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Answers to Textbook Questions and Problems
CHAPTER 1 The Science of Macroeconomics
‘Questions for Review
1. Microeconomics isthe study of how individual firms and households make decisions, and how they
interact with one anoher. Microeconomic models of fms and households are based on principles of
‘optimization firms and households do the bes they can given the constraints they face. For example,
houscholds choose which goods to purchase inorder to maximize thei utility, whereas fms decide
how much to preduce inorder to maximize profs. In contrat, macroeconomics ste study ofthe
‘economy a+ a whole; focuses on fesoes sch a how total output, otal employment, andthe overall
price level are determined. These economyewide variables are based onthe intcrcton of many
Fouscholds and many firms; therefore, microeconomics forms the basis for macroeconomics.
2 Economists build models a a means of summarizing the relationships among economic variables.
“Models are wef because they abstract fromthe many details inthe economy and allow one to focus
‘on the mast important economic connections.
3. A market clearing model is one in which prices adjust to equilibrate supply and demand, Market-
‘clearing models are useful i situations where prices are leuble. Yet in many stations, exible
‘prices may not be a realistic assumption. For example, labor contracts fen st wages for up othe
‘ears Or, fms such as magazine publishers change tei prices only every thre to four years. Most
‘macroeconomists belive tht price Hexblity is a easonabe assumption for staying long-run issues.
‘Over the long run, pices respond to changes in demand or supply, eventhough inthe shor run they
may be slow to adjust
Problems and Applications
1. Monetary policy inthe United States and the European Union hasbeen 2 hig topic of conversation in
‘early 2018. The EU embarked upon a quantitative easing policy in March 2018 in an attempt to
Srulat growth and prevent deflation. There has been some concer at the inflation rate a Europe
will tun negative In the Unite States, thee is continued discussion and speculation concerning when
‘the Federal Reserve might choose to increase the aret federal funds rate. Also inthe United Stats,
‘he unemployment rte has declined to about 5.5 percent and this izessts that wages may begin to
inrease. The Federal Reserve willbe watching for wage and pice increases as they decide when to
2. Many philosophers of scence believe that the defining characteristic of scence i the use of the
scientific method of inquiry fo establish table relationships. Scientists examine data, often provided by
controled experiments. to support or disprove a hypothesis. Economists are more limited in their use
‘of experiments. They cannot conduct controled experiments onthe economy: they must ely onthe
natural course of developments inthe economy to collet data. To the extent that economists use the
scientific method of inquiry that, developing hypotheses and testing them, economics has the
Shuracteristics of science
3. Wecan use simple variant ofthe supply-and-demand model for piza to answer this question.
Assume that the quantity of ice cream demanded depends not ool onthe pie of ice eam and
income, but also on the price of fazen yogurt:
= DP. Pry.D-
We expect that demand for icecream rss when the price of fozen yogurt ries, because ice cream
and frozen yogurt are substitutes. Thats, when the price of frozen yout goes up, I consume less of it
and, instead, fulfill move of my frozen dessert urges through the consumption of ice ream.
Chapter ‘The next part of the model isthe supply function for ice eeamn, "= {Px Finally,
‘equilibrium, spply must equal demand, 0 that "= QF Y and Pry ae the exogenous variables, and
‘and Pc ae the endogenous variables. Figure 1-1 uses this model to show that afl in the pice of
fforca yogurt result n an inward sift of the demand curve frie eam. The new equilitrium has a
lower price and quantity of icecream,
Figure 11
Pe
Price ofice cream
Quantity fee
4. The price of haircuts changes rather infequemty. Prom casual observation, bartyliss tend o charge
the sme price over a one- or two-year period irrespective ofthe demand fo baits or the supply of
caters. A market-clearing model for analyzing the market for hates has the unrealistic assumption
of flexible prices. Such an assumption is unrealistic in the short run when we observe that prises are
ingexible. Over the long run, however, te price of haircuts does tend wo adjust; a market-cearing
‘models therefore appropriate
(Chapter The Science of Macrocconemics Answers to Textbook Questions and Problems
CHAPTER2 The Data of Macrocconomics
‘Questions for Review
1. GDP measures the total income earned from te production ofthe new final goods and services in the
‘economy, andi measures the tal expenditures on the new final goods and services produced in the
conomy. GDP can measure two things at once because the total expenditures onthe new final goods
Sn services by the buyers ms be equ 0 the income eared by the sller ofthe new ital goods ad
services As the cvcula flow diagram inthe tet illustrates, then are allemative, equivalent ways of
‘measuring the flow of dollars in the economy.
