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We analyze a Cournot-Betrand model where one firm competes in output and the other competes in price. With general demand functions and perfectly homogeneous products, we show that the unique Nash equilibrium is the perfectly competitive equilibrium. Equilibrium price equals marginal cost, the Cournot-type firm produces the perfectly competitive level of market output, and the Bertrand-type firm exits the market. Even with just one firm in the market, the presence of a potential Bertrand-type competitor provides sufficient discipline to guarantee a competitive outcome

A General Cournot-Bertrand Model with Homogeneous Goods