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ECO365–IntermediateMicroeconomicsLectureNotes
Monopoly MarketenvironmentwherethereisonlyonefirminthemarketFirmfacesALLofdemandSomonopolyprofit=p(y)y–c(y)Wherep(y)=inversemarketdemandletp(y)y=r(y)revenuefunctionMonopolisticproblem:ChooseytoMaxr(y)–c(y)Firstorderconditionsaregivenby:MR=MC
ThesameconditionwegotwithperfectcompetitionButnowMRdoesnotequalP(i.e.firmsnotpricetakers)Twoeffectsofchangingy(sayincreasey)onrevenues1-sellmoresorevenueincreases2-pricedecreasessorevenuedecreases?r(y)=p?y+y?p?r(y)/?y=MR=p+y?p/?yor:Forpricetakers?p=0=?r=p?yButnowPdecreasesasyincreasessothesecondtermmatters.
Nowboth1and2measureMarginalRevenue(MR)MR=?r/?y=p+y?p/?y=p(1+(y/p)(?p/?y)=p(y)(1+1/ε)Sinceε=priceelasticityofdemand=(p/y)(?y/?p)=canre-writeoptimalcondition,MR=MCas:p(y)(1+1/ε(y))=mc(y)Orp(y)(1-1/|ε(y)|)=mc(y)Sinceε0Alsorecallthat|ε|0elastic|ε|1inelasticSothatifdemandelasticregions|ε|1MR0butifdemandinelasticMR0
TheaboveimpliesthattheMonopolistonlyoperatesinelasticportionofDemandsinceMR0whendemandinelasticandprofitmax.requiresMR=MCbutMC0isunlikely(impossible).Nowwithlineardemand…P(y)=a–bySoR(y)=ay–by2=MR=a–2byNotice3things:1.MR=Daty=02.slopeofMR=2timestheslopeofdemand(i.e.,twiceassteep).3.MR=0where|ε|=1(thisisalwaystruenotjustforlinearDemand)
Lookattaxexample:supposec(y)=cy=mc=cP(y)=a-bysoMR=a-2byMCACMRYmyPmD
Nowsupposeataxonthemonopolist=t(quantitytax)sopc=ps+tSomcw/taxisc+torc(y)=(c+t)y=beforeprofitmaxwherec=a-2byOry*=a-c/2bNowMC=c+t=a–2by=MRSoy*=(a-c-t)/2b=Δy/Δt=-1/(2b)(why?)Whatistheimpactofthetaxonprice,p?Recallslopeofdemandfunction=Δp/Δy=-b,soThetaxisimposed=ychanges
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