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CHAPTER3CONSUMER BEHAVIORTEACHINGNOTESChapter3builds thefoundation toderive the demand curve in Chapter
4.In order to understand demand theory,studentsmust havea firmgrasp of indifference curves,the marginal rate of substitution,the budget line,and optimalconsumer choice.Utility theorymay bediscussed independentlyfrom consumer choice.Many studentsfind utility functions tobe amore abstractconceptthan preferencerelationships.However,if youplan todiscuss uncertaintyin Chapter5,you willneed tocover marginalutility.Even if you coverutility theoryonly briefly,make surestudents arecomfortable with the termutility becauseitappears frequentlyin Chapter
4.When introducingindifference curves,stress thatphysical quantitiesare representedon the two axes.After discussingsupplyand demand,students maythink that price shouldbe on the vertical axis.To developindifference curves,start withanypoint in the Cartesianplane and ask forpoints that are moreand lesspreferred.This willdivide theplane intofourquadrants.Then askbetween whichpoints they will be indifferent.Once studentsgrasp theconcept ofpreference points,introduce thenotion of a preferencehill.Using theexample of a topographicalmap or a well-drawn threedimensional figure,point outthat athree-dimensional figureis beingcollapsed intotwo dimensions.The marginal rate of substitution,MRS,is confusingto students.Some confuse the MRSwith the ratio of the two quantities.If thisis the case,point outthat the slope is equal to the ratio of therise,AY,and therun,AX.This ratiois equalto the ratio of theintercepts of a linejust tangentto the indifference curve.As wemove alonga convexindifference curve,these interceptsand theMRSchange.Another problemis theterminology“of XforY This is confusingbecause weare notsubstituting“X for匕”but Yfor one unit of X.Exercise6discusses this point,but youmay wantto offerother exercisestostress it.REVIEW QUESTIONS
1.What doestransitivity of preferences meanTransitivityofpreferencesimplies that if someoneprefers Ato Band prefersBto C,then heor sheprefers AtoC.
2.Suppose thata set ofindifference curves wasnot negativelysloped.What couldyou sayabout thedesirabilityof the two goodsU is preferred to the indifference curve
23.Explain whytwo indifference curves cannotintersect.A.We knowfrom thedefinition of an indifference curve thata consumerhas the same level of utilityalong anygivencurve.In thiscase,the consumeris indifferent between bundlesAand Bbecause they bothlie onindifference curveUSimilarly,the consumeris indifferent between bundlesA and C because they bothlie onindifference curveU.v2By thetransitivity ofpreferences thisconsumer shouldalso beindifferent betweenCand B.However,we seefromthe graphthat Cliesabove B,so Cmust be preferred to B.Thus,the factthat indifference curves cannotintersectis proven.
4.Draw aset ofindifference curvesfor which the marginalrate ofsubstitution isconstant.Draw twobudget lines withdifferent slopes;show what the satisfaction-maximizing choicewill bein eachcase.What conclusionscan youdrawX andGood Yare perfect substitutes and,thus,theindifference curves arestraight lines,U and U.For goods}2that are perfectsubstitutes,the consumer will alwaysprefer topurchase thecheaper of thetwo goods toobtainmaximum utility.For example,if GoodYis cheaperthan GoodX,the consumer would facethe budget constraint L and2would maximizeutility at point A.On the other hand,if GoodXwere cheaperthan GoodY,the consumerwould facethe budget constraintLandwould maximizeutility atpoint B.If GoodXand GoodYhave the same price,the budgetxconstraintwould coincidewith U,and the consumerwould beindifferentbetween anypoint on the curve.
