and Where It Goes Questions for Review CHAPTER 3 National Income: Where It Comes From

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1 CHAPTER 3 National Income: Whee It Comes Fom and Whee It Goes Questions fo Review. The factos of poduction and the poduction technology detemine the amount of output an economy can poduce. The 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.. When a fim decides how much of a facto of poduction to hie o demand, 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 pe unit. 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: ΔPofit ΔRevenue ΔCost (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 Δpofit 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 egading how much capital to hie: 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. A Cobb Douglas poduction function function has the fom F(K,L) AK α L α. The text showed that the paamete α gives capital s shae of income. (Since income equals output fo the oveall economy, it is also capital s shae of output.) So if capital eans onefouth of total income, then a 0.5. Hence, F(K,L) AK 0.5 L 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.

2 Answes to Textbook Questions and Poblems 6. Govenment puchases ae a measue of the dolla value of goods and sevices puchased diectly by the govenment. Fo example, the govenment buys missiles and tanks, builds oads, and povides 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. 7. 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. 8. 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. 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. Given a Cobb Douglas poduction function, the incease in the labo foce will incease the maginal poduct of capital and will incease the eal ental pice of capital. With moe wokes, the capital will be used moe intensively and will be moe poductive. 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. Given a Cobb Douglas poduction function, the decease in the capital stock will decease the maginal poduct of labo and will decease the eal wage. With less capital, each woke becomes less poductive. 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. d. High inflation that doubles the nominal wage and the pice level will have no impact on the eal wage. Similaly, high inflation that doubles the nominal ental pice of capital and the pice level will have no impact on the eal ental pice of capital.. a. To find the amount of output poduced, substitute the given values fo labo and land into the poduction function: Y b. Accoding to the text, the fomulas fo the maginal poduct of labo and the maginal poduct of capital (land) ae: MPL ( α)ak α L α MPK αak α L α

3 Chapte 3 National Income: Whee It Comes Fom and Whee It Goes 3 In this poblem, α is 0.5 and A is. Substitute in the given values fo labo and land to find the maginal poduct of labo is 0.5 and maginal poduct of capital (land) is 0.5. We know that the eal wage equals the maginal poduct of labo and the eal ental pice of land equals the maginal poduct of capital (land). c. Labo s shae of the output is given by the maginal poduct of labo times the quantity of labo, o 50. d. The new level of output is e. The new wage is 0.7. The new ental pice of land is f. Labo now eceives 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 scale. 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 the population gows. Fo example, if only 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. But if many wokes build a ca, then each one can specialize in a paticula task and become vey fast at it. 4. a. A Cobb Douglas poduction function has the fom Y AK α L α. The text showed that the maginal poducts fo the Cobb Douglas poduction function ae: MPL ( α)y/l. MPK αy/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 ( α)y/l. Rewiting this: R/P MPK αy/k. (W/P)L MPL L ( α)y. (R/P)K MPK K αy. 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 (o income), which is ( 0.3), and capital eceives 30 pecent of total output (o income). b. To detemine what happens to total output when the labo foce inceases by 0 pecent, conside the fomula fo the Cobb Douglas poduction function: Y AK α L α. Let Y equal the initial value of output and Y equal final output. We know that α 0.3. We also know that labo L inceases by 0 pecent: Y AK 0.3 L 0.7. Y AK 0.3 (.L) 0.7. Note that we multiplied L by. to eflect the 0-pecent incease in the labo foce.

