1. A large number of economic statistics are released regularly. These include the following:

Transcription

1 CHAPTER 2 The Data of Macoeconomics Questions fo Review 1. GDP measues both the total income of eveyone in the economy and the total expenditue on the economy s output of goods and sevices. GDP can measue two things at once because both ae eally the same thing: fo an economy as a whole, income must equal expenditue. As the cicula flow diagam in the text illustates, these ae altenative, equivalent ways of measuing the flow of dollas in the economy. 2. The consume pice index measues the oveall level of pices in the economy. It tells us the pice of a fixed basket of goods elative to the pice of the same basket in the base yea. 3. The Bueau of Labo Statistics classifies each peson into one of the following thee categoies: employed, unemployed, o not in the labo foce. The unemployment ate, which is the pecentage of the labo foce that is unemployed, is computed as follows: Numbe of Unemployed 100 Unemployment Rate =. Labo Foce Note that the labo foce is the numbe of people employed plus the numbe of people unemployed. 4. Okun s law efes to the negative elationship that exists between unemployment and eal GDP. Employed wokes help poduce goods and sevices wheeas unemployed wokes do not. Inceases in the unemployment ate ae theefoe associated with deceases in eal GDP. Okun s law can be summaized by the equation: % Real GDP = 3% 2 ( Unemployment Rate). That is, if unemployment does not change, the gowth ate of eal GDP is 3 pecent. Fo evey pecentage-point change in unemployment (fo example, a fall fom 6 pecent to 5 pecent, o an incease fom 6 pecent to 7 pecent), output changes by 2 pecent in the opposite diection. Poblems and Applications 1. A lage numbe of economic statistics ae eleased egulaly. These include the following: Goss Domestic Poduct the maket value of all final goods and sevices poduced in a yea. The Unemployment Rate the pecentage of the civilian labo foce who do not have a job. Copoate Pofits the accounting pofits emaining afte taxes of all manufactuing copoations. It gives an indication of the geneal financial health of the copoate secto. The Consume Pice Index (CPI) a measue of the aveage pice that consumes pay fo the goods they buy; changes in the CPI ae a measue of inflation. The Tade Balance the diffeence between the value of goods expoted aboad and the value of goods impoted fom aboad. 5

2 6 Answes to Textbook Questions and Poblems 2. Value added by each peson is the value of the good poduced minus the amount the peson paid fo the mateials necessay to make the good. Theefoe, the value added by the fame is $1.00 ($1 0 = $1). The value added by the mille is $2: she sells the flou to the bake fo $3 but paid $1 fo the flou. The value added by the bake is $3: she sells the bead to the enginee fo $6 but paid the mille $3 fo the flou. GDP is the total value added, o $1 + $2 + $3 = $6. Note that GDP equals the value of the final good (the bead). 3. When a woman maies he butle, GDP falls by the amount of the butle s salay. This happens because measued total income, and theefoe measued GDP, falls by the amount of the butle s loss in salay. If GDP tuly measued the value of all goods and sevices, then the maiage would not affect GDP since the total amount of economic activity is unchanged. Actual GDP, howeve, is an impefect measue of economic activity because the value of some goods and sevices is left out. Once the butle s wok becomes pat of his household choes, his sevices ae no longe counted in GDP. As this example illustates, GDP does not include the value of any output poduced in the home. Similaly, GDP does not include othe goods and sevices, such as the imputed ent on duable goods (e.g., cas and efigeatos) and any illegal tade. 4. a. govenment puchases b. investment c. net expots d. consumption e. investment 5. Data on pats (a) to (g) can be downloaded fom the Bueau of Economic Analysis ( follow the links to GDP and elated data). Most of the data (not necessaily the ealiest yea) can also be found in the Economic Repot of the Pesident. By dividing each component (a) to (g) by nominal GDP and multiplying by 100, we obtain the following pecentages: a. Pesonal consumption expenditues 65.5% 63.0% 68.2% b. Goss pivate domestic investment 18.4% 14.1% 17.9% c. Govenment consumption puchases 15.9% 22.1% 17.6% d. Net expots 0.2% 0.8% 3.7% e. National defense puchases 6.7% 6.6% 3.8% f. State and local puchases 7.1% 12.8% 11.7% g. Impots 3.9% 7.5% 14.9% (Note: These data wee downloaded Febuay 5, 2002 fom the BEA web site.) Among othe things, we obseve the following tends in the economy ove the peiod : (a) Pesonal consumption expenditues have been aound two-thids of GDP, although the shae inceased about 5 pecentage points between 1975 and (b) The shae of GDP going to goss pivate domestic investment fell fom 1950 to 1975 but then ebounded. (c) The shae going to govenment consumption puchases ose moe than 6 pecentage points fom 1950 to 1975 but has eceded somewhat since then. (d) Net expots, which wee positive in 1950 and 1975, wee substantially negative in (e) The shae going to national defense puchases fell fom 1975 to (f) The shae going to state and local puchases ose fom 1950 to (g) Impots have gown apidly elative to GDP.