2 The four components of GDP are consumption, iavestment, government purchases, and net exports
“The consumption category of GDP consists of household expenditures on new final goods and services,
suchas the purchase ofa now television, The investment category of GDP consists of business fixed
Investment, residential fixed investment and inventry investment. When a business Buys BW
quipment his counts as investment. Government purchases consists of purchases af 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 serves solo other countries minus the value of goods
and services foreigners sel us. When te US, sll com to foreign countries, t counts in the met export
category of GDP.
3. The consumer price index (CP!) measures the overall level of pices inthe ecoosny. It tll us the
Price of fixed basket of goods relative to the price ofthe same basket in the base yea. The GDP
{deflator isthe ratio of nominal GDP to eal GDP in given year. The GDP deflator measures the prices
‘ofall goods and services produced, whereas the CP only measures prices of goods and services
bought by consumers. The GDP deflator includes only domestically produced goods, whereas the
Includes domestic and foreign goods bought by consumcs.Fnaly, the CP sa Laspeyres index that
sign fixed weights othe pies of different goods, whereas the GDP deflator ia Pasche index that
‘signs changing weights othe pices of diferent goods In prctce,the two price indices tend to
‘move together and do nt often diverge.
4. The CPI measures the price ofa fixed basket of goods relative othe pice ofthe same basket inthe
‘base ear. The PCE defstor isthe ratio of aominal consumer spending wo real consumer spending. The
(CPI and the PCE deflator are similar in that they both only include the prices of goods purchased by
‘consumes, and they bath include te price of impor goods as well x domestically produced goods.
‘The two measures difer becuse the CP! measures th change inthe price ofa fixed baskot whereas
‘the goods measured by the PCE deflator change from year o year depending oa What consumers are
purchasing in that particular yea.
‘5. The Bureau of Labor Statistics (BLS) classifies each person into one ofthe flowing tre categorie:
“employed, unemployed, or nat inthe labor fore. The unemployment ae, which ithe percentage of
the labor force that is unemployed, s computed a follows:
‘Note that the labor foes the numberof poople employed plus the numberof people unemployed.
{6 Every month the Bureau of Labor Stasis undertakes two surveys to measure employment Fist, the
[BLS surveys about 60,000 houschols and thereby obtains an estimate ofthe share of people who say
they are working. The BLS mauliplies this share by an estimate ofthe population to estimate the
‘numberof poople working. Second, the BLS surveys about 160,000 busines establishments and asks
Sow many peopl thy employ. Each say singers the two mass of employment ot
(Chapter 2—The Data of Macrocconamics 3 Problems and Applications
1. From the main bea gov Web page click onthe interactive data tab atthe tp, select GDP, begin using
‘the data, section I, and then ble 11.1. Real GDP grew at arate of 22 percent in quarter 4 of 2014
When compared to growth rates of 21 percent, 4 percent. and S percent forthe fs thee
of 2014, te rats of 32 prcont was slightly below average. From the main bis gov Web page select the
uta tons tab, then op picks. Check the box for the unemployment rat and etreve the data. The
‘unemployment atin March 2015 was 5.5 percent, which was about equal to de natural ate of |
‘unemployment ofthe long run average rate From he mai bls go page sclect the economic releases
tab then inflaton and pices. Access the report forthe CPL. In February 2015, the inflaton rate forall
items was 0 percent, and if food and energy were excluded the rate was 1.7 percent, The ination rate
‘was below average and below the Federal Reserve's target of? percent.
2 Value added by each person is equal othe value ofthe good produced minus the amount the person
i forthe materials need to make the good, Therefore, the value added by the farmer i SOO ($1 —
(01), The value added by th miler i $2: she sells the Nour tthe baker fr S3 bt paid 1 forthe
flour. The vale aed by the baker is S3: she sls the bread to the engineer for Sb pa he miller
3 forthe Nour. GDP isthe total value add, oF $1 + $2 + $3 Sb. Note that GDP equals the value of
‘the final good (the bread)
3. When a woman mais her bur. GDP fllsby the amount of the butlers salary. This happens
‘because GDP menses tot income, snd therefore GDP, falls by the amount of the bates oso
salary. IFGDP truly measures the value ofall gods and services, then the martiage would not affect
GDP since the total amount of economic activity is unchanged. Actual GDP, however, is am imperfect
‘mesure of economic activity because the vale of some goods and services is lef out Once the
butle's work becomes par of his houschold chores, his services are o longer counted ia GDP. As this
example illustrates, GDP does at inchde the value of any output produced nthe home
4. Thesilane sold tothe US. Ai Forse counts as goverment purchases cause the Ai Fore is
tof the government
1 Theale sold o American Aiines counts nvcsiment beac ti cpt god sod ta
at em
«= Theaplae sold to Air France counts san export bcs ti sold oa fosignr.
