Chaoter 3

to estimate dre effect of reducing the price of a conrrnodiry on dre clernancl of othe r

related conr.nodiries that dre firnr sells. ,\ irigh cross-price elrsticin' oI dcrn rrrd is

also used to define an industry.

5. For the analysis of demand, the firm should first identify all the irnportant variables.that affect the demand for the product it sells. Bv using regression analysis (dis-

cussed in Chapter 4), the fimr could obtain reliable esdmates of the effect of a

change in each ofthese variables on demand for the product.

7.

There is an increasing trend ofconverqing tastes around the s'orld.'Lrstes in theUn.ited States affect tastes around the *'orld, and tastes abroad stronglv influencetastes in the United States, \\rl.rile sorne national differences s'ill surely reurain,the information revolution and cross-fertiliz',rtion oI cr.rlrurcs c..rn be erpe cted toaccelerate the global convergence of tastes. This has irnportant implications forall firms.

Since t}le rnid-1990s, the Internet has given rise to electronic commerce, u'hich is

revolutioniz-ing traditional business relationships. E-cornrlcrce refcrs to the pro-ducdon, advertising, slle, nncl distribr.rtion of products trrrcl scrvices fronr businessto business and fronr business to consumers thror.rgh tl're Internet. Thc bigeesthrres oIe-commerce for consunrers ire tl)c convenience of har.ing roun(l-the-clockacccss to the virrual storc and the,rbilin'to cng',rge irr corrrprirtivt shopping:rtminimrl cost and effort. Through e-cornmerce, sellers can sharply reduce theircost of executing sales and procuring inputs, reformulate supply chains and logis-rics, and redefine custoner relationship managenlent.

(a) If our main interest in managerial economics is the demand that a firm faces

for is product, why do \r'e srudy consumer demand dreorv? (&) \Mrat is the dis-tinction beween inferior goods and normal goods? Benveen the substirution ef-fect and the income effect? Benveen a change in the quantiw dernlrndecl and a

change in demand?

(a) Iiorv many ty?es of demand functions are drere? (&) In which tlpe cf demrndare we most interested in rnrnaeerial economics? \\hy? (r) \4hy do 1ve then srudl'thc other r)?es of denlend?

(a) What are d1e most important deterrninants of the dernand function that a finnfaces for the con.rrnodin' it sells? (/l) \\hat is nreant b1' producers' goodsi Bt' de-rived demand? (r) \\hy is the demand for durable goods (bodr consunrers' andproducers') less stable than the demand for nondurable goods?

@V>What is the advantage of using the price elasticiry rather than the slope of thev i.-".ra curve or is inverse to measure the resoonsiveness in the ouanriw de-rnanded of a commodiry- to a change in it-s price? (l') \afty and horv is the formulafor arc price elasticiq'of dernancl diffcrcnt frorn rhe forrnula for point pricc clas-ticity of dcrnand?

(! (r) State the rcledonship benveen the total revcnue of a firnr and the price el'.rstic-ity of dernand for a price ino'ense alonq a linear derran<l curvc. (l) Explain tlre rcr-son for the relationship tl'rrt vou stlted in part (a).

6. (a) Explain rvhy a firm facing a negatively slopeC demand curve rvould never pro-duce in the inelasric pordon of the demand cun'e. (l') \\''l-ren ri'ould the firm u'antto operate at the point rvhere its demand cun,e is unitan'elrsdc?

Demand Theory 727

DiscussionQuestions

2.

j,5o+l lt r/

Part 2 Demand Anatysis

7. (a) \\buld you erpect the price elasticiry of demrnd to be higher for Chewolet

tomobiles or for automobiles in general? \\hv? (l) \\rould )'ou expect the pd

elasticirl'ofdernand for electricir)"for residential ttse to be higher or lorver

indusrial use? \\/try? (c) Would you er?ect *re price elasticity of demand for

triciry to be higher er lorverin the shon run as compared u"ith the long mn?