3 Chapte 2 The Data of Macoeconomics 7 6. a. i. Nominal GDP is the total value of goods and sevices measued at cuent pices. Theefoe, Nominal GDP 2000 = (P cas Q cas ) + (P bead Q bead ) = ($50, ) + ($10 500,000) = $5,000,000 + $5,000,000 = $10,000, Nominal GDP 2010 = (P cas Q cas ) + (P bead Q bead ) = ($60, ) + ($20 400,000) = $7,200,000 + $8,000,000 = $15,200,000. ii. Real GDP is the total value of goods and sevices measued at constant pices. Theefoe, to calculate eal GDP in 2010 (with base yea 2000), multiply the quantities puchased in the yea 2010 by the 2000 pices: Real GDP 2010 = (P cas Q cas ) + (P bead Q bead ) = ($50, ) + ($10 400,000) = $6,000,000+ $4,000,000 = $10,000,000. Real GDP fo 2000 is calculated by multiplying the quantities in 2000 by the pices in Since the base yea is 2000, eal GDP 2000 equals nominal GDP 2000, which is $10,000,000. Hence, eal GDP stayed the same between 2000 and iii. The implicit pice deflato fo GDP compaes the cuent pices of all goods and sevices poduced to the pices of the same goods and sevices in a base yea. It is calculated as follows: iv. Nominal GDP Implicit Pice Deflato 2010 = Real GDP 2010 Using the values fo Nominal GDP 2010 and eal GDP 2010 calculated above: $15,200,000 Implicit Pice Deflato 2010 = $10,000,000 = This calculation eveals that pices of the goods poduced in the yea 2010 inceased by 52 pecent compaed to the pices that the goods in the economy sold fo in (Because 2000 is the base yea, the value fo the implicit pice deflato fo the yea 2000 is 1.0 because nominal and eal GDP ae the same fo the base yea.) The consume pice index (CPI) measues the level of pices in the economy. The CPI is called a fixed-weight index because it uses a fixed basket of goods ove time to weight pices. If the base yea is 2000, the CPI in 2010 is an aveage of pices in 2010, but weighted by the composition of goods poduced in The CPI 2010 is calculated as follows: ( Pcas Qcas ) + ( Pbead Qbead ) CPI 2010 = 2000 ( P Q 2000 ) + ( P 2000 Q 2000 ) cas cas bead bead ($60, ) + ($20 500,000) = ($50, ) + ($10 500,000) $16,000,000 = $10,000,000 = 1.6.

4 8 Answes to Textbook Questions and Poblems This calculation shows that the pice of goods puchased in 2010 inceased by 60 pecent compaed to the pices these goods would have sold fo in The CPI fo 2000, the base yea, equals 1.0. b. The implicit pice deflato is a Paasche index because it is computed with a changing basket of goods; the CPI is a Laspeyes index because it is computed with a fixed basket of goods. Fom (5.a.iii), the implicit pice deflato fo the yea 2010 is 1.52, which indicates that pices ose by 52 pecent fom what they wee in the yea Fom (5.a.iv.), the CPI fo the yea 2010 is 1.6, which indicates that pices ose by 60 pecent fom what they wee in the yea If pices of all goods ose by, say, 50 pecent, then one could say unambiguously that the pice level ose by 50 pecent. et, in ou example, elative pices have changed. The pice of cas ose by 20 pecent; the pice of bead ose by 100 pecent, making bead elatively moe expensive. As the discepancy between the CPI and the implicit pice deflato illustates, the change in the pice level depends on how the goods pices ae weighted. The CPI weights the pice of goods by the quantities puchased in the yea The implicit pice deflato weights the pice of goods by the quantities puchased in the yea The quantity of bead consumed was highe in 2000 than in 2010, so the CPI places a highe weight on bead. Since the pice of bead inceased elatively moe than the pice of cas, the CPI shows a lage incease in the pice level. c. Thee is no clea-cut answe to this question. Ideally, one wants a measue of the pice level that accuately captues the cost of living. As a good becomes elatively moe expensive, people buy less of it and moe of othe goods. In this example, consumes bought less bead and moe cas. An index with fixed weights, such as the CPI, oveestimates the change in the cost of living because it does not take into account that people can substitute less expensive goods fo the ones that become moe expensive. On the othe hand, an index with changing weights, such as the GDP deflato, undeestimates 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 consume pice index uses the consumption bundle in yea 1 to figue out how much weight to put on the pice of a given good: ( P CPI 2 ed Qed ) + ( Pgeen Qgeen ) = ( Ped Qed ) + ( Pgeen Qge en ) ($2 10) + ($1 0) = ($1 10) + ($2 0) = 2. Accoding to the CPI, pices have doubled. b. Nominal spending is the total value of output poduced in each yea. In yea 1 and yea 2, Abby buys 10 apples fo $1 each, so he nominal spending emains constant at $10. Fo example, Nominal Spending 2 = (P Q ) + (P Q ) ed = ($2 0) + ($1 10) = $10. ed geen geen

5 Chapte 2 The Data of Macoeconomics 9 c. Real spending is the total value of output poduced in each yea valued at the pices pevailing in yea 1. In yea 1, the base yea, he eal spending equals he nominal spending of $10. In yea 2, she consumes 10 geen apples that ae each valued at thei yea 1 pice of $2, so he eal spending is $20. That is, Real Spending 2 = (P Q ) + (P Q ) ed = ($1 0) + ($2 10) = $20. Hence, Abby s eal spending ises fom $10 to $20. d. The implicit pice deflato is calculated by dividing Abby s nominal spending in yea 2 by he eal spending that yea: Implicit Pice Deflato 2 = Nominal Spending 2 Real Spending 2 $10 = $20 = 0.5. Thus, the implicit pice deflato suggests that pices have fallen by half. The eason fo this is that the deflato estimates how much Abby values he apples using pices pevailing in yea 1. Fom this pespective geen apples appea vey valuable. In yea 2, when Abby consumes 10 geen apples, it appeas that he consumption has inceased because the deflato values geen apples moe highly than ed apples. The only way she could still be spending $10 on a highe consumption bundle is if the pice of the good she was consuming feel. e. If Abby thinks of ed apples and geen apples as pefect substitutes, then the cost of living in this economy has not changed in eithe yea it costs $10 to consume 10 apples. Accoding to the CPI, howeve, the cost of living has doubled. This is because the CPI only takes into account the fact that the ed apple pice has doubled; the CPI ignoes the fall in the pice of geen apples because they wee not in the consumption bundle in yea 1. In contast to the CPI, the implicit pice deflato estimates the cost of living has halved. Thus, the CPI, a Laspeyes index, ovestates the incease in the cost of living and the deflato, a Paasche index, undestates it. This chapte of the text discusses the diffeence between Laspeyes and Paasche indices in moe detail. 8. a. Real GDP falls because Disney does not poduce any sevices while it is closed. This coesponds to a decease in economic well-being because the income of wokes and shaeholdes of Disney falls (the income side of the national accounts), and people s consumption of Disney falls (the expenditue side of the national accounts). b. Real GDP ises because the oiginal capital and labo in fam poduction now poduce moe wheat. This coesponds to an incease in the economic well-being of society, since people can now consume moe wheat. (If people do not want to consume moe wheat, then fames and famland can be shifted to poducing othe goods that society values.) c. Real GDP falls because with fewe wokes on the job, fims poduce less. This accuately eflects a fall in economic well-being. d. Real GDP falls because the fims that lay off wokes poduce less. This deceases economic well-being because wokes incomes fall (the income side), and thee ae fewe goods fo people to buy (the expenditue side). e. Real GDP is likely to fall, as fims shift towad poduction methods that poduce fewe goods but emit less pollution. Economic well-being, howeve, may ise. The economy now poduces less measued output but moe clean ai; clean ai is not ed geen geen