4 4 Answes to Textbook Questions and Poblems To calculate the pecentage change in output, divide Y by Y : Y AK 0.3 (.L) 0.7 Y AK 0.3 L 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 L α. We know that α 0.3. We also know that labo (L) inceases by 0 pecent. Let (R/P) equal the initial value of the ental pice of capital, and (R/P) equal the final ental pice of capital afte the labo foce inceases by 0 pecent. To find (R/P), multiply L by. to eflect the 0-pecent incease in the labo foce: (R/P) 0.3AK 0.7 L 0.7. (R/P) 0.3AK 0.7 (.L) 0.7. The ental pice inceases by the atio (R/P) 0.3AK 0.7 (.L) 0.7 (R/P) 0.3AK 0.7 L 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 ( α)ak α L α. We know that α 0.3. We also know that labo (L) inceases by 0 pecent. Let (W/P) equal the initial value of the eal wage and (W/P) equal the final value of the eal wage. To find (W/P), multiply L by. to eflect the 0-pecent incease in the labo foce: (W/P) ( 0.3)AK 0.3 L 0.3. (W/P) ( 0.3)AK 0.3 (.L) 0.3. To calculate the pecentage change in the eal wage, divide (W/P) by (W/P) : ( W/P) ( 0. 3) AK (. L) ( W/P) ( 0. 3) AK L (.) That is, the eal wage falls by.8 pecent. c. We can use the same logic as in pat (b) to set Y AK 0.3 L 0.7. Y A(.K) 0.3 L 0.7. Theefoe, we have: Y Y A(.K) 0.3 L 0.7 AK 0.3 L 0.7 (.)

5 Chapte 3 National Income: Whee It Comes Fom and Whee It Goes 5 This equation shows that output inceases by about 3 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 in pat (b) fo the change in the eal ental pice of capital: (R/P) 0.3A(.K) 0.7 L 0.7 (R/P) 0.3AK 0.7 L 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. Finally, the change in the eal wage is: (W/P) 0.7A(.K) 0.3 L 0.3 (W/P) 0.7AK 0.3 L 0.3 (.) Hence, eal wages incease by.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: Y (.A)K 0.3 L 0.7 Y AK 0.3 L This equation shows that output inceases by 0 pecent. Similaly, the ental pice of capital and the eal wage also incease by 0 pecent: (R/P) 0.3(.A)K 0.7 L 0.7 (R/P) 0.3AK 0.7 L Labo income is defined as (W/P) (W/P) W P L WL. P Labo s shae of income is defined as 0.7(.A)K 0.3 L AK 0.3 L ÊWLˆ WL Y Ë Á P /. PY If this atio is about constant at, say, a value of 0.7, then it must be the case that W/P 0.7*Y/L. This means that the eal wage is oughly popotional to labo poductivity. Hence, any tend in labo poductivity must be matched by an equal tend in eal wages othewise, labo s shae would deviate fom 0.7. Thus, the fist fact (a constant labo shae) implies the second fact (the tend in eal wages closely tacks the tend in labo poductivity) 6. a. Accoding to the neoclassical theoy, technical pogess that inceases the maginal poduct of fames causes thei eal wage to ise.

6 6 Answes to Textbook Questions and Poblems b. The eal wage fo fames is measued as units of fam output pe woke. The eal wage is W/P F, and this is equal to ($/woke)/($/unit of fam output). c. If the maginal poductivity of babes is unchanged, then thei eal wage is unchanged. d. The eal wage fo babes is measued as haicuts pe woke. The eal wage is W/P B, and this is equal to ($/woke)/($/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. 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 ae the same. Since the maginal poduct of labo fo babes has not changed and the maginal poduct of labo fo fames has isen, the pice of a haicut must have isen elative to the pice of the fam output. If we put it in gowth-ate tems, then the gowth of the fam pice + the gowth of the maginal poduct of the fam labo the gowth of the haicut pice. g. Both goups benefit fom technological pogess in faming. 7. a. The maginal poduct of labo MPL is found by diffeentiating the poduction function with espect to labo: dy MPL dl K /3 H /3 L /3. 3 An incease in human capital will incease the maginal poduct of labo 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: dy MPH dh K /3 L /3 H /3. 3 An incease in human capital will decease the maginal poduct of 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. 3 We can use the same logic to find the human capital shae: ( 3 K /3 L /3 H /3 ) H Human Capital Shae K /3 H /3 L /3, 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.

