Lambert-Rogers Co. is a manufacturer of petrochemical products. The firm’s resea
ID: 1228565 • Letter: L
Question
Lambert-Rogers Co. is a manufacturer of petrochemical products. The firm’s researchefforts have resulted in the development of a new auto fuel injection cleaner that is
considerably more effective than other products on the market. Another firm, GH Squires
Co., independently developed a very similar product that is as effective as the Lambert-
Rogers formula. To avoid a lengthy court battle over conflicting patent claims, the two
firms have decided to cross-license each other’s patents and proceed with production. It is
unlikely that other petrochemical companies will be able to duplicate the product, making
the market a duopoly for the foreseeable future. Lambert-Rogers estimates the demand
curve given by Q=300,000-25,000P. Marginal cost is estimated to be constant at $2 per
bottle.
(a) Lambert-Rogers and GH Squires have very similar operating strategies.
Consequently, the management of Lambert-Rogers believes that the Cournot model is
appropriate for analyzing the market, provided that both firms enter at the same time.
Calculate Lambert-Rogers’ profit-maximizing output and price according to this model.
Explanation / Answer
Denote Lambert-Rogers price and quantity as PL, QL and Squires as PS, QS. Demand function is given as: Q = 300,000 - 25,000P Solve for P: Q - 300,000 = -25,000P P = 12 - 0.00004Q Outcome under Cournot model: a. TRL = PL ú QL TRL = (12 - 0.00004Q)QL Q = QL + QS TRL = [12 - 0.00004(QL + QS)]QL 2 TRL = 12QL - 0.00004QL - 0.00004QLQS MRL = 12 - 0.00008QL - 0.00004QS Set MRL = MC 12 - 0.00008QL - 0.00004QS = 2 -0.00008QL - 0.00004QS = -10 QL = 125,000 - 0.5QS So, QS = 125,000 - 0.5QL Substitute for QS: QL = 62,500 + 0.25QL 62,500 Q = Q = ÄÄÄÄÄÄ = 83,333 0.75 Q = QL + QS Q = 83,333 + 83,333 = 166,666 P = 12 - .00004(166,666) P = 12 - 6.67 = $5.33 P = $5.33 per bottle 166,666 bottles sold per month b. The Stackelberg model is appropriate when one firm enters first. Lambert-Rogers determines their output, which Squires then takes as given. Lambert's total revenue function is given as: 2 TRL = 12QL - 0.00004QL - 0.00004QLQS Squires reaction function QS = 125,000 - 0.5QL can be substituted into TRL, since Squires will take Lambert's output as given. 2 TRL = 12QL - 0.00004QL - 0.00004QL(125,000 - .5QL) 2 2 TRL = 12QL - 0.00004QL - 5QL + 0.00002QL 2 TRL = 7QL - 0.00002QL MRL = 7 - 0.00004QL Set MRL = MC 7 - 0.00004QL = 2 -0.00004QL = -5 QL = 125,000 To find QS substitute QL into S reaction function QS = 125,000 - 0.5QL QS = 125,000 - 0.5(125,000) QS = 62,500 Q = QL + QS Q = 125,000 + 62,500 Q = 187,500 P = 12 - 0.0004(187,500) P = 12 - 7.5 = $4.50 Lambert-Rogers gets a much larger share of the market by entering first. They should advance their schedule in order to enter first. 8.68 - 7.34 L = ÄÄÄÄÄÄÄÄÄÄÄ = 0.15 8.68
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