6 10 Answes to Textbook Questions and Poblems taded in makets and, thus, does not show up in measued GDP, but is nevetheless a good that people value. f. Real GDP ises because the high-school students go fom an activity in which they ae not poducing maket goods and sevices to one in which they ae. Economic well-being, howeve, may decease. In ideal national accounts, attending school would show up as investment because it pesumably inceases the futue poductivity of the woke. Actual national accounts do not measue this type of investment. Note also that futue GDP may be lowe than it would be if the students stayed in school, since the futue wok foce will be less educated. g. Measued eal GDP falls because fathes spend less time poducing maket goods and sevices. The actual poduction of goods and sevices need not have fallen, howeve. Measued poduction (what the fathes ae paid to do) falls, but unmeasued poduction of child-eaing sevices ises. 9. As Senato Robet Kennedy pointed out, GDP is an impefect measue of economic pefomance o well-being. In addition to the left-out items that Kennedy cited, GDP also ignoes the imputed ent on duable goods such as cas, efigeatos, and lawnmowes; many sevices and poducts poduced as pat of household activity, such as cooking and cleaning; and the value of goods poduced and sold in illegal activities, such as the dug tade. These impefections in the measuement of GDP do not necessaily educe its usefulness. As long as these measuement poblems stay constant ove time, then GDP is useful in compaing economic activity fom yea to yea. Moeove, a lage GDP allows us to affod bette medical cae fo ou childen, newe books fo thei education, and moe toys fo thei play.

7 CHAPTER 3 National Income: Whee It Comes Fom and Whee It Goes Questions fo Review 1. Factos of poduction and the poduction technology detemine the amount of output an economy can poduce. Factos of poduction ae the inputs used to poduce goods and sevices: the most impotant factos ae capital and labo. The poduction technology detemines how much output can be poduced fom any given amounts of these inputs. An incease in one of the factos of poduction o an impovement in technology leads to an incease in the economy s output. 2. When a fim decides how much of a facto of poduction to hie, it consides how this decision affects pofits. Fo example, hiing an exta unit of labo inceases output and theefoe inceases evenue; the fim compaes this additional evenue to the additional cost fom the highe wage bill. The additional evenue the fim eceives depends on the maginal poduct of labo (MPL) and the pice of the good poduced (P). An additional unit of labo poduces MPL units of additional output, which sells fo P dollas. Theefoe, the additional evenue to the fim is P MPL. The cost of hiing the additional unit of labo is the wage W. Thus, this hiing decision has the following effect on pofits: Pofit = Revenue Cost = (P MPL) W. If the additional evenue, P MPL, exceeds the cost (W) of hiing the additional unit of labo, then pofit inceases. The fim will hie labo until it is no longe pofitable to do so that is, until the MPL falls to the point whee the change in pofit is zeo. In the equation above, the fim hies labo until pofit = 0, which is when (P MPL) = W. This condition can be ewitten as: MPL = W/P. Theefoe, a competitive pofit-maximizing fim hies labo until the maginal poduct of labo equals the eal wage. The same logic applies to the fim s decision to hie capital: the fim will hie capital until the maginal poduct of capital equals the eal ental pice. 3. A poduction function has constant etuns to scale if an equal pecentage incease in all factos of poduction causes an incease in output of the same pecentage. Fo example, if a fim inceases its use of capital and labo by 50 pecent, and output inceases by 50 pecent, then the poduction function has constant etuns to scale. If the poduction function has constant etuns to scale, then total income (o equivalently, total output) in an economy of competitive pofit-maximizing fims is divided between the etun to labo, MPL L, and the etun to capital, MPK K. That is, unde constant etuns to scale, economic pofit is zeo. 4. Consumption depends positively on disposable income the amount of income afte all taxes have been paid. The highe disposable income is, the geate consumption is. The quantity of investment goods demanded depends negatively on the eal inteest ate. Fo an investment to be pofitable, its etun must be geate than its cost. Because the eal inteest ate measues the cost of funds, a highe eal inteest ate makes it moe costly to invest, so the demand fo investment goods falls. 5. Govenment puchases ae those goods and sevices puchased diectly by the govenment. Fo example, the govenment buys missiles and tanks, builds oads, and povides 11

