Varian_Chapter24_Monopoly

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1、Chapter24MonopolyPureMonopoly•Amonopolizedmarkethasasingleseller.•Themonopolist’sdemandcurveisthe(downwardsloping)marketdemandcurve.•Sothemonopolistcanalterthemarketpricebyadjustingitsoutputlevel.PureMonopoly$/outputunitHigheroutputycausesap(y)lowermarketprice,p(y).OutputLevel

2、,yWhyMonopolies?•Whatcausesmonopolies?–alegalfiat;e.g.USPostalService–apatent;e.g.anewdrug–soleownershipofaresource;e.g.atollhighway–formationofacartel;e.g.OPEC–largeeconomiesofscale;e.g.localutilitycompanies.PureMonopoly•Supposethatthemonopolistseekstomaximizeitseconomicprofi

3、t,Π(y)=p(y)y−c(y).•Whatoutputlevely*maximizesprofit?Profit-MaximizationΠ(y)=p(y)y−c(y).Attheprofit-maximizingoutputlevely*dΠ(y)ddc(y)=(p(y)y)−=0dydydyso,fory=y*,ddc(y)(p(y)y)=.dydyProfit-Maximization$R(y)=p(y)yc(y)y*yΠ(y)Profit-Maximization$R(y)=p(y)yc(y)y*yAttheprofit-maximiz

4、ingoutputleveltheslopesoftherevenueandtotalcostΠ(y)curvesareequal;MR(y*)=MC(y*).MarginalRevenueMarginalrevenueistherate-of-changeofrevenueastheoutputlevelyincreases;ddp(y)MR(y)=(p(y)y)=p(y)+y.dydydp(y)/dyistheslopeofthemarketinversedemandfunctionsodp(y)/dy<0.Thereforedp(y)MR(y

5、)=p(y)+y0.MarginalRevenueE.g.ifp(y)=a-bythenR(y)=p(y)y=ay-by2andsoMR(y)=a-2by0.ap(y)=a-bya/2ba/byMR(y)=a-2byMarginalCostMarginalcostistherate-of-changeoftotalcostastheoutputlevelyincreases;dc(y)MC(y)=.dyE.g.ifc(y)=F+αy+βy2thenMC(y)=α+2βy.$MarginalCos

6、tc(y)=F+αy+βy2Fy$/outputunitMC(y)=α+2βyαyProfit-Maximization;AnExampleAttheprofit-maximizingoutputlevely*,MR(y*)=MC(y*).Soifp(y)=a-byandifc(y)=F+αy+βy2thenMR(y*)=a−2by*=α+2βy*=MC(y*)andtheprofit-maximizingoutputlevelisa−αy*=2(b+β)causingthemarketpricetobea−αp(y*)=a−by*=a−b.2(b

7、+β)Profit-Maximization;AnExample$/outputunitap(y)=a-byp(y*)=a−αa−bMC(y)=α+2βy2(b+β)αy*=ya−αMR(y)=a-2by2(b+β)MonopolisticPricing&Own-PriceElasticityofDemand•Supposethatmarketdemandbecomeslesssensitivetochangesinprice(i.e.theown-priceelasticityofdemandbecomeslessnegative).Doesth

8、emonopolistexploitthisbycausingthemarketpricetorise?Monopolis