs. c. Greater variability in relative prices. If firms change their prices infrequently, then inflation causes greater variability in relative prices. Since free - market economies rely on relative prices to allocate resources efficiently, inflation leads to microeconomic inefficiencies. d. Altered tax liabilities. Many provisions of the tax code do not take into account the effect of inflation. Hence, inflation can alter individuals’ and firms’ tax liabilities, often in ways that lawmakers did not intend. e. The inconvenience of a changing price level. It is inconvenient to live in a world with a changing price level. Money is the yardstick with which we measure economic transactions. Money is a less useful measure when its value is always changing. There is an additional cost to unexpected inflation: f. Arbitrary redistributions of wealth. Unexpected inflation arbitrarily redistributes wealth among individuals. For example, if inflation is higher than expected, debtors gain and creditors lose. Also, people with fixed pensions are hurt because their dollars buy fewer goods. 6. Hyperinflation is always a reflection of monetary policy. That is, the price level cannot grow rapidly unless the sup ply of money also grows rapidly, and hyperinflations do not end unless the government drastically reduces money growth. This explanation, however, begs a central question: w hy does the government start and then stop printing large quantities of lots of money? The answer almost always lies in fiscal policy: w hen the government has a large budget deficit (for example due to a recent war or some other major event) that it cannot fund by borrowing, it resorts to printi ng money to pay its bills. O nly when th e fiscal problem is alleviated , — by reducing government spending and / or collecting more taxes , — can the government hope to slow its rate of money growth. 7. Real variables are measured in physical units, and nominal variables are measured in terms of money. Real variables have been adjusted for inflation and are often measured in terms of constant dollars, while nominal variables are measured in terms of current dollars. For example, real GDP is measured in terms of constant base - year dollars, while nominal GDP is measured in current dollars. An increase in real GDP means we have produced a larger total quantity of goods and services, valued in base - year dollars. As another example, the real interest rate measures the increase in your purchasing power, the quantity of goods and services you can buy with your dollars, while the nominal interest rate measures the increase in the amount of current dollars you possess. The interest rat e you are quoted by your bank, for example 8 percent, is a nominal rate. If the inflation rate is 3 percent, then the real interest rate is 5 percent, meaning your purchasing power has only increased by 5 percent and not 8 percent. The quantity of dollars you possess has increased by 8 percent but you can only afford to buy 5 percent more goods and services with these dollars.
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Chapter 5 — Inflation: Its Causes, Effects, and Social Costs 30 Problems and Applications 1. a. To find the growth rate of nominal GDP, we start with the quantity equation MV = PY, and note that PY is equal to nominal GDP, or the value of the goods and services produced measured in current dollars. If we express this formula in percentage change form we have: % Change in M + % Change in V = % Change in PY . If we assume the percentage change in velocity is zero, then the percentage change in nominal GDP is equal to the percentage change in the money supply, or 8 percent. b. To find the inflation rate, express the quantity equation in percentage change form: b . To find the inflation rate, express the quantity equation in percentage change form: % Change in M + % Change in V = % Change in P + % Change in Y. Rearranging this equation tells us that the inflation rate is given by: % Change in P = % Change in M + % Change in V – % Change in Y. Substituting the information given in the problem, we thus find: % Change in P = 8 % + 0% – 3 % = 5 %. c . The real interest rate is 4 percent: the nominal interest rate of 9 percent minus the inflation rate of 5 percent. 2 . The money demand function is given as M P æ è ç ç ö ø ÷ ÷ d = kY . a. To find the average inflation rate the money demand function can be expressed in terms of growth rates: % G rowth M d – % G rowth P = % G rowth Y. The parameter k is a constant, so it can be ignored. The percentage change in nominal money demand M d is the same as the growth in the money supply because nominal money demand has to equal nominal money supply. If nominal money demand grows 12 percent and real income ( Y ) grows 4 percent then the growth of the price level or the inflation rate is 8 percent. b. From the answer to part (a), it follows that an increase in real income growth will result in a lower average inflation rate. For example, if real income grows at 6 percent and money supply growth remains at 12 percent, then inflation falls to 6 percent. In this case, a larger money supply is required to support a higher level of GDP, resulting in lower inflation. c. The parameter k defines how much money people want to hold for every dollar of income. The parameter k is inversely related to the velocity of money. All else remaining the same, if people are holding fewer dollars, then each dollar must be used more times to purchase the same quantity of goods and services. d. If velocity growth is positive, then all remaining else the same inflation will be higher. From the quantity equation we know that:
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