Problem 8-1 A monopoly faces the inverse demand function: p = 100 -20, with the corresponding marginal revenue function, MR = 100 - 40. The firm's total cost of production is C = 50 + 10Q + 3Q", with a corresponding marginal cost of MC = 10 + 6Q. P 100 2Q MR II 100 40 50 10 0 + + + MC 10 6 0 a) Calculate the prices, price elasticity of demand, revenues, marginal revenues, costs, marginal costs, and profits for Q =1, 2, 3, ..., 15. Using the MR = MC rule, determine the profit-maximizing output and price for the firm and the consequent level of profit. b) Calculate the Lemer Index of monopoly power at the profit-maximizing level of output. Determine the type of the relationship with the value of the price elasticity of demand at the profit-maximizing level of output. c) Now suppose that a specific tax of 20 per unit is imposed on the monopoly. Fill in the second part of the table in part (a) (with the 2 subscript denoting the cost, marginal cost, and profit level with the specific tax). Determine the effect on the monopoly's profit-maximizing price. Tax $20 a) Q P R MR C MC C, MC 1 2 3 12 13 14 15 The optimal output, where MR=MC is units. The corresponding price is At this output profit reaches its maximum level of bj Lerner Index is The price elasticity of demand at the profit-maximizing output-price combination is Thus, the Lerner Index is the of the value of the price elasticity of demand. c) After a specific tax is imposed on the monopoly the profit-maximizing output is The corresponding price is The post-tax optimal profit is