The cost of production under Cournot model is
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P'(y1* + y2*)y2* + P(y1* + y2*) = MC2(y2*). In particular, unless P'(y1* + y2*) = 0 (the demand curve is horizontal) the price P(y1* + y2*) is not equal to either firm's marginal cost at the output the firm produces.
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