‘4. The aiplae sold to Amelia Eahart count a consumption Because ts sd wa private
Individual
‘© Thealmplane ul tobe sold nox yea counts a investment. tn particular, the aplane i counted
a veo investment, which s where gods that are produc in one Year and sold in nother
rae counted.
‘5. Data on pars (a 1 () can be downloaded from the Bares of Esnomic Analysis. Go tthe bn gov
Website ck on the nteractive data abt the top selet GDP, hep using te da, Seton Ian
then bie 1.1.5. Choose the "manil the a” option ose te year you in which you ae
interested. By diving exch component (2) (0 by nominal GDP and mulplyngby TOP, we obtain
the flowing percentages
e “
3 Pesoml consumption expendires 40% 61.3% 68.5%
1 Gross privatedamestc investment IKE IKS% 16.49%
© Government consumption purchases 169% 206% 182%
4d Netexpors 02% 05% 3%
«National defense purchases 16% 639% 4a
{lmpons___39% 103% _16.3%
(Nets: The above data was dowaloaded April 3, 2015, fom the BEA Web site)
Among oer things, we observe the following trends inthe economy over the period 1950-2015:
‘2 Personal consumption expenditures have been around two-thirds of GDP between 1980 and 2015.
The share of GDP going to gross private domestic investment remained fly steady.
(Chapter 2—The Data of Macrocconamics 4 ‘The share gong to goverment consumption purchases rose sharply from 1950 t 1980.
[Net exports which were postive in 1980, have Been negative since that ie.
‘The shar gong to national defense purchases has fallen
Imports have grown rapidly relative to GDP.
npas
(GDP measures the valu of the final goods and services produce, oF S1,000,00.
[NNP is equal to GNP minus depreciation. In this example, GDP is equal to GNP because there are
‘foreign wansactions. Therefore, NNP is equal to $875,000.
‘National income is equal to NNP. or $875,000.
Enployee compensation is equal to $600,000.
Proprietors” income measures the income ofthe owner, and is equa 0 150,000.
(Corporate profits equal o corporate taxes pls dividends plus retained earnings, o $275 00.
‘Retined earings calculated as sles mics wages minus dividends minus depreciation minus
corporate tax, 0 $75, 00.
‘Personal income is equal to employee compensation plus dividends $750,000
Disposable personal income is perso income minis axes, or $830,000.
nres
re
7. i Nominal GDP is the ttl value of goods and services measure at cuent prices. Therefore,
(Pat * Orta) * (Pe * Cea)
m2 30) +53 «30
=o St
=Si.00.
‘Nominal GDP 201s ~ (PS, xOR) (Pane xO)
St 350) (54500)
[Stn $2000
T3000.
[Nominal CDP x6
{i Real GDP isthe total vale of goods and services measured at constant prices. Therefore to
¢aleulte real GDP in 2015 (with base year 2010), multiply the quantities purchased i the
eae 2015 by the 2010 prices:
Real ODPas = (P28 xO8,) (PEE *OZS.)
= (52250) +83 500)
#3500 + $1500
=52,000,
‘Real GDP for 2010 is calculatod by muliplyng the quate in 2010 bythe prices in 2010.
Since the base yar is 2010, real GDP equals nominal GDPas, whichis $10,00. Hence,
‘eal GDP increased betwosn 2010 and 2015,
ii. The implicit rice deflator for GDP compares the curent ries ofall goods and services
prsiuced tothe prices ofthe same goods and services ina bse year Itiscalulted as
follows
Nominal GDP,
ict Price Deaton =
‘ow Real GDP,
Using the values for Nominal GDP. and real GDP gs calculated above:
Implicit Price Deflstorsns ~ $2208
(Chapter 2—The Data of Macrocconamics s =150
“This calculation evel that pices of the gous produced i the year 2015 increased by 80 percent
conga othe pcs dat the godin he comnts frin 2010 (Because 2010 sth ase ea he
‘alu otic pce defor he year 2010 LObecase noni and eal GDP ate sae fr
the bse year}
fx. Tee consumer pice index (CP) measures the evel of pices inthe ecomomy. The CP is
called a fixedeneiht index becaze es fxd bask of gods Over ime to weight ese.
Ife bas year 2010 the CPT i 2018s measuring the cost ofthe bk 2018 eave
the cost in 2010. The CPlns i calcula follows:
OO) PG)
Eas) as Grnn)
sino
‘0,000,000
=16.