25.Explain whya personsmarginalrate ofsubstitutionbetween two goods mustequal the ratio of theprice of the goodsfor the consumer to achieve maximumsatisfaction.The MRSdescribes the rateat whichthe consumeris willing totrade one good for another tomaintain the same levelof satisfaction.The ratioof pricesdescribesthetrade-off that the marketis willing to makebetween the sametwo goods.The tangencyof theindifference curvewith the budget linerepresents thepoint atwhichthetrade-offsare equaland consumersatisfaction ismaximized.If theMRSbetween two goods is not equal to theratioof prices,thenATRP Q]-P]Q]P]Qi，or a1percent decline.dd lTherefore,sales revenuefrom computer chips decreasessubstantially,-12percent,while the sales revenuefrom diskdrivesis almostunchanged,-1percent.b.Can youtell from the availableinformation whichproduct willgenerate the most revenuefor thefirmIf yes,why Ifnot,what additionalinformation would you needNo.Although we know theresponsiveness of demand tochanges in price,we need to knowboth quantitiesand pricesof the productsto determinetotal salesrevenue.income levels.As arough approximation,the domestic demand curvein1990was Q=1200-55P.DDExport demand,however,remained about the same,due toprotectionist policiesthat limitedwheatimports.Calculate anddraw the aggregate demand curve forwheat in
1990.Given thedomesticdemand curve forwheat asQ=1,200-55P,we findintercepts of1,200onDD】Jthe quantity axis and an intercept of=
21.82on the price axis.The exportdemand55curve forwheat,Q=2,550-220P,has aninterceptof2,550on the quantityaxis and anDE.+-2,55011HQintercept of----------=1l.bO
2203.Vera isshopping for a newvideocassette recorder.She hearsthat the Betamax format istechnologically superiorto theVHS system.However,she asksher friendsand itturns outthey allhaveVHS machines.They agreethat theBetamax formatprovides abetter picture,but theyadd that at thelocalvideo store,theBetaformat sectionseems tobe gettingsmaller andsmaller.Based on what sheobserves,Vera buys a VHSmachine.Can you explain herdecision Speculateonwhat would occurif anew8mm videoformatis introduced.Vera isconsuming underthe influenceofapositive network externality nota bandwagoneffect.Since herreasonfor buyinga VCRis towatch rentedvideos,she maximizesher choiceof videosby choosinga VHSmachine.If heronlypurpose hadbeen torecord andplay backtelevision programming,she mighthave purchaseda VCR with theBetamaxformat.The8mm videoformat was introduced withvideo camerashandheld camcorders.The primarypurpose ofcamcorders istodocument businessand personalevents.At thistime,there islittle demand for pre-recorded8mm cassettes.Therefore,it isunlikely that the typeof positivenetworkexternalitythat influencedthe consumerin thepurchase ofa VHSVCRwill functionhere.8mm standardbecause almosteveryone elsehas one.With hundredsof thousandsof8mm camcordersin use,manufacturersmight introduce8mm VCRs,prompting videosin the8mm format.Then the8mm formatsection at the localvideo storemightget largerand larger,thus promptingconsumers topurchase aVCRwith the8mm formatas theyreplace theirVCRs.As more8mm arepurchased,more8mm videoswill becomeavailable,eventually crowdingouttheVHS format.
4.Suppose youare incharge ofa tollbridge that is essentiallycost free.The demand for bridgecrossingsQ is given by P=12-2Q.a.Draw the demand curvefor bridgecrossings.b.How manypeople wouldcross thebridge if there wereno tollAta price of zero,the quantity demanded wouldbe
6.c.What is the lossof consumersurplus associated withthecharge ofa bridgetoll of$6For goodsthat areperfect complements,such asright shoesand leftshoes,we know that theindifference curvesareL-shaped.The point of utility maximization occurswhen the budget constraints,and Ltouch thekink ofU and2xU2In thecase ofperfect complements,the income consumption curveis aline throughthe cornersof theL
6.Heathers marginalrate ofsubstitution ofmovie ticketsfor rental videos isknown tobe the same nomatter how manyrentalvideosshe wants.Draw Heathersincomeconsumptioncurve and her Engelcurvefor videos.If welet the price ofmovie ticketsbe less than the price ofa videorental,the budget constraint,L
7.You aremanaging a$300,000city budgetin whichmonies arespent onschools andpublic safetyonly.You areabout toreceive aidfromthefederal governmentto supporta specialanti-drug lawenforcementprogram.Two programsthat areavailable are1a$100,000grant thatmust bespent onlawenforcement;and2a100percent matchinggrant,in whicheach dollarof localspending onlawenforcement ismatched bya dollarof federalmoney.The federalmatching programlimits itspaymentto eachcity to a maximumof$100,
000.SCHOOLS SAFETYSAFETY SAFETYNoGovt.Program1Program2Assistancea.Complete thetable belowwiththe amounts available for safety.$0$50,000$100,000$150,000$200,000$250,000$300,00SCHOOLS SAFETYSAFETY SAFETYNoGovt.Program1ProgramAssistance2$6$300,000$400,000$400,000$50,000$250,000$350,000$350,000$100,000$200,000$300,000$300,000$150,000$150,000$250,000$200,000$100,000$250,000$200,000$250,000$50,000$0$200,000$150,000$300,000$100,000$100,0000b.Which programwouldyouthe managerchoose ifyou wishto maximizethe satisfactionof thecitizensifyouallocate$50,000of the$300,000to schoolsWhat about$250,000With$50,000to schoolsand$250,000to lawenforcement,both aidprograms yieldthe sameamount,8100,000,so youareindifferentbetween the programs.With$250,000to schoolsand$50,000to lawenforcement,program1yields$100,000and program2yields$50,000,so youprefer program
1.c.Draw the budget constraintsfor thethree options:no aid,program1,or program
