Handout 8 key - Handout8key Q1,

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Unformatted text preview: Handout8key Q1, Onefirmusesonlylaborasinputtoproducehotdogs.Thepriceforonehotdogis$1.Therearetwo kindsoflabors:skilledworkers(S)andunskilledworkers(U).Thewageforskilledworkeris$5,whilefor unskilledworkersis$2. Theskilledworkers’technologyisgivenbytablebelow: Q of S 1 2 3 4 5 6 Output 7 15 21 25 28 30 MP 7 8 6 4 3 2 MP*P 7 8 6 4 3 2 Wage 5 5 5 5 5 5 7 31 1 1 5  Theunskilledworkers’technologyisgivenbytablebelow: Q of U 1 2 3 4 5 6 Output 4 7 10 12 13 13.5 MP 4 3 3 2 1 .5 MP*P 4 3 3 2 1 .5 Wage 2 2 2 2 2 2 7 13 -.5 -.5 2  a. Thetwotablesaboveiscompleted. b. Shouldthefirmonlyhireskilledorunskilledworkers?Why? Answer:No,thefirmshouldhirebothskilledlaborsandunskilledlabors.Thebenefitofhiringa laborisMP*P,thecostofhiringalaboriswage.Fortheskilledlabor,whenQislargerthanzero (Q=1,2,3),benefitlargerthancost,sohireskilledlabor.Fortheunskilledlabor,whenQislarger thanzero(Q=1,2,3),benefitlargerthancost,sohireunskilledlabor. c. Howmanyskilledworkersthefirmshouldhire?Howmanyunskilledworkersthefirmshould hire?Whatistheoutputamountofthisfirm? Answer:Thefirmshouldhire3skilledworkersand4unskilledworkers.Thetotal output=21+12=33. d. NowtheNewYorkTimestellspeoplethathotdogisakindofhealthyfood,sothedemandof hotdogincreases.Thepriceofhotdogchangesto$2.Otherpricesdonotchange.Howmany skilledworkersthefirmshouldhire?Howmanyunskilledworkersthefirmshouldhire?Whatis theoutputamountofthisfirm? Answer:priceequal2.Nowthefirmshouldhire5skilledlaborsand5unskilledlabors.Thetotal output=28+13=41.  Q2,  Afirm’stechnologyis:Q=2K+4L. HereQisquantityofoutput,LisquantityoflaborandKisquantityofcapital. a. Isthistechnologyconstant,decreasingorincreasingreturntoscale? Answer:Constantreturntoscale. b. Inthelongrun,thewageis$3,andthepriceofcapitalis$1,iftheoutputamountis4,howmuch laborthisfirmwilluse?Howmuchcapitalthisfirmwilluse? Answer:Themarginalproductionofcapitalis2,themarginalproductionoflaboris4.Ifwespend onedollaronlabor,wecanget1/3labor,thereforeweget4/3outputs.Ifwespendonedollaron capital,wecanget1capital,thereforeweget2outputs.Soweshouldusecapital,notuselaborin theproduction. c. Whatisthelongrunequilibriumpriceofoutput? Answer:inthelongrun,allinputusediscapital.SoQ=2K.Andthefirm’sprofitiszero.SoP=AC=Pk/2, Pkisthepriceofcapital.SoP=1/2.  Q3, Arepresentativefirmusescapitalandlabortoproducestudydesks.Thisfirmneedstopaythebillof utility(waterandelasticity)ifitwantstoproduce.Thetotalstipendonutilityis$2.Arepresentative firm’stechnologyis:  Q 2 L 2 K , MPK 1 K , MPL 1 L . HereQisquantityofoutput,LisquantityoflaborandKisquantityofcapital. a. Isthistechnologyconstant,decreasingorincreasingreturntoscale? Decreasing b. IfthewageisS1,andpriceofcapitalis$1.Priceofstudydeskis$1.Howmanylaborswillthis firmhire?Howmanycapitalswillthisfirmuse? MPL*P=w,soL=1 MPk*P=Pk,soK=1 Q=2+2=4 c. Whatistheoutputamountofthisfirm,whatistheprofitofthisfirm? Q=2+2=4 Profit=TR ­TC=4 ­2=2 d. Wage=$1,Priceofcapital=$1,thefirmwanttoproduceQamountofdesks,howmanylabors willthisfirmhire?Howmanycapitalswillthisfirmuse? MPL/w=MPk/Pk,sotheamountoflaborshouldequaltoamountofcapital.L=K,andthetotal amountofoutputisQ.SoLisQ*Q/16,KisQ*Q/16. e. Whatisthetotalcostintheshortrun? Intheshortrun,thebillofelectricityandwaterisFC.SoFC=2. MoneyspendofLaborandcapitalisvariablecost.IftheoutputamountisQ,thenweknowL andK,priceofLandKareboth$1.SoTVC=(Q*Q/16)*2=Q*Q/8. TC=2+Q*Q/8(Q>=0) f. Whatisthetotalcostinthelongrun? Inthelongrun,thefirmcanquit. SOTC=2+Q*Q/8ifQ>0; TC=oifQ=0. g. TheMarginalcostinthelongrunisMC=Q/4,whatistheequilibriumpriceinthelongrun? Inthelongrun,profitmaximization:P=MC,equilibrium:P=AC,soMC=AC Q/4=2/Q+Q/8,soQ=4.P=MC=1 h. P=1001 ­Qisthedemandcurve.Howmanyfirmsexistinthismarketinthelongrun? P=1,soDemand=1000.Andforeachfirm,Q=4.Sothereare250firms. ...
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