Phas =
“This calculation shows thatthe price of goods purchased in 2015 increased by 60 percent
compared tothe prices these goods would bave sold for in 2010. The CPI for 2010, the base
year, qual 1.0,
1b. The implicit price deflator is a Paasche index becaue it is computed with a changing basket of
goods; the CPlis a Laspeyres index because its computed with a fixed basket of goods From
(Gras) the plicit price deflator forthe year 2015 i150, which indicates that pices rose by SO
Percent from what they were i the year 2010, From (7), the CPL forthe year 2015 i818,
‘which indicates that peices rose by 60 percent fom what they were in the year 2010.
prices ofall goods rose by, fr example, 80 percent, then one could say unambiguously tht
the price eve rose by 50 percent Yet, nour example, relative prices have changed. The price of
hotdogs ose by 1020 percent: the price of hamburgers rose by 33.3 percent, making hamburgers
relatively less
‘Aste discrepancy between the CPL andthe implicit price deflator illustrates, the change in
the price level depends on bow the goods prices are weighted. Th CPI weights the price of goods
by the quantities purchased inthe yea 2010. The implicit price deflator weight the price of goods
‘by the quantities purchaned inthe yea 2015. Since the quantity ofthe two goods was the same
2010, the CP spacing equal weight on the two price changes. In 2015, he quantity of
Jhamburger was fice a lage as ot dogs, 30 thee is ice ax uch weight placed onthe
‘hamburger price relative othe hot dog price For this reason, the CP shows larger inflation rate
= more weigh i placed onthe good with the larger price increase.
a. Theconsumer price index uses the consumption bundle in yea 0 figure out how mach weight
to put on the price ofa given good:
ce = (2210) (800)
(61x10) (820)
a an
(Peas O4) (Pn Orn)
~
Acconting tothe CP, prices have double.
(Chapter 2—The Data of Macrocconamics 6 Nominal spending i the total valu of output produced in each yea. In year 1 and year 2, Abby
‘bays 10 apples for SI each, o he nominal spending remains constant a $10, For example,
Nomina Spendings = (x02) (Pag*Oena)
(82 +0) 1 «10,
=si0
Real spending isthe total value of output predced in cach yer valued atthe pics prevailing in
year I In year I the base year, hr real spending cquals her nominal spending of S10. In year 2,
‘he consumes 10 green apps that are cach vad at thei year | price of $2, 0 er real spending
is $20. That is,
Real Spenings = (PO) («Oh n)
=(S1 x0) (82 10)
=30,
Hence, Abby's eal spending rises fram $10 10 $20,
‘The implicit price deflator is cleulsted by dividing Abby's nominal spending in year 2 by her eal
spending that year:
Imp Pie Der, » Noni Seed,
wal speig,
03,
‘Thus, the implicit price deflator suggests that prices have fallen by half The reason fo thsi that
the deflator estimates how much Abby values her apples using prices prevailing in year I. From
this perspective green apples appear very valuable In year 2, when Abby consumes 10 green
apples, appears hat her consumption has inereased horas the deflator vale gree apes
‘ore highly than red apples. The oaly way she could sl be spending $10 ona higher
‘consumption bundle ifthe price ofthe good she was consuming fl,
Abby thinks of ed apple and green apples as perfect substimtcs, then the cos of living inthis
‘conomty as not changed—in ciber yar it cos $10 to consume iO apples. According othe CP,
hhowever, the cost of living bas doubled. This s because the CPI only takes into account the fact
thatthe ed apple pic has doubled the CP ignores the fll inthe price of gree apples because
they were aot inthe consumption bundle in year I. In contrast tothe CPI. the implicit price
L andthe rotwrn to capital, MPK'x K. Thats, under constant returns to seal, economic profit
4. A Cobb-Douglas production function has the form FUK.L)= AK"L!~ The text showed thatthe
parameter a gives capital's share of income. So if capital ears one-fourth of total income, then =
(025. Hence, FUL) = AKL.
‘5. Consumption depends posively on disposable income—ie. the amount of acome afterall axes have
been pat. Higher disponabe income means higher consumption.
"The quantity of investment goods demanded depends negatively onthe real interest rate. For an
‘avesment 1g be profitable, s return muse greater than is cost. Because the real interest ae
‘measures the cost of funds, a higher eal interest rate makes it more costly to invest, so the demand for
investment goods fall.