2.FigureWith noaid,the budget constraint is the linesegment AB,from$300,000for schoolsand nothing for lawenforcementto$300,000for lawenforcement andnothingforschools.With program1,the budget constraint,ACE,has twolinesegments,one parallelto thehorizontal axis,until expenditures on safetyequal$100,000,and asecond slopingdownwarduntil$400,000is spent on safety.With program2,thebudget constraint,ADE,has twoline segments,one from$0,$300,000to$200,000,$200,000and anotherfrom$200,000,$200,000to$400,000,$
0.a.Bill spendsall hisincome onbooks andcoffee.He finds$20while rummagingthrough ausedpaperback bin atthebookstore.He immediatelybuysanew hardcoverbook ofpoetry.Books area normal good sincehis consumption of booksincreases withincome.Coffee is a normalor neutralgoodsince consumptionof coffeedid notfall whenincome increased.b.Bill loses$10he wasgoing touse to buy adouble espresso.He decidesto sellhis newbook atadiscount tohis friendand usethe moneytobuycoffee.Coffee isclearly anormalgood.c.Being bohemianbecomes thelatest teenfad.As aresult,coffee andbook pricesrise by25percent.Bill lowershis consumptionof both goods by the samepercentage.Books andcoffee areboth normal goods sincehis responseto adecline inreal income is todecrease consumptionof both goods.The WallStreet Journaland drinksbottled mineralwater.His tasteshave changedcompletely,and wedo notknow why.We coulduse moreinformation regardinghis level of income,his desirefor sleep,and maybeeven achange inpolitical affiliation.10,000a yearon food,and that the price of food is$2andher incomeis$25,
000.a.If a$2sales taxon foodwere tocausethe price of food todouble,whatwouldhappen toherconsumption of food HintzSince alarge price change isinvolved,you shouldassume that the priceelasticitymeasures anarc elasticity,rather thana pointelasticity.The price of fooddoubles from$2to$4,so arcelasticity shouldbe used:1We know that E=-l P=2,AP=2,and Q=5,000+Thus,ifthere isnochange inpf2income,we maysolve forAQ:2+425,000+5,000+AQBy cross-multiplying andrearranging terms,we findthat AQ=-2,
500.This meansthat shedecreases herconsumptionof foodfrom5,000to2,500units.b.Suppose that she is given atax rebate of$5,000to easethe effect of the tax.What wouldherconsumption of food benowA tax rebateof$5,000implies anincome increaseof$5,
000.To calculatethe responseof demandto thetaxrebate,usethedefinition of the arcelasticity of income.We knowthat E1=25,000,Al=5,000,QAQ.f25,000+30,
000、
20.5=5,0002,500+2,500+AQ*2By cross-multiplying andrearranging terms,we findthat AQ=
238.This meansthat sheincreases herconsumptionof foodfrom2,500to2,738units.c.Is shebetter or worse off when givena rebateequal to thesales tax paymentsDiscuss.We wantto knowif heroriginal indifference curve liesabove orbelow herfinal indifferencecurve after the salestaxand after thetaxrebate.On herfinal indifferencecurve,she choosesto consume2,738units offood for$10,952and$19,048of other goods.Was this combination attainablewith heroriginal budgetAt the original foodpriceof$2,thiscombinationwould havecost her2,738$2+$19,048二$24,524,thus leavingher anextra$476to spendoneither foodor otherconsumption.Therefore,she wouldhave beenbetter offbefore thesalestaxand taxrebate.She couldhave purchasedmore ofboth food and other goods thanshe couldhave afterthe taxes.the consumercould tradeonegoodfor anotherat market prices toobtain higher levels of satisfaction.This tradingcontinuesuntil thehighest level ofsatisfactionis achieved.
6.Explain whyconsumers arelikely tobe worse offwhena productthat theyconsume isrationed.If themaximum quantity ofa good isfixed bydecree anddesired quantitiesare notavailableforpurchase,thenthere isno guaranteethat thehighest levelofsatisfactioncan be achieved.The consumerwill not be ableto giveup the consumptionof othergoods inorder toobtain more of therationed good.Only ifthe amountrationed isgreaterthan thedesired levelof consumptioncan the consumer stillmaximize satisfactionwithout constraint.Note:rationing mayimply ahigher levelof socialwelfarebecause ofequity orfairness considerationsacross consumers.
7.Upon mergingwith WestGermanys economy,East Germanconsumers indicateda preferenceforMercedes-Benz automobilesover Volkswagenautomobiles.However,when theyconverted theirsavingsinto deutsche marks,they flockedto Volkswagendealerships.How can youexplainthisapparent paradoxThreeassumptions arerequired to address thisquestion:1thataMercedes costsmore thana Volkswagen;2that theEast Germanconsumers utility function comprisestwo goods,automobiles andall othergoodsevaluated indeutschemarks;and3that East Germans haveincomes.Based on these assumptions,we cansurmisethat whileonce-EastGermanconsumers mayprefer aMercedes to a Volkswagen,they eithercannot affordaMercedes orthey prefera bundle of othergoods plusa Volkswagento aMercedes alone.
8.Describe the equal marginal principle.Explain whythis principlemay nothold ifincreasingmarginal utility is associatedwiththe consumptionof one orbothgoods.The equalmarginal principlestates thattheratioof the marginal utilityto pricemust beequal acrossallgoods toobtain maximumsatisfaction.This explanationfollows fromthe samelogic examinedin ReviewQuestion
5.Utility maximizationis achievedwhen thebudget isallocated sothatthe marginal utilityperdollar ofexpenditure isthe samefor each good.If marginal utility isincreasing,theconsumermaximizes satisfactionby consumingever largeramounts of the good.Thus,theconsumerwould spendall income on onegood,assuming aconstant price,resulting ina corner solution.With acornersolution,theequalmarginalprinciplecannot hold.
