Lambert-Rogers Co. is a manufacturer of petrochemical products. The firm's research efforts 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.
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.