8.

9.

If there hasbeen a I0 percent inbrease in consumers'income berrveen nvoperi

rvhat rvas the percentage change in the demand for foreigJn travel? Forproducts? For flour? (Hirrt: Use the inconre-el';lsticin'r"llues iu Thble 3-4.)

Agriculrural commodities arc kno*'n to ha';e a price-inelastic clemand and to

necessities. Florr can this inforrn:rtion lllorv us to ernhin rvlrl thc incorne ofers falls (a) after a good han-est? (l') In relation to the inconres in otherthe economv?

10. Suppose that the cross-price elasriciry of demand becween Mclntosh and

Delicious apples is 0.8, ber*'een apples and apple juice is 0.5, benveen apples

cheesc is 0.4, and benveen apples and beer is 0.1. \\Ihat crn )'ou sly rrboutthelationship benvecn each set of comrnoditics?

ll (r) !\/hat othcr elrsticities of dcrnanrl ilrc thcre lrcsirlcs pricc, irrcornc, and

price? (D) l\h:rt is the usefulness to the firm of the clasticio' of dcmand forvariables over rvhich the firm has some control? (c) Of the clasticiw ofover rvhich the firm has no conrrol? (d) \\thy is it essential for the firm to use

elasciciry of all the variables included in the dernancl ftrnction?

(,2) \\ftv are txstes converqingl around the u'orld? (l) \\rhat is thethis for U.S. finns?

Horv is e-commerce revolutionizine tie brrsiness rvorld?

PfOb[gmS L John Smith, che research manager for rnarkering ar the Cherrolet Dir.isionof thc

General Motors Corporation, has specified the foilorving general demand firnc.

tion for Cherrolets in the United States:

Qc -- f(Pc, N, 1, Pr, PG,,,1, Pr)

rvhere Q6. is the quantiw demanded of Chevrolets per I'exr, P6. is the priceChevrolets, N is population, 1is disposabie incorne, P, is the price o[Fordmobiles, P6 is the price of gasoline, I is the amounr of advercising for Cheand P1 is credit incentives to purchase Chevrolets. Indicare rvhether you expect

each independent or explanatoryr vx.ir61. to be directly or inversely related totiequandry demanded ofChevrolets and the reason for vour cxpectarion.

Pe=A=P,=

t2.

lJ.

(a) Indicateeach unit cl

of Q" if tne

s8,0oo, Pcthe demant

3. Starting wiassume dra

million, I :

(i.e., the ircurve for (

graPh, Plo

^ \d4rat is th

G.)rn" t"" cV son of the

administrtdemand a:

mand forgression a

where th,parlor, arscheduleeach dollder.'rand I

$5 and P

i. Showhccream gl

Also shofor ice cr

6. For thesimilar I

enuer aI

demandfigure sr

,mand is

andMI7. The tot

iion whthe Pri'--0.4.IoperatradoPt?clurge

6o

1,t(

Suppose that Gtr'l's Smith estimated rhe follorving resression equation for

Chewolet autonrobiles:

Qr..= 100,000 - 100/'}r- + 2,000N + 501 + .101)/,

1,000P6 +,i.4 + 40,0001,/

rvhere Q6 : quantit)' clernandcd per vear of Chcvrolet arrtorncrbilesP6 : price of Cherrolet atrtomobiles, in dollarsN: popularion of the United States, in rnillions

1 = per crpitrr disposrrble income, in dollrrsPp : price of Ford nrtornobiles, in doll..rrs