8 12 Answes to Textbook Questions and Poblems sevices such as ai taffic contol. All of these activities ae pat of GDP. Tansfe payments ae govenment payments to individuals that ae not in exchange fo goods o sevices. They ae the opposite of taxes: taxes educe household disposable income, wheeas tansfe payments incease it. Examples of tansfe payments include Social Secuity payments to the eldely, unemployment insuance, and veteans benefits. 6. Consumption, investment, and govenment puchases detemine demand fo the economy s output, wheeas the factos of poduction and the poduction function detemine the supply of output. The eal inteest ate adjusts to ensue that the demand fo the economy s goods equals the supply. At the equilibium inteest ate, the demand fo goods and sevices equals the supply. 7. When the govenment inceases taxes, disposable income falls, and theefoe consumption falls as well. The decease in consumption equals the amount that taxes incease multiplied by the maginal popensity to consume (MPC). The highe the MPC is, the geate is the negative effect of the tax incease on consumption. Because output is fixed by the factos of poduction and the poduction technology, and govenment puchases have not changed, the decease in consumption must be offset by an incease in investment. Fo investment to ise, the eal inteest ate must fall. Theefoe, a tax incease leads to a decease in consumption, an incease in investment, and a fall in the eal inteest ate. Poblems and Applications 1. a. Accoding to the neoclassical theoy of distibution, the eal wage equals the maginal poduct of labo. Because of diminishing etuns to labo, an incease in the labo foce causes the maginal poduct of labo to fall. Hence, the eal wage falls. b. The eal ental pice equals the maginal poduct of capital. If an eathquake destoys some of the capital stock (yet miaculously does not kill anyone and lowe the labo foce), the maginal poduct of capital ises and, hence, the eal ental pice ises. c. If a technological advance impoves the poduction function, this is likely to incease the maginal poducts of both capital and labo. Hence, the eal wage and the eal ental pice both incease. 2. A poduction function has deceasing etuns to scale if an equal pecentage incease in all factos of poduction leads to a smalle pecentage incease in output. Fo example, if we double the amounts of capital and labo, and output less than doubles, then the poduction function has deceasing etuns to capital and labo. This may happen if thee is a fixed facto such as land in the poduction function, and this fixed facto becomes scace as the economy gows lage. A poduction function has inceasing etuns to scale if an equal pecentage incease in all factos of poduction leads to a lage pecentage incease in output. Fo example, if doubling inputs of capital and labo moe than doubles output, then the poduction function has inceasing etuns to scale. This may happen if specialization of labo becomes geate as population gows. Fo example, if one woke builds a ca, then it takes him a long time because he has to lean many diffeent skills, and he must constantly change tasks and tools; all of this is faily slow. But if many wokes build a ca, then each one can specialize in a paticula task and become vey fast at it. 3. a. Accoding to the neoclassical theoy, technical pogess that inceases the maginal poduct of fames causes thei eal wage to ise. b. The eal wage in (a) is measued in tems of fam goods. That is, if the nominal wage is in dollas, then the eal wage is W/PF, whee PF is the dolla pice of fam goods.

9 Chapte 3 National Income: Whee It Comes Fom and Whee It Goes 13 c. If the maginal poductivity of babes is unchanged, then thei eal wage is unchanged. d. The eal wage in (c) is measued in tems of haicuts. That is, if the nominal wage is in dollas, then the eal wage is W/PH, whee PH is the dolla pice of a haicut. e. If wokes can move feely between being fames and being babes, then they must be paid the same wage W in each secto. f. If the nominal wage W is the same in both sectos, but the eal wage in tems of fam goods is geate than the eal wage in tems of haicuts, then the pice of haicuts must have isen elative to the pice of fam goods. g. Both goups benefit fom technological pogess in faming. 4. The effect of a govenment tax incease of $100 billion on (a) public saving, (b) pivate saving, and (c) national saving can be analyzed by using the following elationships: National Saving = [Pivate Saving] + [Public Saving] = [ T C( T)] + [T G] = C( T) G. a. Public Saving The tax incease causes a 1-fo-1 incease in public saving. T inceases by $100 billion and, theefoe, public saving inceases by $100 billion. b. Pivate Saving The incease in taxes deceases disposable income, T, by $100 billion. Since the maginal popensity to consume (MPC) is 0.6, consumption falls by 0.6 $100 billion, o $60 billion. Hence, Pivate Saving = $100b 0.6 ( $100b) = $40b. Pivate saving falls $40 billion. c. National Saving Because national saving is the sum of pivate and public saving, we can conclude that the $100 billion tax incease leads to a $60 billion incease in national saving. Anothe way to see this is by using the thid equation fo national saving expessed above, that national saving equals C( T) G. The $100 billion tax incease educes disposable income and causes consumption to fall by $60 billion. Since neithe G no changes, national saving thus ises by $60 billion. d. Investment To detemine the effect of the tax incease on investment, ecall the national accounts identity: = C( T) + I() + G. Reaanging, we find C( T) G = I(). The left-hand side of this equation is national saving, so the equation just says the national saving equals investment. Since national saving inceases by $60 billion, investment must also incease by $60 billion.

10 14 Answes to Textbook Questions and Poblems How does this incease in investment take place? We know that investment depends on the eal inteest ate. Fo investment to ise, the eal inteest ate must fall. Figue 3 1 gaphs saving and investment as a function of the eal inteest ate. S 1 S 2 Figue Figue Real inteest ate 1 2 I () Investment, Saving I, S The tax incease causes national saving to ise, so the supply cuve fo loanable funds shifts to the ight. The equilibium eal inteest ate falls, and investment ises. 5. If consumes incease the amount that they consume today, then pivate saving and, theefoe, national saving will fall. We know this fom the definition of national saving: National Saving = [Pivate Saving] + [Public Saving] = [ T C( T)] + [T G]. An incease in consumption deceases pivate saving, so national saving falls. Figue 3 2 gaphs saving and investment as a function of the eal inteest ate. If national saving deceases, the supply cuve fo loanable funds shifts to the left, theeby aising the eal inteest ate and educing investment. S 2 S 1 Figue 3 2 Figue 3 2 Real inteest ate 1 2 I () Investment, Saving I, S

11 Chapte 3 National Income: Whee It Comes Fom and Whee It Goes a. Pivate saving is the amount of disposable income, T, that is not consumed: S pivate = T C = 5,000 1,000 ( (5,000 1,000)) = 750. Public saving is the amount of taxes the govenment has left ove afte it makes its puchases: S public = T G = 1,000 1,000 = 0. Total saving is the sum of pivate saving and public saving: S = S pivate + S public = = 750. b. The equilibium inteest ate is the value of that cleas the maket fo loanable funds. We aleady know that national saving is 750, so we just need to set it equal to investment: S = I 750 = 1, Solving this equation fo, we find: = 5%. c. When the govenment inceases its spending, pivate saving emains the same as befoe (notice that G does not appea in the S pivate above) while govenment saving deceases. Putting the new G into the equations above: S pivate = 750 S public = T G = 1,000 1,250 = 250. Thus, S = S pivate + S public = ( 250) = 500. d. Once again the equilibium inteest ate cleas the maket fo loanable funds: S = I 500 = 1, Solving this equation fo, we find: = 10%. 7. To detemine the effect on investment of an equal incease in both taxes and govenment spending, conside the national income accounts identity fo national saving: National Saving = [Pivate Saving] + [Public Saving] = [ T C( T)] + [T G]. We know that is fixed by the factos of poduction. We also know that the change in consumption equals the maginal popensity to consume (MPC) times the change in disposable income. This tells us that National Saving = [ T (MPC ( T))] + [ T G] = [ T + (MPC T)] + 0 = (MPC 1) T.

