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profit-maximizing equilibrium

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A market's total demand is given by P = 80-(z/2). This market is supplied by a "dominant firm" and by other, relatively "small firms". The small firms' total supply is given by P=4y. The dominant firm's total cost function is TC = (x^2)/20 + (17x/9) + 10, marginal cost function is MC = (x/10) + 17/9, marginal revenue curve is MR = (640-8x)/9

(a) Find the equation of the dominant firm's derived-demand function(p as a function of x)
(b) find the equation of the dominant firm's total revenue(TR)

(c) calculate the dominant firm's output X and price P at its profit-maximizing equilibrium.

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This posting finds profit-maximizing equilibrium.

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A market's total demand is given by P = 80-(z/2). This market is supplied by a "dominant firm" and by other, relatively "small firms". The small firms' total supply is given by P=4y. The dominant firm's total cost function is TC ...

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