9.What isthe differencebetween ordinalutility andcardinal utilityExplain why the assumptionofcardinal utilityis notneeded inorderto rank consumerchoices.Ordinal utilityimplies anordering amongalternatives withoutregard forintensity ofpreference.Forexample,the consumersfirst choiceis preferred to theirsecond choice.Cardinal utilityimplies thattheintensity ofpreferences may be quantified.An ordinalranking isall that is neededtorankconsumerchoices.It isnot necessaryto knowhow intenselya consumerprefers basketAover basketB;it isenoughto knowthat Ais preferredto B.
10.The price of computershas fallensubstantially overthe pasttwo decades.Use thisdrop in price toexplainwhytheConsumer PriceIndex is likely tosubstantially understatethe cost-of-living index forindividuals whouse computers intensively.The consumerprice indexmeasures the changes in the weightedaverage of the prices of thebundle ofgoodspurchased byconsumers.The weightsequal theshare ofconsumers expenditureson allof the goods in thebundle.A baseyear ischosen,and theweights forthat yearare usedto computethe CPIin thatand subsequentyears.When the price ofagoodfalls substantiallythen aconsumerwillsubstitute towardsthat good,alteringthe shareof thatconsumers income spent oneachgood.By using the baseyears weightsthe CPIdoes nottakeinto accountthat largeprice changesalter theseexpenditure shares,and sogives aninaccurate measureofchanges in the cost of living.For example,assume Fredspends10%of hisincomeon computersin1970,and thatFreds expenditure sharesin1970were usedas theweights tocalculate Fred*s CPIin subsequentyears.If Fredsdemand forcomputerswas inelastic,then reductionsinthe price ofcomputers relativeto othergoods wouldreduce theshareof hisincomespent oncomputers.After1970a CPIthat usedFred*s1970expendituresharesas weightswouldgive a10%weight to the fallingprice ofcomputers,even thoughFred spentless that10%of hisincomeon computers.So longas the prices of othergoodsrose,or fellless than10%,then theCPI givestoo littleweightto thechanges inthe prices ofothergoods,and understatesthechanges in Fredscost ofliving.EXERCISES
1.In this chapter,consumer preferences for variouscommodities didnot changeduring theanalysis.Yet insome situations,preferences dochange asconsumption occurs.Discuss whyand howpreferencesmight changeover timewith consumptionof these two commodities:a.cigarettesThe assumptionthat preferencesdo not change isa reasonableone ifchoices areindependent acrosstime.It doesnothold,however,when“habit-forming“or addictivebehavior isinvolved,asinthecaseof cigarettes:theconsumption ofcigarettes in one periodinfluences theirconsumption inthe nextperiod.b.dinner for the firsttime ata restaurantwith aspecial cuisineWhilethere maynotbeanything physicallyaddictive indining atnew and different restaurants,one canbecome betterinformedabout a particular restaurant.One mayenjoy choosingmore newand differentrestaurants,oronemay betiredof choosinganother newanddifferentplace toeat.In eitherof thesecases,choices changeas consumptionoccurs.
2.Draw theindifference curvesfor the following individuals9preferencesfortwo goods:hamburgersand beer.a.Al likesbeer buthates hamburgers.He alwaysprefers morebeer nomatterhowmanyhamburgers he has.For Al,hamburgers area bad.His indifference curves slopeupward andto theright ratherthan downward and totheleft.For Al,U ispreferredto U andUispreferredto U；.122b.Betty is indifferentbetweenbundles ofeither threebeers ortwo hamburgers.Her preferencesdo not changeas she consumes anymoreofeither food.Since Bettyis indifferentbetween threebeers andtwo burgers,an indifferencecurve connectsthese twopoints.Bettys indifferencecurves area seriesof parallellines with slope of—%.c.Chris eatsone hamburgerand washesit downwith onebeer.He willnot consumean additionalunit of oneitem withoutan additional unitof theother.L-shaped,with cornerson a45-degree lineout of theorigin.Figured.Doreen lovesbeer butis allergicto beefEvery timeshe eatsa hamburgershe breaksout inhives.For Doreen,hamburgers arenot considereda“good”but rathera“bad,and thusher preferredposition isnotupwards andto theright,but ratherdownwardandto theright.For Doreen,Uis preferredtoUandUis preferredx22toU.
33.The price of recordsis$8and the priceoftapes is$
10.Philip has a budgetof$80and has alreadypurchased4records.He thushas$48more to spend onadditional recordsand tapes.Draw hisbudgetline.If hisremaining expenditureis madeon1record and4tapes,show Philipsconsumption choiceonthe budget line.
