Question
1.Supposedemandforamonopolist'sproductisgivenbyP=4008Ywhilethemonopolist'smarginalcostisgivenbyMC=80. A.Derivethemarginalrevenuecurve.Sketchandlabelthemarginalrevenuecurve,demandcurveandmarginalcostcurve. B.Whataretheprofit maximizingquantityofoutputandpriceforthismonopolist?Whatarethecompetitiveequilibriumoutputandprice?Clearlyshowandlabeltheminthediagram. C.Assumethatthereisafixedcostof200andtheonlyadditionalcostisvariableinYanditisrepresentedinthemarginalcostfunction.Whatistheaveragecostfunction? D.Isthisanaturalmonopoly?Ifso,discusstwowayshowthegovernmentcanregulatetheindustrytobemoreefficient.Calculatethelossincurredbythemonopolyattheefficientoutputlevelanddiscusshowtocalculatetheefficientoutput/pricelevelcanbedeterminedwherethefirmismakingzeroprofit.Ifnot,discusshowmuchthegovernmentmustsubsidizethemonopolistforittoproduceatthemarketefficientlevel. 2..JanedrinksBeer(B)onlywhensheconsumesbagsofChips(C)Janealwaysconsumestwobottlesofbeeralongwithabagofchips.TheyareperfectcomplementsforJane.Priceofabottleofbeeris$2whilethepriceofabagofChipsis$2.Assumeyoucanconsumefractionsordecimalsofeachproduct.Jane'sincomeis$50.A.SetupJane'sutilityfunction.DrawandlabeltwoofJane'sindifferencecurves.B.Calculatethenumberof{B,C}pairJaneconsumesandcorrespondinglevelofutilityforJane,assetupinpartA).Whatistheintuitionbehindthesolution?Drawandlabelthebudgetconstraint,solveforJane'soptimalchoiceandpresentyouranswergraphically.C.SupposethequantitydiscountisimposedonBeer.ThepriceofBeeris$2upto10bottlesofBeer,and$1fromthe10thbottleofBeerandup.Howdoesherchoiceandbudgetconstraintchange?Whathappenstoher utility?(Presentyouranswergraphicallyaswell). 3.Considerthemarketforspeakers.Thedemandisgivenby:Q=10P,whilethesupplyisgivenby:Q=9P.Answerthefollowingquestions.A.Whatistheequilibriumpriceandquantityinthismarket?Graphit.B.Howcanyouinterprettheslopeofthedemandcurve?C.Calculatethepriceelasticityofdemandattheequilibrium.D.Supposethewagerosefrom$5/hourto$7/hoursofirmssupplyfewerspeakersatagivenprice,thatthesupplycurvemadeaparallelshiftbackwards.Asaresult,theequilibriumpriceroseto $3.Whatisthenewequilibriumquantity?Besuretodrawthenewequilibriumonyourgraph.E.Atwhatpointonthedemandcurvewouldthetotalexpenditurereachitsmaximum? 4..AfirmhastheproductionfunctionQ=LK.Thefirminitiallyfacesinputpricesw1=$1andr=$1andisrequiredtoproduceQ=100units.Laterthe priceoflaborwgoesuptow2=$9andthepriceofcapitalrremainsunchanged.A.Graphicallyrepresentthesituation.Makesureyouwritedown equationsforisoquantcurve,isocostlines.B.Findtheoptimalinputcombinationsforeachsetofprices.
1.Supposedemandforamonopolist'sproductisgivenbyP=4008Ywhilethemonopolist'smarginalcostisgivenbyMC=80.
A.Derivethemarginalrevenuecurve.Sketchandlabelthemarginalrevenuecurve,demandcurveandmarginalcostcurve.
B.Whataretheprofit maximizingquantityofoutputandpriceforthismonopolist?Whatarethecompetitiveequilibriumoutputandprice?Clearlyshowandlabeltheminthediagram.
C.Assumethatthereisafixedcostof200andtheonlyadditionalcostisvariableinYanditisrepresentedinthemarginalcostfunction.Whatistheaveragecostfunction?
D.Isthisanaturalmonopoly?Ifso,discusstwowayshowthegovernmentcanregulatetheindustrytobemoreefficient.Calculatethelossincurredbythemonopolyattheefficientoutputlevelanddiscusshowtocalculatetheefficientoutput/pricelevelcanbedeterminedwherethefirmismakingzeroprofit.Ifnot,discusshowmuchthegovernmentmustsubsidizethemonopolistforittoproduceatthemarketefficientlevel.
2..JanedrinksBeer(B)onlywhensheconsumesbagsofChips(C)Janealwaysconsumestwobottlesofbeeralongwithabagofchips.TheyareperfectcomplementsforJane.Priceofabottleofbeeris$2whilethepriceofabagofChipsis$2.Assumeyoucanconsumefractionsordecimalsofeachproduct.Jane'sincomeis$50.A.SetupJane'sutilityfunction.DrawandlabeltwoofJane'sindifferencecurves.B.Calculatethenumberof{B,C}pairJaneconsumesandcorrespondinglevelofutilityforJane,assetupinpartA).Whatistheintuitionbehindthesolution?Drawandlabelthebudgetconstraint,solveforJane'soptimalchoiceandpresentyouranswergraphically.C.SupposethequantitydiscountisimposedonBeer.ThepriceofBeeris$2upto10bottlesofBeer,and$1fromthe10thbottleofBeerandup.Howdoesherchoiceandbudgetconstraintchange?Whathappenstoher
utility?(Presentyouranswergraphicallyaswell).
3.Considerthemarketforspeakers.Thedemandisgivenby:Q=10P,whilethesupplyisgivenby:Q=9P.Answerthefollowingquestions.A.Whatistheequilibriumpriceandquantityinthismarket?Graphit.B.Howcanyouinterprettheslopeofthedemandcurve?C.Calculatethepriceelasticityofdemandattheequilibrium.D.Supposethewagerosefrom$5/hourto$7/hoursofirmssupplyfewerspeakersatagivenprice,thatthesupplycurvemadeaparallelshiftbackwards.Asaresult,theequilibriumpriceroseto
$3.Whatisthenewequilibriumquantity?Besuretodrawthenewequilibriumonyourgraph.E.Atwhatpointonthedemandcurvewouldthetotalexpenditurereachitsmaximum?
4..AfirmhastheproductionfunctionQ=LK.Thefirminitiallyfacesinputpricesw1=$1andr=$1andisrequiredtoproduceQ=100units.Laterthe
priceoflaborwgoesuptow2=$9andthepriceofcapitalrremainsunchanged.A.Graphicallyrepresentthesituation.Makesureyouwritedown
equationsforisoquantcurve,isocostlines.B.Findtheoptimalinputcombinationsforeachsetofprices.
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