(Chapter 3—Nationl Income: Where It Comes From and Where It Goes 9 {6 Government purchases ae a measure ofthe value of goods and service purchased directly bythe
_governmont For example, the government buys missles and tanks, buds roads, an provides services
Such as ar traffic contol. Al ofthese activities ae part of GDP. Transfer payments are government
Payments to individuals that are notin exchange for goods or services. Thy are the oppoit of tas
{axes rice housebld disposable income, wheras transfer payments increase. Examples of transfor
ym ile Sov Sent pj othe ly tennessee vas
7. Consumption, investment, and government purchases determine demand forthe esonomy'seutput,
whereas the factors of production and the production function determine the supply of outpt. The eal
‘trent rate adjust core tht the demand forthe cen)» gool uals the supply At he
cular intrest ate, the detnand for goods an crvicen equals the upp
When te government increases taxes, disposable income falls and therefore consumption fll 28 wll
‘The decreae consumption equals the amount that axes increase mulupied by the marginal
‘propensity to consume (MPC). The higher the MPC is, the greater isthe negative effect of the tax
{nctease on consumption. Because out is fined by the factors of production and the prodction
‘cchnolngy and goverment purchases have not changed, the docrese in consumption mast be oft
by an increase in invesment. Fr investment to ss the real intrest at must fall. Therefor, a ax
increas leads toa decrease in consumption am increase in investment anda fallin the fel iterest
Problems and Applications
La According tthe negclassical theory of distribution, the real wage equals the marginal product of
labor: Because of diminishing returs to labor, an increase in the labor force causes the marginal
‘product oflabor ofall Hence, the eal wage falls
Given a Cobb-Douglas production function, the increas inthe labor Force will increase the
‘marginal prc of eaptal and wil increase the eal ental price of capital. With more worksrs,
the capital willbe used more intensively and willbe more productive
The real rental price equals the marginal product of capital. fan earthquake destroys some ofthe
capital stock (yet miraculously doesnot il anyone and lower the labor fore) the marginal
Product of eapital rises ad, hence, the real rental pice rises.
Given a Cobb-Douglas production function, the decrease inthe capital stock wil decrease the
‘marginal product of labor and will ocrease the real wage. With les capital, each worker bocomss
less prodactive.
© Ifa technological advance improves the production funtion this is likly to increase the marginal
‘products ofboth capital and labor. Hence, the real wage andthe real rental pice bath increase
‘4. High inflaton that doubles th nomial wage and the price level wil have no impact onthe real
‘wage. Similarly, high inflaton that doubles the nominal rental price of eapital and the price level
‘sill have no impact on the real rental price of capital.
“To find the amount of output prodaced, subsite the given values fr labor and and ino the
reduction function:
Y= 1018510085 = 100,
16 According to the txt, the formulas forthe marginal product of labor and the marginal product of
capital (and are:
(Chapter 3—Nationl Income: Where It Comes From and Where It Goes 10 4
In this problem, i 0.5 and i 1. Subsite inthe given ales for Iabor and and to ind the
‘marginal product of labor is 0.8 and marginal podoct of capital nd) i 0. We know that the
‘eal wage equals the marginal product of labor and te el rental price of land equals the marginal
‘product ofepital (and).
Labor's share ofthe output is given by the marginal product of labor tines the quant of labor, oF
0.
4. The now level of outpt i 70.7
‘&Thenew wage 0.71. The new renal price of ands 035.
{Labor now receives 35:36.
A production function has decreasing fetums io scale ifan equal percentage increase in all fetes of
production leads wa smaller percentage increase in outpu. For example if we double the amounts of
‘apal and laber ouput increases by les than double thn the prodiction function has decreasing
‘etums to scale. The may happen fhe sa ied factor such sland inthe production function and
‘this fixed factor becomes scarce asthe economy grows argc.
‘A production function has increasing returns to eae if an equal percentage increase in all factors
lof production leads to larger percentage increase i op. For example if doubling the amount of
‘capital and labor inreases the outpat by more than double. then the production function has increasing
‘etums to sale. This may happen if specialization of labor becomes greater asthe popalaton grows.
For example, if nly one worker builds aca, then it takes him along tne because he ast lara
‘mary different sill and be must constantly change tasks and tol. But f many worker Build 3 car,
then each one can specialize in a particular ask ad become more prouctive-
4A Cobb-Douglas production Function has the form Y= AA™L. The text showed that the marginal
products forthe Cobb-Douglas production function are
MPL=(1~ayYA.
MPK~a¥Kk
Compctitve proit-marimiring firms hire labor until its marginal product equals the real wage,
and hire capital unis marginal product equals the real rental rate Using these facts and the
shove marginal products forthe Cobb-Douglas reduction function, we find:
W/P = MPL=(\ =a).
RP = MPK= ak.
Resting his
(17P)L= MPLxL=(1~a)¥.
(RPK =MPKxK=aY.
‘Not that he terms (7P\. and (R/P\K ae the wage bill and total return to capita, respectively
Given thatthe value of a= 0.3 thon the above formulas indicts that labor receives 70 porcet of
‘oul output (or income) and capital ocsives 30 percent of total ouput (r incom).
To determine what happens total output when the labor force increases by 10 percent, consider
the formula forthe Cobb-Douglas production function:
Yo ane
(Chapter 3—Nationl Income: Where It Comes From and Where It Goes u Let ¥ equal the initial vale of output and Ys equal fina ouput, We know that a= 03. We also
‘know tat labor L increases by 10 percent
Yinka
Ye AKOILILP?,
[Note that we muiptied by 1.1 o reflect the 10-percent increase inthe labor fre.