12 16 Answes to Textbook Questions and Poblems The above expession tells us that the impact on saving of an equal incease in T and G depends on the size of the maginal popensity to consume. The close the MPC is to 1, the smalle is the fall in saving. Fo example, if the MPC equals 1, then the fall in consumption equals the ise in govenment puchases, so national saving [ C( T) G] is unchanged. The close the MPC is to 0 (and theefoe the lage is the amount saved athe than spent fo a one-dolla change in disposable income), the geate is the impact on saving. Because we assume that the MPC is less than 1, we expect that national saving falls in esponse to an equal incease in taxes and govenment spending. The eduction in saving means that the supply of loanable funds cuve shifts to the left in Figue 3 3. The eal inteest ate ises, and investment falls. S 2 S 1 Figue Real inteest ate 2 1 I () Investment, Saving I, S 8. a. The demand cuve fo business investment shifts out because the subsidy inceases the numbe of pofitable investment oppotunities fo any given inteest ate. The demand cuve fo esidential investment emains unchanged. b. The total demand cuve fo investment in the economy shifts out since it epesents the sum of business investment, which shifts out, and esidential investment, which is unchanged. As a esult the eal inteest ate ises as in Figue 3 4.

13 Chapte 3 National Income: Whee It Comes Fom and Whee It Goes 17 Figue S Real inteest ate aises the inteest ate. B A 1. An incease in desied investment... I 2 I 1 I, S Investment, Saving c. The total quantity of investment does not change because it is constained by the inelastic supply of savings. The investment tax cedit leads to a ise in business investment, but an offsetting fall in esidential investment. That is, the highe inteest ate means that esidential investment falls (a shift along the cuve), wheeas the outwad shift of the business investment cuve leads business investment to ise by an equal amount. Figue 3 5 shows this change. Note that B R B R I + I = I + I = S Figue I 1 B I 2 B Business Business Investment investment I 1 R I 2 R Residential Investment investment 9. In this chapte, we concluded that an incease in govenment expenditues educes national saving and aises the inteest ate; it theefoe cowds out investment by the full amount of the incease in govenment expenditue. Similaly, a tax cut inceases disposable income and hence consumption; this incease in consumption tanslates into a fall in national saving again, it cowds out investment.

14 18 Answes to Textbook Questions and Poblems If consumption depends on the inteest ate, then these conclusions about fiscal policy ae modified somewhat. If consumption depends on the inteest ate, then so does saving. The highe the inteest ate, the geate the etun to saving. Hence, it seems easonable to think that an incease in the inteest ate might incease saving and educe consumption. Figue 3 6 shows saving as an inceasing function of the inteest ate. S() Figue 3 6 Figue 3 6 Conside what happens when govenment puchases incease. At any given level of the inteest ate, national saving falls by the change in govenment puchases, as shown in Figue 3 7. The figue shows that if the saving function slopes upwad, investment falls by less than the amount that govenment puchases ise; this happens because consumption falls and saving inceases in esponse to the highe inteest ate. Hence, the moe esponsive consumption is to the inteest ate, the less govenment puchases cowd out investment. S 2 () S 1 () Figue Figue Real inteest ate Real inteest ate Saving S 1 G I() I 1 I Investment, Saving I, S

15 Chapte 3 National Income: Whee It Comes Fom and Whee It Goes 19 Moe Poblems and Applications to Chapte 3 1. a. A Cobb Douglas poduction function has the fom = AK α L 1 α. In the appendix we showed that the maginal poducts fo the Cobb Douglas poduction function ae: MPL = (1 α)/l. MPK = α/k. Competitive pofit-maximizing fims hie labo until its maginal poduct equals the eal wage, and hie capital until its maginal poduct equals the eal ental ate. Using these facts and the above maginal poducts fo the Cobb Douglas poduction function, we find: W/P = MPL = (1 α)/l. Rewiting this: R/P = MPK = α/k. (W/P)L = MPL L = (1 α). (R/P)K = MPK K = α. Note that the tems (W/P)L and (R/P)K ae the wage bill and total etun to capital, espectively. Given that the value of α = 0.3, then the above fomulas indicate that labo eceives 70 pecent of total output, which is (1 0.3), and capital eceives 30 pecent of total output. b. To detemine what happens to total output when the labo foce inceases by 10 pecent, conside the fomula fo the Cobb Douglas poduction function: = AK α L 1 α. Let 1 equal the initial value of output and 2 equal final output. We know that α = 0.3. We also know that labo L inceases by 10 pecent: 1 = AK 0.3 L = AK 0.3 (1.1L) 0.7. Note that we multiplied L by 1.1 to eflect the 10-pecent incease in the labo foce. To calculate the pecentage change in output, divide 2 by 1 : 2 1 = AK 0.3 (1.1L) 0.7 AK 0.3 L 0.7 = (1.1) 0.7 = That is, output inceases by 6.9 pecent. To detemine how the incease in the labo foce affects the ental pice of capital, conside the fomula fo the eal ental pice of capital R/P: R/P = MPK = αak α 1 L 1 α. We know that α = 0.3. We also know that labo (L) inceases by 10 pecent. Let (R/P) 1 equal the initial value of the ental pice of capital, and (R/P) 2 equal the final ental pice of capital afte the labo foce inceases by 10 pecent. To find (R/P) 2, multiply L by 1.1 to eflect the 10-pecent incease in the labo foce: (R/P) 1 = 0.3AK 0.7 L 0.7. (R/P) 2 = 0.3AK 0.7 (1.1L) 0.7.

