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Requires calculus in the model of a dominant firm assume

Question: (Requires calculus) In the model of a dominant firm, assume that the fringe supply curve is given by Q = -1 + 0.2P, where P is market price and Q is output. Demand is given by Q = 11 - P. What will price and output be if there is no dominant firm? Now assume that there is a dominant firm, whose marginal cost is constant at $6. Derive the residual demand curve that it faces and calculate its profit-maximizing output and price.

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