‘To caleulate the percontage change in output, divide Y= by
akan
3
ur
9.
‘at cnt ee by 69 pon
"To determine how the increase in the Ibor force affects the rental price of espital, consider
the formula forthe eal rental price of eaptal UP
RP = MPR ak,
‘We know that «= 0.3. We also know that labor () increases by 10 percent. Let (A/F) equal the
initial vale ofthe rental price of capital, and let (AZP)s equal the final renal price of capital after
the labor free increases by 10 percent. To find (RP), aulipy L by 1.1 to eet the 1O-percent
increase inthe abo force:
(RiP) = 034K7L
(RiP) = 034K*(1.1L)
‘The renal rice increase by the aio
Rip), osak (Lu)
(air), aR
(Ay
L069
So the rental price increases by 6.9 percent. To determine how the increas inthe labor force
affects the eal wage, consider the formula for the real wage W/P:
W/P = MPL =(\ asl
‘We know that «03. We also know that Iabor (L) increases by 10 percent Let (9/P) ua the
inal value ofthe real wage, and let (W/P)z equal the final value ofthe real wage. To find (W/P)s,
‘multiply Ly 1.11 reflect the 10sprcent increase i the labor force:
wey =
wey =(
03yaKer,
0.3 )AK%1 ILE
‘To caleulte the percentage change inthe real wage divide (W/P)s by (WIP):
(Chapter National Income: Wher It Comes From and Wher It Goes 2 wie), (0 ospaxe(uiz)
wir), (0 03yan"
()"
oon
‘Thats the eal wage fi by 28 percent
= Weean use the same logic asin part (6) 1 et
Yaak,
Yea thL,
‘Therefore, we have:
x a(tiky
aK
t
1029
‘This equation shows that output increases by about 3 percent. Notice hata <0.S means that
‘roportional increases to capital wil increase output by less than the same proportional increase 1
labor.
‘Again using the same logic sin part () forthe change in the real rental price of capital:
RiP), osa(tany*”
(er), 0saK
uy"
ons
‘The real rental price of epital falls by 65 percent because thee are diminishing returns to capitals
‘hat when capita ncremcs, st marginal proc alls
Fly, the change i the real wage
wer), ora(uany ns
wir), ora
(uy
L029
Hence real wages increase by 29 percent because the added capital increases the marginal
productivity ofthe existing worker. (Notice that the wage ad output have bath increased by the
Same amount, leaving the labor share unchanged a feature of Cobb-Douglas tchnologies)
‘4. Using the same formal, we find that the change in opti
hdr
ee
(Chapter Notional Income: Where t Comes From and Where It Goes B ‘This equation shows hat out increases by 10 percent, Simla, the rental pice of pital and
there wage ao ineease by 10 percent
(RP), oxnayaere”
(er, 034K
u
(rrr), onuaaynrne
win,
‘Labor income is defined as
For example if this ati is about constant ata value of 0.7, then the value of W1P'= 0.7 VIL. This
‘means thatthe real wage is roughly proportional to labor productivity Hence, any trend in labor
productivity must be matched by an equal trend in eal wages. Otherwise, labor’ share would deviate
{rom 0.7. Thus, the fist fact (a constant labor share) impli the second fact (the rend in eal wages
lossy tacks the rend in Inbor prodctiviy).
6. a. Nominal wages are measured as dollars per hour worked Prices are measured a dollars per unit
produced (ether a haieut or a unit of farm output). Marginal productivity is measured a wits of
‘output produced per hour worked.
1 According to the nooclsscal hoor, technical progress that increases the marginal product of
farmers etuses thew real wage to ric. The veal wage for fmers ix peasured ss unite of fe
‘output per hou woeked. The real wage is W7P,, and thsi equal to (Sthour wocked (Shit of
‘am output).
‘© Ifthe marginal productivity of barbers is unchanged, then their el wage is unchanged. The real
‘wage for barbers is measured as haircuts per hour worked. The real wage is W7Pr, and this
‘oq to (Sthour worked MSsircut).
14. If workers can move icly between being farmers and being barbers, then they must be pid the
same wage Win each sector.
Ifthe nominal wage isthe 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 10
‘he price of farm goods, We know that 17P = MPL so that W= Px MPL This mans tht
PeMPLy PulfPLy, given thatthe nominal wages are the same. Since the marginal produc of
labor fr barbers fas not changed andthe marginal produto labor fr farmers has rin the price
a aircut ast have rion eave othe pie ofthe frm output If we expres thisin growth
‘ate tr, then the growth ofthe fan rive * the growth ofthe marginal product ofthe fa
Tabor the growth of the hate price.