16 20 Answes to Textbook Questions and Poblems The ental pice inceases by the atio (R/P) 0.3AK 0.7 (1.1L) = (R/P) 0.3AK 0.7 L = (1.1) 0.7 = So the ental pice inceases by 6.9 pecent. To detemine how the incease in the labo foce affects the eal wage, conside the fomula fo the eal wage W/P: W/P = MPL = (1 α)ak α L α. We know that α = 0.3. We also know that labo (L) inceases by 10 pecent. Let (W/P) 1 equal the initial value of the eal wage and (W/P) 2 equal the final value of the eal wage. To find (W/P) 2, multiply L by 1.1 to eflect the 10-pecent incease in the labo foce: (W/P) 1 = (1 0.3)AK 0.3 L 0.3. (W/P) 2 = (1 0.3)AK 0.3 (1.1L) 0.3. To calculate the pecentage change in the eal wage, divide (W/P) 2 by (W/P) 1 : ( W/P) 2 ( ) AK ( 1. 1L) = ( W/P) ( ) AK L = (1.1) 0.3 = That is, the eal wage falls by 2.8 pecent. c. We can use the same logic as (b) to set 1 = AK 0.3 L 0.7. Theefoe, we have: 1 2 = A(1.1K) 0.3 L = A(1.1K) 0.3 L 1.7 AK 0.3 L 0.7 = (1.1) 0.3 = This equation shows that output inceases by 2 pecent. Notice that α < 0.5 means that popotional inceases to capital will incease output by less than the same popotional incease to labo. Again using the same logic as (b) fo the change in the eal ental pice of capital: (R/P) 0.3A(1.1K) 0.7 L = (R/P) 0.3AK 0.7 L = (1.1) 0.7 = The eal ental pice of capital falls by 6.5 pecent because thee ae diminishing etuns to capital; that is, when capital inceases, its maginal poduct falls.

17 Chapte 3 National Income: Whee It Comes Fom and Whee It Goes 21 Finally, the change in the eal wage is: (W/P) 0.7A(1.1K) 0.7 L = (W/P) 0.7AK 0.7 L (1.1) 0.3 = Hence, eal wages incease by 2.9 pecent because the added capital inceases the maginal poductivity of the existing wokes. (Notice that the wage and output have both inceased by the same amount, leaving the labo shae unchanged a featue of Cobb Douglas technologies.) d. Using the same fomula, we find that the change in output is: (1.1A)K 0.3 L = AK 0.3 L = 1.1. This equation shows that output inceases by 10 pecent. Similaly, the ental pice of capital and the eal wage also incease by 10 pecent: (R/P) 0.3(1.1A)K 0.7 L = (R/P) 0.3AK 0.7 L = 1.1. (W/P) 0.7(1.1A)K 0.3 L = (W/P) 0.7AK 0.3 L = a. The maginal poduct of labo MPL is found by diffeentiating the poduction function with espect to labo: d MPL = dl 1 = K 1/3 H 1/3 L 2/3. 3 This equation is inceasing in human capital because moe human capital makes all the existing labo moe poductive. b. The maginal poduct of human capital MPH is found by diffeentiating the poduction function with espect to human capital: d MPH = dh 1 = K 1/3 L 1/3 H 2/3. 3 This equation is deceasing in human capital because thee ae diminishing etuns. c. The labo shae of output is the popotion of output that goes to labo. The total amount of output that goes to labo is the eal wage (which, unde pefect competition, equals the maginal poduct of labo) times the quantity of labo. This quantity is divided by the total amount of output to compute the labo shae: ( 3 K H L ) L Labo Shae = K H L 1 =. 3

18 22 Answes to Textbook Questions and Poblems We can use the same logic to find the human capital shae: 1 ( 3 K 1/3 L 1/3 H 2/3 ) H Human Capital Shae = K 1/3 H 1/3 L 1/3 1 =, 3 so labo gets one-thid of the output, and human capital gets one-thid of the output. Since wokes own thei human capital (we hope!), it will appea that labo gets two-thids of output. d. The atio of the skilled wage to the unskilled wage is: W skilled W unskilled = = MPL + MPH MPL 1 K 1/3 L 2/3 H 1/ K 1/3 L 1/3 H 2/3 3 1 K 1/3 L 2/3 H 1/3 3 L = 1 +. H Notice that the atio is always geate than 1 because skilled wokes get paid moe than unskilled wokes. Also, when H inceases this atio falls because the diminishing etuns to human capital lowe its etun, while at the same time inceasing the maginal poduct of unskilled wokes. e. If moe college scholaships incease H, then it does lead to a moe egalitaian society. The policy lowes the etuns to education, deceasing the gap between the wages of moe and less educated wokes. Moe impotantly, the policy even aises the absolute wage of unskilled wokes because thei maginal poduct ises when the numbe of skilled wokes ises.

19 CHAPTER 4 Money and Inflation Questions fo Review 1. Money has thee functions: it is a stoe of value, a unit of account, and a medium of exchange. As a stoe of value, money povides a way to tansfe puchasing powe fom the pesent to the futue. As a unit of account, money povides the tems in which pices ae quoted and debts ae ecoded. As a medium of exchange, money is what we use to buy goods and sevices. 2. Fiat money is established as money by the govenment but has no intinsic value. Fo example, a U.S. dolla bill is fiat money. Commodity money is money that is based on a commodity with some intinsic value. Gold, when used as money, is an example of commodity money. 3. In many counties, a cental bank contols the money supply. In the United States, the cental bank is the Fedeal Reseve often called the Fed. The contol of the money supply is called monetay policy. The pimay way that the Fed contols the money supply is though open-maket opeations, which involve the puchase o sale of govenment bonds. To incease the money supply, the Fed uses dollas to buy govenment bonds fom the public, putting moe dollas into the hands of the public. To decease the money supply, the Fed sells some of its govenment bonds, taking dollas out of the hands of the public. 4. The quantity equation is an identity that expesses the link between the numbe of tansactions that people make and how much money they hold. We wite it as Money Velocity = Pice Tansactions M V = P T. The ight-hand side of the quantity equation tells us about the total numbe of tansactions that occu duing a given peiod of time, say, a yea. T epesents the total numbe of times that any two individuals exchange goods o sevices fo money. P epesents the pice of a typical tansaction. Hence, the poduct P T epesents the numbe of dollas exchanged in a yea. The left-hand side of the quantity equation tells us about the money used to make these tansactions. M epesents the quantity of money in the economy. V epesents the tansactions velocity of money the ate at which money ciculates in the economy. Because the numbe of tansactions is difficult to measue, economists usually use a slightly diffeent vesion of the quantity equation, in which the total output of the economy eplaces the numbe of tansactions T: Money Velocity = Pice Output M V = P. P now epesents the pice of one unit of output, so that P is the dolla value of output nominal GDP. V epesents the income velocity of money the numbe of times a dolla bill becomes a pat of someone s income. 5. If we assume that velocity in the quantity equation is constant, then we can view the quantity equation as a theoy of nominal GDP. The quantity equation with fixed velocity states that MV = P. If velocity V is constant, then a change in the quantity of money (M) causes a popotionate change in nominal GDP (P). If we assume futhe that output is fixed by the factos of poduction and the poduction technology, then we can conclude that the 23

