11. Assume a monopolistic firm that sells a single product whose quantity is defined by Qin three separate markets; henc

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11 Assume A Monopolistic Firm That Sells A Single Product Whose Quantity Is Defined By Qin Three Separate Markets Henc 1 (44.85 KiB) Viewed 24 times

11. Assume a monopolistic firm that sells a single product whose quantity is defined by Qin three separate markets; hence the firm must decide upon the quantities (0...0.0) to be supplied to the respective markets in order to maximise profits, when Q = Q+Q: + Q. The firm faces a cost function for total product C = C(Q), and three different demand functions of its product for each market, so, three different revenue functions, given by Ri = R (0) for each market i = 1,2,3 (a) State formally the firm's maximisation problem and derive the equilibrium condition (5 marks) (b) Prove in any market the negative relationship between the marginal revenue and the elasticity of demand (in absolute terms) (5 marks) For the remaining questions, assume that the total cost function and the three demand functions are given respectively, by EC206 2021.2 A 800 Turn over Page 8 C = 40 + 300 P.-126-8 P = 210 - 100 Ps= 150-120 (c) Use the previously derived equilibrium condition to compute the optimal quantities that maximise profits (6 marks) (d) Check that those quantities represent a maximum using the Hessian determinant 4 marks) (e) Compute the total quantity that the firm will produce the prices that the firm is going to set at each market and the maximum profits (5 marks) Compute the elasticity of demand for each demand function given above at equilibrium Comment on the relationship between the price that the firm sets and the elasticity of demand (5 marks)