7 7 Answes to Textbook Questions and Poblems d. The atio of the skilled wage to the unskilled wage is: W skilled W unskilled MPL + MPH MPL K /3 L /3 H / K /3 L /3 H /3 K /3 L /3 H /3 3 L +. H Notice that the atio is always geate than 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. 8. The effect of a govenment tax incease of $00 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] [Y T C(Y T)] + [T G] Y C(Y T) G. a. Public Saving The tax incease causes a -fo- incease in public saving. T inceases by $00 billion and, theefoe, public saving inceases by $00 billion. b. Pivate Saving The incease in taxes deceases disposable income, Y T, by $00 billion. Since the maginal popensity to consume (MPC) is 0.6, consumption falls by 0.6 $00 billion, o $60 billion. Hence, ΔPivate Saving $00b 0.6 ( $00b) $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 $00 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 Y C(Y T) G. The $00 billion tax incease educes disposable income and causes consumption to fall by $60 billion. Since neithe G no Y 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: Y C(Y T) + I() + G. Reaanging, we find Y C(Y T) G I(). The left-hand side of this equation is national saving, so the equation just says that national saving equals investment. Since national saving inceases by $60 billion, investment must also incease by $60 billion. 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- illustates saving and investment as a function of the eal inteest ate.

8 8 Answes to Textbook Questions and Poblems S S Figue 3- Real inteest ate I () 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. 9. 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] [Y T C(Y T)] + [T G]. An incease in consumption deceases pivate saving, so national saving falls. Figue 3- illustates 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 S Figue 3- Real inteest ate I () 0. a. Pivate saving is the amount of disposable income, Y T, that is not consumed: S pivate Y T C 5,000,000 ( (5,000,000)) 750.

9 9 Answes to Textbook Questions and Poblems Public saving is the amount of taxes the govenment has left ove afte it makes its puchases: S public T G,000, Total saving is the sum of pivate saving and public saving: S S pivate + S public 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, 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,000, Thus, S S pivate + S public ( 50) 500. d. Once again the equilibium inteest ate cleas the maket fo loanable funds: S I 500, Solving this equation fo, we find: 0%.. 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] [Y T C(Y T)] + [T G]. We know that Y 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 ΔNational Saving [ ΔT (MPC ( ΔT))] + [ΔT ΔG] [ ΔT + (MPC ΔT)] + 0 (MPC ) ΔT. 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, the smalle is the fall in saving. Fo example, if the MPC equals, then the fall in consumption equals the ise in govenment puchases, so national saving [Y C(Y T) G] is unchanged. The close the MPC is to 0 (and theefoe the lage is the

10 0 Answes to Textbook Questions and Poblems 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, 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 S Figue 3-3 Real inteest ate I (). a. The demand cuve fo business investment shifts out to the ight 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 to the ight since it epesents the sum of business investment, which shifts out to the ight, and esidential investment, which is unchanged. As a esult the eal inteest ate ises as in Figue 3-4. Figue 3-4 S Real inteest ate.... aises the inteest ate. B A. An incease in desied investment... I I 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 movement along the

11 Answes to Textbook Questions and Poblems cuve), wheeas the ightwad shift of the business investment cuve leads business investment to ise by an equal amount. Figue 3-5 shows this change. Note B R B R that I + I I + I S. Figue 3-5 I B I B Business investment I R I R Residential investment 3. 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 by the full amount of the incease in consumption. 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 Real inteest ate Saving S 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 ises by; 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.

12 Answes to Textbook Questions and Poblems S () S () Figue 3-7 Real inteest ate ΔG I() I I 4. a. Figue 3-8 shows the case whee the demand fo loanable funds is stable but the supply of funds (the saving schedule) fluctuates pehaps eflecting tempoay shocks to income, changes in govenment spending, o changes in consume confidence. In this case, when inteest ates fall, investment ises; when inteest ates ise, investment falls. We would expect a negative coelation between investment and inteest ates. S () S () Figue 3-8 Real inteest ate I() b. Figue 3-9 shows the case whee the supply of loanable funds (saving) is stable, wheeas the demand fo loanable funds fluctuates, pehaps eflecting changes in fims expectations about the maginal poduct of capital. We would now find a positive coelation between investment and the inteest ate when demand fo funds ises, this pushes up the inteest ate, so we see investment incease and the eal inteest ate incease at the same time.

13 3 Answes to Textbook Questions and Poblems S() Figue 3-9 Real inteest ate I () () I c. If both cuves shift, we might geneate a scatte plot as in Figue 3-0, whee 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 clea elationship between investment and inteest ates. S () S () Figue 3-0 Real inteest ate A B D C I () I () d. Situation (c) seems faily easonable both the supply of and demand fo loanable funds fluctuate ove time in esponse to changes in the economy.