The farmers and the barbers are equally well eff alr the technoloyical progres ia farming given
(Chapter 3—Nationl Income: Where It Comes From and Where It Goes “ 2
‘the assumption that abo sficely mobile between the two sectors ad oth fy of people
‘ona the same basket of goods. Given thatthe nominal wage ends up equal foreach ype of
‘worker and that they pay the sare pices fo inal goods, they are equally well in tems of what
‘hey can buy with their nominal income. The real wage isa measure of how many unite of ouput
are produced per work. Technological progress in farming increased the units of farm out
‘reduced per hour worked. Movernent of labor between sectors then equalized the nominal wage.
‘2 The marginal product of labor (MPL) i found by diferentiting the production function with
respect to labor:
Mr
a.
lyeigaim
‘An increase inhuman capital wil increase the marginal product of labor because more human
capital makes al the exiting labor more productive.
The marginal product of human capital (MPI found by difereatiting the production function
‘with respect human capital
a
wen
at
ena
‘An increase inhuman capital wil decrease the marginal product of human capital Because there
se diminiahing reurs.
{& The labor share of ouput isthe proportion of output that goes to labor. The total amount of output
that goes t aor s the cl wage (which, under perfect competition, equals the marginal prodact
of labor times the quantity of labor. This quan is divided by the total amount of ouput 6
‘ompute the labor share:
Lato sare GEHL
Ure
4
3
‘We can use the same logo find he human capil shar:
Geen \n
Kou?
‘human Capital Share
1
3
se labor gets one-third ofthe cups, and human capital ges one-shird ofthe Outpt Since workers
‘own thei human capital (we hope!) it will appear that labor gets two-thirds of cup.
‘4. The ati ofthe sie wage tthe mailed wage ie:
(Chapter 3—Nationl Income: Where It Comes From and Where It Goes is aera
‘Notice that tho ratio is always greater than | because sillod workers get pad more than unskilled
wworkars. Also, whe increases this ratio falls Bocause the diminishing fetus o human capital
Tower its uum, while atthe same time inreasing the marginal product of unskilled worksrs
€Ifmore colleges provide scholarships, it willierease H, and it does lad toa more egalitarian
society. The policy lowers the returns o education, decreasing the gap between the wages of more
and less educated workers. More importa, the policy even raises the absolute wape of unskilled
‘worker became tow arginal product se when the numberof silled workers Fes
The effect ofa government tx increase of $100 bilion o (a) public saving, (b) private saving, and (c)
rational saving can be analyzed by using the following relationships
‘Nationa Saving = [Private Saving] + [Public Saving}
=U-T-ay= N+ (=a
rY-ar-0)=6.
|. Publie Saving—The tax increase cases 8 I-fr- increase in public saving. Tinereases by $100
billion and, therefore, public saving increases by $100 bilicn.
b. Private Saving—The increase in taxes decreases disposable income, ¥~T, by 100 billion. Since
‘he marginal propensity to consume (MPC) is 0.6, coasumpsion falls by 0.6 x $100 bilion or $60
billion. Hence,
_APrivate Saving =-$100b ~ 0,6 ($1008) =-S40b,
Private saving falls $40 billion
Nationa Saving-—Because national saving isthe sum of private and public saving. we can
‘conclude thatthe $100 billion tax increase lads 4 2 $60 Pilon increne in national saving.
"Another way to ace thin shy aig the third equation for ational wving expressed above,
‘hat national saving equals Y~C(Y~ 1)~C. The $100 billion ax inrease reduces disposable
‘income and causes consumption to fal by S60 billion. Sine nether G nor Y changes, atonal
saving thus ses by $60 billion.
| Investiment—To detrine the effect ofthe tax increase on investment, reall be national
scvounte deny:
yeqr-n+na+6.
Rexranging, we find
yeav=n-G=10,
‘Thee ideo tis eqpaton a national saving, othe epation ut tha ational saving
resent Siace national eving crocs by SoD bin, ivestnent test once
qual
Sco lion
ow docs his increase in investment tak plac? We know that mesimt depends ome
(Chapter National Income: Wher t Comes From and Where It Goes 6 ‘eal nterest rate, For investment 10 ris, the real ntret rate mus fall
and investment asa faction of the real intrest ate
‘The tx increase causes ational saving 1 ris, so the supply curve for loanablefands shifts to
the ight. The equirium real intrest ate falls, and investment rics.
9. If consumers increase the amount that they consume today then private saving and, therefore, national
saving wil al. We know this frm te dfition of national saving:
[National Saving. = [Private Saving] + [Pubic Saving]
= -T-C9-)+(7-G
‘An increase in consumption decreases private saving, so ational saving falls
igure 3-2 lustats saving and investment aa function ofthe rel interes rte. I national
saving decreas, the supply curv for loanable funds shifts othe left thereby rising the real ncrest
{te and reducing investment.