4.Suppose Billviews butter and margarineas perfectlysubstitutable foreach other.a.Draw aset ofindifferencecurvesthat describesBilFs preferencesfor butterand margarine,b.Arethese indifferencecurves convexWhyecause theconsumer considersbutterand margarine tobe perfectsubstitutes,thereisno diminishingmarginalutility,and theresultant indifferencecurves arestraight lines.Straight-lineindifferencecurvesarenotstrictlyconvex.c.If buttercosts$2per package,while margarinecosts only$1,and Billhas a$20budget tospend forthemonth,which butter-margarine marketbasket willhe chooseCan youshow thisgraphicallyLetBills incomebe represented by Y,the priceof butterbyP,the quantityof butterby B,the priceof margarineBbyP,and thequantityof margarine byM.Then thegeneral form of thebudgetconstraint is:MY=P B+P M.B MSubstitutingfor thegiven valuesof Y,P,and P,we obtainthe specificrepresentation ofBilFs budgetconstraint:B M20=2B+IM,orB=10-M.Because Billisindifferentbetween butterandmargarine,and the priceofbutter isgreater than the priceofmargarine,Bill willonly buymargarine.Thisisa cornersolution,becausetheoptimal choiceoccurs onan axis.In FigureBillsutility maximizingbundle ispoint A.Figure
5.Suppose thatJones andSmith havedecided toallocate$1,000per yearon liquidrefreshments intheformof alcoholic or nonalcoholic drinks.Jones andSmith differsubstantially intheir preferencesforthese twoforms ofrefreshment.Jones prefersalcoholic tononalcoholic drinks,while Smithprefersthe nonalcoholicoption.a.Draw asetofindifferencecurvesfor Jonesandasecond setfor Smith.b.Discuss whythetwosets ofcurves aredifferent fromeach otherusingtheconcept ofmarginalrate ofsubstitution.At anycombination ofalcoholic,A,and nonalcoholic,N,drinks,Jones iswilling to give upa lotof Nforan additionalunitof A;whereas,Smith iswilling togive upa lotof Aforanadditionalunitof N.Because Jonesneeds moreNtocompensate himfor givingup someA,hehas a lowermarginalrate ofsubstitution ofalcoholic for nonalcoholicbeveragesthan Smith.With alcoholicbeverages onthe verticalaxis,Jones5indifferencecurves are lesssteep thanSmithsat anypoint onthe graph.c.If bothSmith and Jones paythesameprices fortheir refreshments,will theirmarginal ratesofsubstitution ofalcoholicfornonalcoholic drinksbe thesame ordifferent Explain.In orderto maximizeutility,theconsumermust consumequantities suchthattheMRS betweenany twocommoditiesis equal to theratioofprices.If SmithandJonesare rationalconsumers,their MRSmust beequal becausetheyface thesame marketprices.But becausethey havedifferent preferences,theywillconsume differentamounts ofthetwogoods,alcoholic andnonalcoholic.At thosedifferent levels,however,their MRSare equal.
6.Anne isa frequentflyer whosefares arereduced throughcoupon giveawaysby25percent aftersheflies25,000miles ayear,and thenby50percent aftershe flies50,000miles.Can yougraph thebudgetline thatAnne facesin makingher flightplans forthe yearM,against all othergoods,G,in dollars.The budgetconstraint is:Y=P M^P G,orM GTheslope ofthebudget line is——.In thiscase,thepriceof miles flown changesas thenumber ofmilesflownPGchanges,so thebudget curveis kinkedat25,000and at50,000miles.Suppose Pis$1per milefor lessthan or equalto25,000Mmiles.Then PM50,000and PM50,
000.Also,let PAto Bis-1,the slope ofthebudgetlinefrom Bto CBto DMM
07.Antonio buys8new collegetextbooks duringhis firstyear atschool ata cost of$50each.Used bookscostonly$30each.When thebookstore announcesthat therewill bea20percent price increase innewtexts anda10percent increase in used texts forthe nextyear,Antonios fatheroffers him$80extra.IsAntonio better off or worseoff aftertheprice changeItfollows fromthe axiomof revealedpreferences that,since Antoniochose topurchase onlynew textbookswhen bothnewand used textbooks wereavailable,it mustbe thecase thatAntonio doesnot considerusedtextbookssubstitutesfor newtextbooks atthe oldprices.With theincreaseinprice,however,to$60for newtextbooks and$33for usedtexts,the relativepriceof newtexts tousedtextsincreases from=
1.67to=
1.
82.Antonio mayreact to3033the relativeprice increaseinoneof twoways:1If newand usedtexts arenot substitutes for AntonioL
8.Suppose thatSamantha andJason bothspend$24per weekon videoand movieentertainment.When theprices ofvideos andmovies areboth$4,they bothrent3videos andbuy3movie tickets.Following avideo pricewar andan increasedcostofmovie tickets,the videoprice fallsto$2and themovie ticket increasesto$
6.Samantha nowrents6videos andbuys2movie tickets;Jason,however,buys1movieticketand rents9videos.a.Is Samanthabetter offor worseoff afterthepricechange、Samanthas originalpointof utilitymaximizationmayberepresentedbypoint AonU inA:$24=$23videos+$63movies.The factthat shechose bundleB revealsshe hasobtained ahigherlevelofutility,U2b.Is Jasonbetter offorworseoffSimilarly,Jason must also be betteroff.
