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ECON 201
Corey Van De Waal

their as reduces A production sproductionasBs production fromof 1 toofor 38takesBtakesAccordinglyAreducestheirAccordinglygiven and thus believes that its own market has shrunk toof its previous sizeWhen B enters the market and takes one quarter A X on the next slide1DThis situation where A takes half of the market and B takes one quarter of the market can be shown to be unstable based on Cournots behavioural assumptionsas a sign to increase their production toModel that we set upYou were asked process continues until As output falls to 13 and Lecture 18B can see graphicallyMR 025BDABAMR 05QAQRecall from last class the Cournot Duopoly to think about the stability of the situation that we describedto refresh your memory heres the graph00In the next round B takes As output reduction of 58 1 38 leaves 58 or 516This Bs output increases to 13 as wePof thethethirdandand ofD be sellingP one to 13 at23 takes taking sellbelievesmonopolyisitaB ifasjointly whatproducersB of claritytwo actingandAthe market since only at this point will there be no further reaction by either firmmarket then A will be happy to produce half of the remaining 23 or 13 of the marketAnd so onIt can be proven that this process will stop when each of thetwoproducerstakesonethirdoftheForclarityifBistaking13oftheFor and taking firms by and sharing the maximum total revenue at twoM colluding at Pavailable marketHowever at this equilibrium joint profits are not maximizedThe duopolists would be better off get a total revenue that is equal to the shaded areaWe have noted that this is a stable equilibrium since each producer maximizes ThetwofirmsAandBjointlysell23atPTheprofitsbytakingofwhatitbelievestobetheprofitsbycolludingandactingasamonopolysellingbythe midpoint of the demand curveXXThe final stable equilibrium in our development of the simple Cournot Duopoly Model looks like thisD1D123 025maxB Q 516DTRmaxTRABB12 03333and so onB13 05A 38QAQAB 1132Q 03333QAAQQ00MDPPPPP
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