enter the market for a new pain reliever | My Assignment Tutor

28) Two large diversified consumer products firms are about to enter the market for a new pain reliever.  The two firms are very similar in terms of their costs, strategic approach, and market outlook.  Moreover, the firms have very similar individual demand curves so that each firm expects to sell one-half of the total market output at any given price.  The market demand curve for the pain reliever is given as: Q = 2600 – 400P. Both firms have constant long-run average costs of $2.00 per bottle.  Patent protection insures that the two firms will operate as a duopoly for the foreseeable future.  Price and quantity values are stated in per-bottle terms.  If the firms act as Cournot duopolists, solve for the firm and market outputs and equilibrium prices. Answer:  Begin by solving for P. Q = 2600 – 400P Q – 2600 = -400P P = 6.5 – 0.0025Q Denote the two firms A and B and solve for reaction functions. TRA = PA ? QA TRA = (6.5 – 0.0025Q)QA TRA = 6.5QA – 0.0025[(QA + QB)QA] TRA = 6.5QA – 0.0025QA2 – 0.0025QAQB MRA = 6.5 – 0.005QA – 0.0025QB Set MRA = MC 6.5 – 0.005QA – 0.0025QB = 2 -0.005QA = 4.5 + 0.0025QB QA = 900 – 0.5QB One can verify that: QB = 900 – 0.5QA Substitute expression for QB into QA QA = 900 – 0.5(900 – 0.5QA) QA = 900 – 450 + 0.25QA QA -0.25QA = 450 QA(1 – 0.25) = 450  =  = 600 Substitute expression for QA into QB QB = 900 – 0.5(900 – 0.5QB) QB = 900 – 450 + 0.25QB QB -0.25QB = 450 QB(1 – 0.25) = 450  = //// = 600 QT = QA + QB QT = 600 + 600 = 1200 P = 6.5 – 0.0025(1200) P = $3.5 per bottle Diff: 3