Abstract
As might be easily conjectured, the Cournot oligopoly solution and perfect competitive equilibrium generally differ. To see this by way of an example due to Mayberry, Nash and Shubik(1953)(see also Shubik (1959)), let two firms’ cost functions in a Cournot duopoly under no product differentiation be given by $$ {{c}_{1}}\left( {{x}_{1}} \right)=4-{{x}_{1}}+x_{1}^{2}, $$ $$ {{c}_{2}}\left( {{x}_{2}} \right)=5-{{x}_{2}}+x_{2}^{2}, $$ and let $$ p=10-2\left( {{x}_{1}}+{{x}_{2}} \right) $$ be the market demand function. If two firms act in perfect competition, marginal costs of both must equal the competitively given market price.
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