Boors and Cudweiser:Cournot competitors

May 22nd, 2016
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Suppose there are two firms, Boors and Cudweiser, each selling identical-tasting nonalcoholic beer. Consumers of this beer have no brand loyalty so market demand can be expressed as P = 5 − .001(Qb + Qc). Boors’ marginal revenue function can be written MR = 5 − .001(2Qb + Qc) and symmetrically for Cudweiser. Boors operates with out-of-date technology and has constant cost of \$2 per unit (MC = AC = 2), whereas Cudweiser has constant cost of \$1 per unit. Assuming the firms behave as Cournot competitors, Boor’s best-response function is: the document discusses in detail about price and NSB under different competitions

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Suppose there are two firms, Boors and Cudweiser, each selling identical-tasting nonalcoholicbeer. Consumers of this beer have no brand loyalty so market demand can be expressed as P= 5 .001(Qb + Qc). Boors marginal revenue function can be written MR = 5 .001(2Qb + Qc)and symmetrically for Cudweiser. Boors operates with out-of-date technology and has constantcost of \$2 per unit (MC = AC = 2), whereas Cudweiser has constant cost of \$1 per unit.Assuming the firms behave as Cournot competitors, Boors best-response function is:At equilibrium,Pb=Pc = P = 5 .001(Qb + Qc)Boors profit isPb = Qb*[5 .001(Qb + Qc)]-2Qb = 3Qb 0.001Qb(Qb+Qc)= 3Qb 0.001Qb^2 0.001QbQcLet dPb/dQb =03-0.002Qb 0.001Qc =0Therefore, Boors best response function isQb = 3/0.002 -0.001Qc/0.002Qb= 1500- 0.5Qc2.Similar to 1, Cudweisers profit isPc = Qc*[5 .001(Qb + Qc)]-Qc = 4Qc 0.001Qc(Qb+Qc)= 4Qc 0.001Qc^2 0.001QbQcLet dPc/dQc = 04-0.002Qc-0.001Qb =0Cudweisers response function isQc = 4/0.002 0.001Qb/0.002 = 2000-0.5 Qb3. under equilibrium we haveQb* = 1500-0.5 Qc*Qc* = 2000-0.5 Qb*Solve for Qb* and Qc*,Qb* = 667 unitsQc* = 1667 units4.The reaction function for both firm is linear function, the intersection point at (Qc,Qb)=(1667,667) is the Nash equilibrium.5. Under perfect competition, the price is determined by MR of Cudweiser, i.e.,P= MRc = 1SinceMCb = 2 < P =1Boor will not produce any beer, because f

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