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ProblemsandApplications1.Inthetextexampleofthefarmerandtherancher,thefarmer’sopportunitycostofproducingonepoundofmeatistwopoundsofpotatoesbecauseforevery20hoursofwork,hecanproduceonepoundofmeatortwopoundsofpotatoes.Withlimitedtimeathisdisposal,producingapoundofmeatmeanshegivesuptheopportunitytoproducetwopoundsofpotatoes.Similarly,therancher’sopportunitycostofproducingonepoundofmeatis1/8poundofpotatoesbecauseforeveryhourofwork,shecanproduceonepoundofmeator1/8poundofpotatoes.Withlimitedtimeatherdisposal,producingapoundofmeatmeansshegivesuptheopportunitytoproduce1/8poundofpotatoes.2.a.SeeFigure3-2.IfMariaspendsallfivehoursstudyingeconomics,shecanread100pages,sothatistheverticalinterceptoftheproductionpossibilitiesfrontier.Ifshespendsallfivehoursstudyingsociology,shecanread250pages,sothatisthehorizontalintercept.Thetimecostsareconstant,sotheproductionpossibilitiesfrontierisastraightline.Figure3-2b.IttakesMariatwohourstoread100pagesofsociology.Inthattime,shecouldread40pagesofeconomics.Sotheopportunitycostof100pagesofsociologyis40pagesofeconomics.3.a.Workersneededtomake:OneCarOneTonofGrainU.S.1/41/10Japan1/41/5b.SeeFigure3-3.With100millionworkersandfourcarsperworker,ifeithereconomyweredevotedcompletelytocars,itcouldmake400millioncars.SinceaU.S.workercanproduce10tonsofgrain,iftheU.S.producedonlygrainitwouldproduce1,000milliontons.SinceaJapaneseworkercanproduce5tonsofgrain,ifJapanproducedonlygrainitwouldproduce500milliontons.Thesearetheinterceptsoftheproductionpossibilitiesfrontiersshowninthefigure.Notethatsincethetradeoffbetweencarsandgrainisconstant,theproductionpossibilitiesfrontierisastraightline.Figure3-3c.SinceaU.S.workerproduceseither4carsor10tonsofgrain,theopportunitycostof1caris2½tonsofgrain,whichis10dividedby4.SinceaJapaneseworkerproduceseither4carsor5tonsofgrain,theopportunitycostof1caris11/4tonsofgrain,whichis5dividedby4.Similarly,theU.S.opportunitycostof1tonofgrainis2/5cars(4dividedby10)andtheJapaneseopportunitycostof1tonofgrainis4/5cars(4dividedby5).Thisgivesthefollowingtable:OpportunityCostof:1Car(intermsoftonsofgraingivenup)1TonofGrain(intermsofcarsgivenup)U.S.21/22/5Japan11/44/5d.Neithercountryhasanabsoluteadvantageinproducingcars,sincethey’reequallyproductive(thesameoutputperworker);theU.S.hasanabsoluteadvantageinproducinggrain,sinceit’smoreproductive(greateroutputperworker).e.Japanhasacomparativeadvantageinproducingcars,sinceithasaloweropportunitycostintermsofgraingivenup.TheU.S.hasacomparativeadvantageinproducinggrain,sinceithasaloweropportunitycostintermsofcarsgivenup.f.Withhalftheworkersineachcountryproducingeachofthegoods,theU.S.wouldproduce200millioncars(that’s50millionworkerstimes4carseach)and500milliontonsofgrain(50millionworkerstimes10tonseach).Japanwouldproduce200millioncars(50millionworkerstimes4carseach)and250milliontonsofgrain(50millionworkerstimes5tonseach).g.Fromanysituationwithnotrade,inwhicheachcountryisproducingsomecarsandsomegrain,supposetheU.S.changed1workerfromproducingcarstoproducinggrain.Thatworkerwouldproduce4fewercarsand10additionaltonsofgrain.ThensupposetheU.S.offerstotrade7tonsofgraintoJapanfor4cars.TheU.S.willdothisbecauseitvalues4carsat10tonsofgrain,soitwillbebetteroffifthetradegoesthrough.SupposeJapanchanges1workerfromproducinggraintoproducingcars.Thatworkerwouldproduce4morecarsand5fewertonsofgrain.Japanwilltakethetradebecauseitvalues4carsat5tonsofgrain,soitwillbebetteroff.Withthetradeandthechangeof1workerinboththeU.S.andJapan,eachcountrygetsthesameamountofcarsasbeforeandbothgetadditionaltonsofgrain(3fortheU.S.and2forJapan).Thusbytradingandchangingtheirproduction,bothcountriesarebetteroff.4.a.Pat’sopportunitycostofmakingapizzais1/2gallonofrootbeer,sinceshecouldbrew1/2galloninthetime(2hours)ittakeshertomakeapizza.Pathasanabsoluteadvantageinmakingpizzasinceshecanmakeoneintwohours,whileittakesKrisfourhours.Kris’sopportunitycostofmakingapizzais2/3gallonsofrootbeer,sinceshecouldbrew2/3ofagalloninthetime(4hours)ittakeshertomakeapizza.SincePat’sopportunitycostofmakingpizzaislessthanKris’s,Pathasacomparativeadvantageinmakingpizza.b.SincePathasacomparativeadvantageinmakingpizza,shewillmakepizzaandexchangeitforrootbeerthatKrismakes.c.Thehighestpriceofpizzaintermsofrootbeerthatwillmakebothroommatesbetteroffis2/3gallonsofrootbeer.Ifthepricewerehigherthanthat,thenKriswouldprefermakingherownpizza(atanopportunitycostof2/3gallonsofrootbeer)ratherthantradingforpizzathatPatmakes.Thelowestpriceofpizzaintermsofrootbeerthatwillmakebothroommatesbetteroffis1/2gallonofrootbeer.Ifthepricewerelowerthanthat,thenPatwouldprefermakingherownrootbeer(shecanmake1/2gallonofrootbeerinsteadofmakingapizza)ratherthantradingforrootbeerthatKrismakes.5.a.SinceaCanadianworkercanmakeeithertwocarsayearor30bushelsofwheat,theopportunitycostofacaris15bushelsofwheat.Similarly,theopportunitycostofabushelofwheatis1/15ofacar.Theopportunitycostsarethereciprocalsofeachother.b.SeeFigure3-4.Ifall10millionworkersproducetwocarseach,theyproduceatotalof20millioncars,whichistheverticalinterceptoftheproductionpossibilitiesfront