Q. A market's total demand is given by P = 40 - Z. This market is supplied by a "dominant firm" and by other, relatively small firms. The small firms' total supply is given by P = 3Y. The dominant firm's total-cost function is TC = (X2/8) + 2X + 3 [In case you have no calculus: Marginal Cost = MC = (X/4) + 2 ].
(a) Find the equation of the dominant firm's derived-demand function
(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.