9.Connie Consumerhas amonthly income of$200which sheallocates amongtwogoods:meat andpotatoes.a.Suppose meatcosts$4per poundand potatoescost$2per pound.Draw her budgetconstraint.Let M=meat and P=potatoes.Connies budgetconstraint is$200=4M+2P,orMP.Mon the verticalaxis,theverticalintercept is
50.The horizontalintercept maybe foundby settingM-0and solvingforP.b.Suppose alsothat her utilityfunctionis given by theequation uM,P=2M+P.Whatcombination of meat and potatoes shouldshe buyto maximizeherutilityHint:Meat andpotatoes areperfectsubstitutes.Connies utilityis equalto100when shebuys50pounds of meat andno potatoesornomeat and100pounds of potatoes.The indifferencecurve forU=100coincides withher budgetconstraint.Any combinationofmeat andpotatoesalongthis linewill provideher withmaximum utility.c.Connies supermarkethas aspecial promotion.If shebuys20pounds of potatoes at$2perpound,she getsthe next10pounds forfree.This offerapplies onlyto thefirst20pounds shebuys.All potatoesin excessofthefirst20pounds excludingbonus potatoesare still$2perpound.Draw herbudgetconstraint.Figure representsConnies budgetconstraint whenthe supermarketruns itsspecial promotionon potatoes.Noticethat herbudgetconstrainthas aslope of-2until Conniehas purchasedtwenty pounds of potatoes,is thenflat,since theten nextpounds ofpotatoesarefree,and thenhasaslope of-2until itintercepts thepotato axisat
110.Figured.An outbreakofpotatorot raisesthepriceofpotatoesto$4per pound.The supermarketends itspromotion.What doesherbudgetconstraint looklike nowWhat combinationofmeatandpotatoes maximizesher utilityU=100atpointA whensheconsumes50poundsofmeatandno potatoes.Thisisacornersolution.
10.The utilitythat Janereceives byconsuming foodF and clothing Cisgivenby:uF,C=FC.Draw theindifferencecurve associatedwith a utility levelof12and theindifference curveassociatedwith autility levelof
24.Are theindifferencecurvesconvexTo findthe basketsoffood,F andclothing,C,which yieldsatisfactions of12and24solve thef+•r12-24equations C=—and C=--.F FU=12Food ClothingFood ClothingU=24The indifferencecurvesareconvex.b.Suppose thatfood costs$1a unit,clothing costs$3a unit,and Janehas$12tospendon foodandclothing.Graph thebudgetlinethatshefaces.The budgetconstraintis:Y=P F+P C,orF c12=IF+3C,or C=4--F.c.What isthe utility-maximizing choiceoffood andclothingHint:Solve theproblemgraphically.F=6and C=
2.To checkthis answer,note thatit exhaustsJanes income,12=P+2PF Cd.What isthemarginalrateofsubstitution offood forclothing whenutilityismaximizedAt theutility-maximizing levelof consumption,theslopeoftheindifferencecurveis equalto theslopeofthebudget constraint.Since theMRSis equalto thenegative slopeoftheindifferencecurve,the MRSinthis problemis equaltoone-third.Thus,Jane wouldbe willingtogive up one-third ofa unitof clothingfor oneunitoffood.e.Suppose thatJane buys3units offood and3units ofclothing withher$12budget.Would hermarginalrateofsubstitutionoffood forclothing be greater orlessthan1/3Explain.MRSis greater than one-third,and thus,attheprices shefaces,she wouldwelcome theopportunity togiveupclothingto getmore food.She iswillingtotrade clothingfor fooduntil herMRSis equaltotheratioofprices.See Figure.Figure
11.The utilitythat Meredithreceives byconsuming foodF andclothing Cisgivenby uF,C=FC.Suppose that Merediths incomein1990is$1,200and thepricesoffood andclothing are$1per unitforeach.However,by1995thepriceoffoodhas increasedto$2and thepriceofclothing to$
3.Let100represent thecostofliving indexfor
1990.Calculate the ideal and the Laspeyrescost-of-living indexforMeredith for
1995.Hint:Meredith willspend equalamounts onfood andclothing withthesepreferences.Laspeyres IndexTheLaspeyres indexrepresents howmuch moreMeredith wouldhave tospend in1995versus1990if sheconsumed thesameamounts offood andclothing in1995as shedid in
1990.That is,the Laspeyresindexfor1995L isgivenby:L=100Y/Ywhere Yrepresents theamount Meredith would spendat1995prices consumingthesameamount offood andclothingas in1990:Y=PZ F+P1C=2F+3C,where F and Crepresent theamounts offood andclothing consumedin
1990.FWe thusneedtocalculate Fand C,which makeup thebundleoffood andclothing whichmaximizes Meredithsutilitygiven1990prices andherincomein
1990.Use thehint tosimplify theproblem:Since shespends equalamounts onbothgoods,P F=P C.Or,you canderive thissame equationmathematically:With thisutilityfunction,MU=F cAU/AC=F,and MU=AU/AF=C.To maximizeutility,Meredith choosesa consumptionbundle suchthat MU.VMU=P VP,F IC hcwhich againyields P F PcC.F二From thebudgetconstraint,we alsoknowthat:P F+P C=YF CCombiningthesetwo equations andsubstituting thevalues forthe1990prices and income yieldsthe systemof equations:C=FandC+F=1,200Solving thesetwoequations,we findthat:C=600and F=600Therefore,the Laspeyrescost-of-living indexis:L=1002F+3C/Y=100[2600+3600]/1200=250Ideal IndexTheideal indexrepresents howmuch moreMeredithwouldhave tospend in1995versus1990if sheconsumed amountsoffood andclothing in1995which wouldgive herthesameamount ofutility asshe hadin