20 24 Answes to Textbook Questions and Poblems quantity of money detemines the pice level. This is called the quantity theoy of money. 6. The holdes of money pay the inflation tax. As pices ise, the eal value of the money that people hold falls that is, a given amount of money buys fewe goods and sevices since pices ae highe. 7. The Fishe equation expesses the elationship between nominal and eal inteest ates. It says that the nominal inteest ate i equals the eal inteest ate plus the inflation ate π: i = + π. This tells us that the nominal inteest ate can change eithe because the eal inteest ate changes o the inflation ate changes. The eal inteest ate is assumed to be unaffected by inflation; as discussed in Chapte 3, it adjusts to equilibate saving and investment. Thee is thus a one-to-one elationship between the inflation ate and the nominal inteest ate: if inflation inceases by 1 pecent, then the nominal inteest ate also inceases by 1 pecent. This one-to-one elationship is called the Fishe effect. If inflation inceases fom 6 to 8 pecent, then the Fishe effect implies that the nominal inteest ate inceases by 2 pecentage points, while the eal inteest ate emains constant. 8. The costs of expected inflation include the following: a. Shoeleathe costs. Highe inflation means highe nominal inteest ates, which mean that people want to hold lowe eal money balances. If people hold lowe money balances, they must make moe fequent tips to the bank to withdaw money. This is inconvenient (and it causes shoes to wea out moe quickly). b. Menu costs. Highe inflation induces fims to change thei posted pices moe often. This may be costly if they must epint thei menus and catalogs. c. Geate vaiability in elative pices. If fims change thei pices infequently, then inflation causes geate vaiability in elative pices. Since fee-maket economies ely on elative pices to allocate esouces efficiently, inflation leads to micoeconomic inefficiencies. d. Alteed tax liabilities. Many povisions of the tax code do not take into account the effect of inflation. Hence, inflation can alte individuals and fims tax liabilities, often in ways that lawmakes did not intend. e. The inconvenience of a changing pice level. It is inconvenient to live in a wold with a changing pice level. Money is the yadstick with which we measue economic tansactions. Money is a less useful measue when its value is always changing. Thee is an additional cost to unexpected inflation: f. Abitay edistibutions of wealth. Unexpected inflation abitaily edistibutes wealth among individuals. Fo example, if inflation is highe than expected, debtos gain and ceditos lose. Also, people with fixed pensions ae hut because thei dollas buy fewe goods. 9. A hypeinflation always eflects monetay policy. That is, the pice level cannot gow apidly unless the supply of money also gows apidly; and hypeinflations do not end unless the govenment dastically educes money gowth. This explanation, howeve, begs a cental question: Why does the govenment stat and then stop pinting lots of money? The answe almost always lies in fiscal policy: When the govenment has a lage budget deficit (possibly due to a ecent wa o some othe majo event) that it cannot fund by boowing, it esots to pinting money to pay its bills. And only when this fiscal poblem is alleviated by educing govenment spending and collecting moe taxes can the govenment hope to slow its ate of money gowth. 10. A eal vaiable is one that is measued in units that ae constant ove time fo example, they might be measued in constant dollas. That is, the units ae adjusted fo

21 Chapte 4 Money and Inflation 25 inflation. A nominal vaiable is one that is measued in cuent dollas; the value of the vaiable is not adjusted fo inflation. Fo example, a eal vaiable could be a Heshey s candy ba; the nominal vaiable is the cuent-pice value of the Heshey s candy ba 5 cents in 1960, say, and 75 cents in The inteest ate you ae quoted by you bank 8 pecent, say is a nominal ate, since it is not adjusted fo inflation. If inflation is, say, 3 pecent, then the eal inteest ate, which measues you puchasing powe, is 5 pecent. Poblems and Applications 1. Money functions as a stoe of value, a medium of exchange, and a unit of account. a. A cedit cad can seve as a medium of exchange because it is accepted in exchange fo goods and sevices. A cedit cad is, aguably, a (negative) stoe of value because you can accumulate debt with it. A cedit cad is not a unit of account a ca, fo example, does not cost 5 VISA cads. b. A Rembandt painting is a stoe of value only. c. A subway token, within the subway system, satisfies all thee functions of money. et outside the subway system, it is not widely used as a unit of account o a medium of exchange, so it is not a fom of money. 2. The eal inteest ate is the diffeence between the nominal inteest ate and the inflation ate. The nominal inteest ate is 11 pecent, but we need to solve fo the inflation ate. We do this with the quantity identity expessed in pecentage-change fom: % Change in M + % Change in V = % Change in P + % Change in. Reaanging this equation tells us that the inflation ate is given by: % Change in P + % Change in M + % Change in V % Change in. Substituting the numbes given in the poblem, we thus find: % Change in P = 14% + 0% 5% = 9%. Thus, the eal inteest ate is 2 pecent: the nominal inteest ate of 11 pecent minus the inflation ate of 9 pecent. 3. a. Legislatos wish to ensue that the eal value of Social Secuity and othe benefits stays constant ove time. This is achieved by indexing benefits to the cost of living as measued by the consume pice index. With indexing, nominal benefits change at the same ate as pices. b. Assuming the inflation is measued coectly (see Chapte 2 fo moe on this issue), senio citizens ae unaffected by the lowe ate of inflation. Although they get less money fom the govenment, the goods they puchase ae cheape; thei puchasing powe is exactly the same as it was with the highe inflation ate. 4. The majo benefit of having a national money is seignioage the ability of the govenment to aise evenue by pinting money. The majo cost is the possibility of inflation, o even hypeinflation, if the govenment elies too heavily on seignioage. The benefits and costs of using a foeign money ae exactly the evese: the benefit of foeign money is that inflation is no longe unde domestic political contol, but the cost is that the domestic govenment loses its ability to aise evenue though seignioage. (Thee is also a subjective cost to having pictues of foeign leades on you cuency.) The foeign county s political stability is a key facto. The pimay eason fo using anothe nation s money is to gain stability. If the foeign county is unstable, then the home county is definitely bette off using its own cuency the home economy emains moe stable, and it keeps the seignioage. 5. A pape weapon might have been effective fo all the easons that a hypeinflation is bad. Fo example, it inceases shoeleathe and menu costs; it makes elative pices moe vaiable; it altes tax liabilities in abitay ways; it inceases vaiability in ela-

