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A monopoly faces the inverse demand function: p=1002Q, with the corresponding marginal revenue function, MR= 1004Q. The firm's total cost of production is C=50+10Q+3Q2, with a corresponding marginal cost of MC=10+6Q. pMRCMC====1001005010++2Q4Q10Q6Q+3Q2 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 Lerner 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 The optimal output, where MR=MC is units. The corresponding price is At this output profit reaches its maximum level of b) 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 A monopoly faces the inverse demand function: p=1002Q, with the corresponding marginal revenue function, MR= 1004Q. The firm's total cost of production is C=50+10Q+3Q2, with a corresponding marginal cost of MC=10+6Q. pMRCMC====1001005010++2Q4Q10Q6Q+3Q2 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 Lerner 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 The optimal output, where MR=MC is units. The corresponding price is At this output profit reaches its maximum level of b) 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