L

Chapter 3

Pc : real price of gasoline, in cents per gallonI : adverrising expendirures br. Cl'revrolet; in dollars per vearPr : credit incentives to purchasc Chevrolets, in percentrge poirtts

belorv the rate of interes! on borro*'ins in the absence ofincentives

(,e) Indicate the change in the number of Chevrolets purchased peryear (Q6) foreach unit change in the independent or explanatory variables. (D) Find dre valueof Q6if the averase value of P6: 59,000, N: 200 nrillion, I: S10,000, Pp=58,000, Pc : 80 cents,.'1 : 5200,000, and iiP, : l. (r) Dcrive the cqu:rtion forthe clcnranrl cun'c for Chcr'r'olets; and (r/) plot it. | : Q*:, td . u>,, $auuStrrting rvith dre cstiuratcd clcrlancl function fi-rr (ihcvrolcts grven in [)roblern 2,

assunle that the average value of the independent vlriables changes to N : 225

million, /: $12,000, Pp: $10,000, Pc: 100 cents, l : 5250,000, and P, = g

(i.e., the incentives are phased out). (r) Find the equation of the new demandcurve for Chewolets and (&) plot this ne*'demand curve, Di, and on the samegraph, plot the demand cun'e for Chevrolets, D6, found in Problem 2(d). fcl!\trat is the relacionsl'rip benveen D6 and Dy' ? \\that explains this relationshipi

Thc Ice Crcam Parlor is the onlf ice creirnr p',rrlor in Smit.htorrn. r\lichlcl, thcson of the orvner, hrs just ccrnre back frorn college, rvhcre he majors in br-rsiness

administration. In his course in rnanagerial econornics, Nlichael has just snrdieddemand analysis, and he decides to applv rvhat he has learned to estimate rhe de-mand for ice cream in his fathcr's parlor during his surnrner vac'.rtion. Llsins re-gression anall'sis, i\licheel estimxtes the follou,ing demand function:

Qr=120-20P1rvhere the subscript 1 refers to ice cream portions sen'ed per day in his fatl'rer'sparlor, and P1 is the dollar price. Ilichael then sets out to (a) derive the demandschedule for ice cream and plot it, (1') find the.point price elasticih'of dernancl ateach dollar price, frorn P : 56 to P : $0, ancl (c)-frxl tfie-i-price elasticin'ofdernrnd benveen consecutive doll':rr prices (i.c., bcnveen 1) = $6:rnd P: S5,1'=$5 and P = 54, and so on). Shorv hos'r\{ichrel rvould gct his results.

Shorv irou,ilichael could havc for.rncl the price elastici$ of dernand (Ip) for rcccrearn graphicall)'at, sx)., Pr : 54 for the dern,rnd function giycn in Probleni 4.

Also shorv graphicalll' that at Py = $4, 8p rvould be the same if the denrand cun'efor ice cream s.ere cun'ilincar but tlngent to the linelr denrrnd cun c 3t Pr = S,1.

For the dernand frinction for ice crearn given in Problem 4, (a) construct a tablesimilar to Thble l-2 in the text, shorving the quantirv- clernanded, the total rer'-enue, and the marginal revenue schedules of the Ice Cream Parlor. (l;) Plot thedemand, the total revenue, and the rnarginal revenue scheclules from part (a) in e

figure similar to Figure l-5 in the text and indicate on it thc range over rvhich de-mand is elastic, inelastic, and unitarv elastic. (c) Derive the equiltion for the 'IR

and ,LIR schedules for the parlor.

The total operating revenues of a public transportation:rr.rthoriq, are $100 rr-ril-

lion l,hile its total operxting costs rrre S120 nrillion. The price of a ride is S1, rndt1.re price elasticiq' ofdenrand for public transPortation has been esdrnrted to be--0.4. By larv, the public transportation audroriw must take steps to eliminate itsoperating deficit. (a) \\4-rat pricing policy should the transportarion authorin'adopt? \\rhv? (1.') \\hat price per ride must the public transportation ,rr.rthorit\'charge to elirnin:rte the deficit if it c:rnnot rednce costs?