22 26 Answes to Textbook Questions and Poblems tive pices; it makes the unit of account less useful; and finally, it inceases uncetainty and causes abitay edistibutions of wealth. If the hypeinflation is sufficiently exteme, it can undemine the public s confidence in the economy and economic policy. Note that if foeign aiplanes dopped the money, then the govenment would not eceive seignioage evenue fom the esulting inflation, so this benefit usually associated with inflation is lost. 6. One way to undestand Coolidge s statement is to think of a govenment that is a net debto in nominal tems to the pivate secto. Let B denote the govenment s outstanding debt measued in U.S. dollas. The debt in eal tems equals B/P, whee P is the pice level. By inceasing inflation, the govenment aises the pice level and educes in eal tems the value of its outstanding debt. In this sense we can say that the govenment epudiates the debt. This only mattes, howeve, when inflation is unexpected. If inflation is expected, people demand a highe nominal inteest ate. Repudiation still occus (i.e., the eal value of the debt still falls when the pice level ises), but it is not at the expense of the holdes of the debt, since they ae compensated with a highe nominal inteest ate. 7. A deflation means a fall in the geneal pice level, which is the same as a ise in the value of money. Unde a gold standad, a ise in the value of money is a ise in the value of gold because money and gold ae in a fixed atio. Theefoe, afte a deflation, an ounce of gold buys moe goods and sevices. This ceates an incentive to look fo new gold deposits and, thus, moe gold is found afte a deflation. 8. An incease in the ate of money gowth leads to an incease in the ate of inflation. Inflation, in tun, causes the nominal inteest ate to ise, which means that the oppotunity cost of holding money inceases. As a esult, eal money balances fall. Since money is pat of wealth, eal wealth also falls. A fall in wealth educes consumption, and, theefoe, inceases saving. The incease in saving leads to an outwad shift of the saving schedule, as in Figue 4 1. This leads to a lowe eal inteest ate. S 1 S 2 Figue 4 1 Real inteest ate 1 2 A B I () Investment, Saving I, S The classical dichotomy states that a change in a nominal vaiable such as inflation does not affect eal vaiables. In this case, the classical dichotomy does not hold; the incease in the ate of inflation leads to a decease in the eal inteest ate. The Fishe effect states that i = + π. In this case, since the eal inteest ate falls, a 1- pecent incease in inflation inceases the nominal inteest ate i by less than 1 pecent.

23 Chapte 4 Money and Inflation 27 Most economists believe that this Mundell Tobin effect is not impotant because eal money balances ae a small faction of wealth. Hence, the impact on saving as illustated in Figue 4 1 is small. 9. The Economist ( is a useful site fo ecent data. [Note: unfotunately, as of this witing (Febuay 2002), you need a paid subsciption to get access to many of the tables online.] Altenatively, the Intenational Monetay Fund has links to county data souces ( follow the links to standads and codes and then to data dissemination). Fo example, in the twelve months ending in Novembe 2001, consume pices in Tukey ose 69 pecent fom a yea ealie, M1 ose 55 pecent while M2 ose 52 pecent, and shot-tem inteest ates wee 54 pecent. By contast, in the United States in the twelve months ending in Decembe 2001, consume pices ose about 2 pecent, M1 ose 8 pecent, M2 ose 14 pecent; and shot-tem inteest ates wee a little unde 2 pecent. These data ae consistent with the theoies in the chapte, in that high-inflation counties have highe ates of money gowth and also highe nominal inteest ates. Moe Poblems and Applications to Chapte 4 1. With constant money gowth at ate µ, the question tells us that the Cagan model implies that p t = m t + γµ. This question daws out the implications of this equation. a. One way to intepet this esult is to eaange to find: m t p t = γµ. That is, eal balances depend on the money gowth ate. As the gowth ate of money ises, eal balances fall. This makes sense in tems of the model in this chapte, since faste money gowth implies faste inflation, which makes it less desiable to hold money balances. b. With unchanged gowth in the money supply, the incease in the level of the money supply m t inceases the pice level p t one-fo-one. c. With unchanged cuent money supply m t, a change in the gowth ate of money µ changes the pice level in the same diection. d. When the cental bank educes the ate of money gowth µ, the pice level will immediately fall. To offset this decline in the pice level, the cental bank can incease the cuent level of the money supply m t, as we found in pat (b). These answes assume that at each point in time, pivate agents expect the gowth ate of money to emain unchanged, so that the change in policy takes them by supise but once it happens, it is completely cedible. A pactical poblem is that the pivate secto might not find it cedible that an incease in the cuent money supply signals a decease in futue money gowth ates. e. If money demand does not depend on the expected ate of inflation, then the pice level changes only when the money supply itself changes. That is, changes in the gowth ate of money µ do not affect the pice level. In pat (d), the cental bank can keep the cuent pice level p t constant simply by keeping the cuent money supply m t constant.