' 5% 5 Pew 2
10, a. Private saving isthe amount of disposable income, YT; tha snot consumed:
nme wy-7-C
= 8.000 ~ 2,000 ~ [1,000 + (2/38,.000~2,000))
= 1000.
Prblic saving isthe amount of taxes the governments lf ver afer it makes its purchases:
(Chapter 3—National Income: Wher It Comes From and Where It Goes ” we er
=2,000-2,500
00,
‘Navona saving isthe sum of private saving and public saving?
a gyre + gate
000 + (500)
= 500,
1b. The equilibrium intrest ate the valve of that clears the market for leanable funds. We leady
‘know that rational saving is S00, so we jst ned io set it equal iavestnent:
sont =r
S00 =1200- 100
Solving thi equation for, we ind
Pe 007 0%.
‘= When he goverment increases its spending private saving remains the same as before (etce
that G does not appear in the °™* equation above) while government saving decreases. Putting
the new Gino the equations above:
Thus,
etn gyms gate
= 1,000 + (0)
= 1,000
‘4. Once agin the equilibrium interest rat clears the market for loanable funds:
—
1.000 =1,200~ 100
‘Solving this equation for r, we find
r= 0.02 02%.
To determine the effect on investment of an equal inereas in both taxes and government spending,
‘onside the national acome accounts went Toe national ng
[National Saving. = [Private Saving] + [Public Saving]
=(Y-7- C=) + 17-4}
Weknow that Yi fxd by the factors of production. We also know thatthe change in consumption
gun the marin pops 1 conse (MPC) tins change a dpoble cme. Tiel ws
‘ANational Saving = (-A7— [MPC x (~ AT} +[47~ AG]
=P ars (uc an)+0
(Chapter 3—Nationl Income: Wher It Comes From and Where It Goes is = wpe) ar.
‘The shove expression ells us that the impoct on national saving ofan equal increase in T and G
depends onthe size of the marginal propensity to consume. The closer the MPC isto the smaller s
‘the fallin saving. For example ifthe MPC equals then the fall in consumption equals the sen
{goverament purchases, so mtional saving [Y~C(Y~7)~ G]is unchanged. The close the MPC isto 0
(Gad therefore the ager ete amount saved rather than spent fora one-dollar change in disposable
income), the greater is the impact on saving. Because we assume thatthe MPCis less than I, we
expect tht national saving falls in response to an equal ineease in axes and government spending.
‘The reduction in saving means tht the supply of loanable funds curve will shift to the le in
Figure 33. The real interest rate rises, and investment falls.
ewes
12, a The demand curve for business investment shifts out othe right because the subsidy increases the
‘umber of profitable ivestment appornte for any given interes rie. The demand curve for
‘residential vestment remains unchanged.
The total demand curve for investment inthe economy shifts out to the right since it represents the
‘sum of business investment, which shifts cut to the right. and residential investment, whichis
‘unchanged. As a esl the real interest rate rises as in Figure 34
ree
(Chapter 3—National Income: Wher It Comes From and Where It Goes 9 13, Inthis chapter, we concluded that an increase in government expenditures reduces national saving and
‘aises the interest rat. The increase in government expenditure therefore crowds out investment by the
{ull amount of the increase. Similarly. atx cu increases disposable income and hence consumption.
“This increase in consumption tanslats int afl ia national saving, andthe increase in consumption
‘crowds out investment by the full amount ofthe increas.
‘if consumprion depends onthe intrest rat, thea saving will also depend on it.The higher he
meres rate, the greater the retur wo saving. Heace it seoms reasonable to think hat an increase in the
eat at mph cee ving and ecm Fg hw ving an eg
7 Meena
so
(Consider what happens when government purchases increase. At any given level of he iterest
‘te, atonal saving falls bythe change in government purchases, a shown in Figure 3-7. The figure
shows that if the saving function slopes upward investment fll by les than the amount that
‘government purchases rises by. This happens because consumption flls and saving increases in
Fesponse to the higher interest rate. Hence the more responsive consumption is othe interest ate, the
Jess investment i rowded ou by goverment purchases.
o 80) yn Meme
(Chapter 3—National Income: Wher It Comes From and Where It Goes » 1M a. Figure 3-8 shows the case where the demand for loanable funds is table bat the supply of fans
(the saving schedule) Ductustes perhaps reflecting temporary shocks to income, changes ia
{government spending. or changes in consumer canfidence. In this case, when ncrest ates fll,
Investmemt nes: when intrest ates se, investment falls, We Would expecta negative corcation
between investment and intrest rates.
1b. Figure 3.9 shows the case where the supply of lonable funds saving) i stable, whereas the