Demand Theory 129

9o r \ I

Part 2 Demand Anatysis

n<-<' \ '8/ The coefficient of income in a regression of the quxntio dernancled of a com-/-\) \,// .7 rnodiq'on price, incorne, and otlier variables is 10. (a) Cirlculatc thc incorne elrrs-

\9'/ dciq'of dernand for tliis cornnrodin'at incornc of S10,000 and salcs of 80,000

units. (/') \4/hat rvould be the income elasticirv of dcmand if sales increased from80,000 to 90,000 units and income rose from $10,000 to $11,000? Whatqpe ofgood is this commodirl'?

9. A researcher esdmated th:rt the price elasticin'of demand for automobiles in the

United States is - 1.2, s'hile thc irrconre el.rsticin' r-.,f de nr'rntl is i,0. Ncrt t'c.rr,

U.S. autornakers intend to increase the average price of autornobiles br' 5 per-cent, and thel expect consurners' disposable incorne to rise lrr' 3 percent. (rf Ifs:rles of domesdcallr- producecl autornobiles are 8 rnillion this velr, hos' nrtnv lu-tornobiles do vou expect U.S. iutonrikers to sell next verr? (l) Bv horv muchshould domestic automakers increase the price of autonrobiles if dre1. rvish to rn-crease sales by 5 percent next year?

I l.

The coefficient of the price of gasoline in the resressic.rn of the quantit)'de-nranded of autonrobiles (in rrrilliorrs of units) on the price of g';rsoline (in doll'rrrs)

and othervarirbles is -14. (rz) Crlculate the cross-price elrsticin'of demrnd be-r\r'ecn autornobiles nnd grsolinc at tlrc gasolirrc price of $l pcr grllon and salcs ofautonrobiles of 8 (rnillion unim). (l) \Vhrt would be the cross-price elasticiw ofdemand benveen automobiles and grsoline if sales of autornobiles declined from8 to 6 with an increase in the gasoline pricc from $l to $1.20 per gallon?

The rnanage ment of the Mini ,\'till Steel Cornpau' cstirnated thc follorving ehs-dciries for a special qpe of steel: Er, = 2, E r = l, and .Eyy = l.5, rvhere X refers tosteel and f to alun'rinunr. Next vear, the firm rvould like to incre:rse the p{ce ofthe steel it sells by 6 percent. The managernent forecasted that income *'ill riseby 4 percent next year and that dre price of alr.rminurn will fall by 2 percent. (a) Ifthe sales this year are 1,200 tons of the steel, horv lnrny tolls can the firm expectto sell next 1'ear? (&) Bv rvhat percentase nrust the firm changc tl-re price of steel

to keep its sales at 1,200 tons ncxt 1'ear?

Integrating ProblemT'he research department of the Corn Flakes Corporation (CFC) cstimated thefollowing regression for the demand of the cornflakes it sellsr

Q..-: 1.0 - 2.0P.y + 1.51 + 0.8P)-- 3.OP,\r + i.0rl

rvhere Q.1'= sales of CFC cornflakes, in millions of l0-ounce boxes perl'earPx: th. price of CFC corrrflakes, in dollars per 10-ourrce box

1 = personal disposable income, in trillions of dollars per yearPy : price of competitive brand of cornflakes, in dollars per I 0-ounce

boxP,11 : price of milk, in dollars per quartI : advertising expendirurcs ofCFC cornflakes, in hundreds of

thousands of dollars per )'earTlrisl'ear, Px: $2,1: 54, Pr = $2.50, Itr: $1, andA = $2. (a) Calculate the sales

ofCFC cornflakes this year; (l) calculate the elasdciry ofsales s'ith rcspecr to crchvariable in drc dernand frrnction; (r) estirnatc dre levcl of sales lrcxr year if CFC rc-duces P1, b.v l0 percent, increases advercising by 20 percent, / rises by 5 percent, Pyis reduced bv 10 percent, and P;q1 remains unchanged. (d) By how nruch should CFCchange its advertising ifit rvants its sales to be 30 percenr higher dran rhis veari

8

10.

t2.

5 o.rl 4tr{A )iA