1990.That is,the idealindexfor1995I isgivenby:I=100Y/Y,where Y=PF+P%=2F+3CFwhere F*andC*are theamount offood andclothing whichgive Merediththesameutility asshe hadin
1990.F andC*mustalsobe suchthatMeredithspends the least amountof moneyat1995prices toattain the1990utilitylevel.The bundle F,Cwill beonthesame indifferencecurveasF,C and theindifferencecurve atthispointwill betangenttoabudgetlinewithslope-P/P%,where P*andP*are thepricesoffoodandclothing in
1995.SinceF cMeredithspends equalamounts onthetwogoods,weknowthat2P=3C〔Since thisbundle liesonthesame indifferencecurveas thebundleF=600,C=600,we alsoknowthatFC=
600600.Solving for F yields:F,[2/3F,]=360,000orF=J[3/2360,000]From this,we obtainC*:We cannow calculatetheidealindex:I=1002F+3CCHAPTER4INDIVIDUAL ANDMARKET DEMANDTEACHINGNOTESChapter4relies ontwo importantideas fromChapter3:the influenceofprice andincomechanges onthebudgetlineand optimalconsumerchoice.The chapterfocuses onprice changes,individual demand,market demand,demand elasticity,andconsumer surplus.These conceptsare crucialto understandingthe applicationof demandand supplyanalysis in Chapter9aswell as the discussion of marketfailure inParts IIIand IV.Chapter4also discussesthe derivation oftheindividuaFs demandcurvewithadiscussion ofsubstitution andincome effects.The analyticaltools studentslearn inthischapterwill beimportantfor thediscussionoffactor supplyanddemandinChapter
14.When discussingthe derivationof demand,review howthebudgetcurve pivotsaround anintercept asprice changesandhow optimalquantities changeasthebudgetlinepivots.Once studentsunderstand theeffectofprice changeson consumerchoice,they cangrasp thederivationofthepriceconsumption pathand theindividual demand curve.Remind studentsthatthepricea consumeriswillingto payisameasure ofthemarginal benefit ofconsuming anotherunit.3P5P3PQ=1—P plusQ=2---------；—to arriveat Q=3-----------or2Q=2---------------.Students mustbe reminded,instead,222to writethe demand curveininverse form,with priceasafunction ofquantity,and thenadd.Thus,we addP=1-QtoP=1-2Q toobtain P=2-3Q.Price elasticity ofdemandand consumersurplus arereferredtothroughout thetext,but themathematics ofprice elasticityofdemand isdifficult formany students.Before discussingthe algebra,encourage studentsto developan intuitivegrasp ofelasticityasameasure ofthe sensitivityof thequantitydemanded tochangesinprice.%AQThe easiestalgebraic representationof elasticityis%APREVIEW QUESTIONS
1.How isan individual demand curvedifferent froma marketdemandcurveWhich curveis likely tobe moreprice elasticHint:Assume thatthere areno networkexternalities.The marketdemandcurveisthehorizontal summationoftheindividualdemandcurves.The graphof marketdemand showstherelation betweeneach priceand thesum ofindividual quantities.Because price elasticities ofdemand mayvaryby individual,theprice elasticity ofdemand islikely tobegreater than someindividual priceelasticities andlessthan others.
2.Is the demand foraparticularbrand ofproduct,such asHead skis,likely tobe morepriceelasticorprice inelastic than the demandfortheaggregateof allbrands,such asdownhill skisExplain.Individual brandscompete withother brands.If thetwo brandsare similar,a smallchange inthepriceofonegoodwill encouragemany consumersto switchtotheother brand.Because substitutesare readilyavailable,the quantityresponsetoachange inone brandsprice is more elastic thanthequantity responsefor allbrands.Thus,the demandforHead skisismoreelasticthanthedemandfor downhillskis.
3.Tickets toa rockconcert sellfor$
10.But atthatprice,thedemand is substantiallygreater thantheavailable numberof tickets.Is thevalue ormarginalbenefitof anadditional ticketgreaterthan,lessthan,orequalto$10How mightyou determinethat valueIf,at$10,demand exceedssupply,then consumersare willingto bidupthemarketpricetoalevel wherethequantitydemandedisequaltothequantity supplied.Since utility-maximizing consumersmustbewillingto paymore than$10,then themarginal increasein satisfactionvalue isgreaterthan$
10.One waytodetermine thevalue of tickets wouldbe toauction offa blockoftickets.The highestbid woulddeterminethe valueofthetickets.
4.Suppose aperson allocatesa givenbudget betweentwogoods,foodandclothing.If foodis aninferiorgood,canyoutell whetherclothing isinferior ornormal Explain.
5.Which ofthe followingcombinations ofgoods are complements and which aresubstitutes Couldtheybe eitherin differentcircumstances Discuss.a.a mathematicsclass andan economics classIf themath classandtheeconomics classdonotconflict inscheduling,then theclasses couldbe eithercomplementsor substitutes.The mathclass mayilluminate economics,andtheeconomicsclasscan motivatemathematics.If theclassesconflict,they aresubstitutes.b.tennis balls anda tennis racketTennisballsandatennisracket areboth neededto playa gameof tennis,thus theyarecomplements.c.steak andlobsterd.a planetrip anda traintrip tothesamedestinationTwo modesof transportationbetweenthesame twopoints aresubstitutes forone another.e.bacon andeggsBacon andeggs areoften eatentogether andare,therefore,complementary goods.By consideringthem inrelationto somethingelse,such aspancakes,bacon andeggs canfunction assubstitutes.
6.a.the removal of quotasontheimportation offoreign clothesTheremovalofquotas will shift thedemandcurveinward fordomestically-produced clothes,because foreign-producedgoods aresubstitutes fordomestically-produced goods.Both theequilibrium priceand quantity will fallas foreignclothesare tradedinafree marketenvironment.b.an increaseintheincomeofcitizensWhen incomerises,expendituresonnormalgoodssuch asclothing increase,causing thedemandcurveto shiftout.The equilibriumquantity andprice willincrease.c.a cutintheindustrys costsof producingdomestic clothesthatispassed ontothemarket intheform oflower clothingpricesA cutin anindustrys costswillshiftthe supplycurve out.The equilibriumpriceandquantitywillincrease.
7.For whichofthefollowing goodsisapriceincreaselikely tolead toa substantialincome aswell assubstitutioneffecta.saltSmallincomeeffect,smallsubstitutioneffect:The amountof incomethatisspent onsalt isrelatively small,butsince thereare fewsubstitutesforsalt,consumers willnot readilysubstitute awayfrom it.As thepriceofsaltrises,real incomewill fallonly slightly,thus leadingtoasmall declinein consumption.b.housingLarge incomeeffect,nosubstitutioneffect:The amountof incomespentonhousing isrelatively largefor mostconsumers.If thepriceofhousing wereto rise,real incomewouldbereduced substantially,thereby reducingtheconsumption ofall othergoods.However,consumers wouldfind itimpossible tosubstitute forhousing,in general.c.theater ticketsSmallincomeeffect,largesubstitutioneffectd.foodLargeincomeeffect,nosubstitutioneffect:As withhousing,theamountofincomespentonfoodisrelatively largeformost consumers.Price increasesfor foodwill reducereal incomesubstantially,thereby reducingthe consumptionofallothercommodities.Although consumerscan substitute out ofparticular foods,they cannotsubstituteoutoffood ingeneral.
8.Suppose thatthe averagehousehold ina stateconsumes500gallons of gasoline peryear.A10-centgasoline taxisintroduced,coupled witha$50annual taxrebate perhousehold.Will the household bebetterorworseoffafterthe newprogram isintroducedIf thehousehold doesnotchangeits consumptionofgasoline,it will be unaffectedbythetax-rebate program.Itstill gets500gallons ofgasoline.To theextent thatthehouseholdreduces itsgas consumptionthrough substitution,it mustbebetteroff.
9.Which ofthefollowingthree groupsislikelyto havethemost,andwhichtheleast,price-elasticdemand for membership inthe Associationof BusinessEconomistsa.studentsThe majordifference amongthe groupsisthelevelofincome.We knowthatiftheconsumptionofagood constitutesalarge percentageofanindividuafs income,then thedemandforthegoodwill be relatively elastic.If weassumethat amembership inthe Associationof BusinessEconomists islikelytobealarge expenditurefor students,wemay concludethatthedemand will berelativelyelastic forthis group.b.junior executivesThelevelofincome forjunior executives willbelarger than that ofstudents,but smallerthan that of seniorexecutives.Therefore,thedemandforamembership forthis groupwillbeless elasticthanthatofthestudentsbut moreelasticthanthatofthe seniorexecutives.c.senior executivesThehigh earningsamong seniorexecutiveswillresult ina relativelyinelastic demandformembership.EXERCISES
1.The ACMEcorporation determinesthatatcurrent pricesthedemandfor itscomputerchipshas apriceelasticity of-2intheshort run,while thepriceelasticityfor itsdisk drivesis-
1.a.If thecorporation decidesto raisethepriceofbothproducts by10percent,what willhappen toitssales Toits salesrevenueWe knowthe formulafortheelasticityofdemandis:%AQFor computerchips,E=-2,so a10percent increaseinpricewill reducethequantitysold by20percent.For diskpdrives,E=-1,so a10percent increaseinpricewill reducesales by10percent.pSales revenueisequalto pricetimes quantitysold.Let TR-PQ be revenue beforethepricechange andTR=P QX XX222berevenueafterthepricechange.For computerchips:△TRg-尸2Q2•P1Q1△TRcc舄Q]-尸]Q]P]Q],ora12percent decline.For diskdrives:△TRdd~P2Q2-P1Q1。
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