Assume a situation where a monopolist of input M sells to a competitive industry Z, and the competitive industry Z has a production function characterized by variable proportions. A second competitive industry sells its output L to the competitive industry Z, and Z combines M and L according to the production function Z=L0.5M0.5. The price of L and its marginal cost are both $1. The demand for the product of industry Z is Z=20PZ. It can be shown that the monopolist will charge $26.90 for M to maximize its profit, given that its marginal cost of M is $1. (This can be found by first obtaining the derived demand facing the monopolist using the price equal marginal cost condition in industry Z, and also using the condition for least-cost production by industry Z.) The competitive industry Z will have a constant marginal cost of $10.37 and sell 9.63 units at a price of $10.37. a. Calculate the competitive industry Z 's actual combination of L and M that it will use to produce the 9.63 units. Find the true economic cost to society of these inputs (not Z 's actual payments to its suppliers; its payment to the monopolist includes a monopoly margin). Hint: The optimal input mix can be found by the simultaneous solution of two equations: the equality of the marginal product per dollar of the inputs and the production function equated to 9.63 units. b. Assume that the monopolist decides to vertically integrate forward into the competitive industry Z, thereby extending its monopoly to cover industry Z. What will be the least-cost combination of L and M and its true economic cost in producing the 9.63 units? Hint: The vertically integrated firm will "charge" itself the marginal cost for M when determining its input mix. c. What is the cost saving that the vertically integrated monopolist will obtain if it produces 9.63 units? That is, what is the saving compared to the cost found in part a? d. What makes this vertical integration profitable? Is it in society's interest if the monopolist holds its output fixed at 9.63 units after vertical integration? e. In fact, after the vertical monopolization of Z, the firm M - Z would have a constant marginal cost of $2. Given this fact, what is the profit-maximizing price Pz and output Z ? Draw a figure to illustrate the overall social benefits and costs of this vertical integration. Assume a situation where a monopolist of input M sells to a competitive industry Z, and the competitive industry Z has a production function characterized by variable proportions. A second competitive industry sells its output L to the competitive industry Z, and Z combines M and L according to the production function Z=L0.5M0.5. The price of L and its marginal cost are both $1. The demand for the product of industry Z is Z=20PZ. It can be shown that the monopolist will charge $26.90 for M to maximize its profit, given that its marginal cost of M is $1. (This can be found by first obtaining the derived demand facing the monopolist using the price equal marginal cost condition in industry Z, and also using the condition for least-cost production by industry Z.) The competitive industry Z will have a constant marginal cost of $10.37 and sell 9.63 units at a price of $10.37. a. Calculate the competitive industry Z 's actual combination of L and M that it will use to produce the 9.63 units. Find the true economic cost to society of these inputs (not Z 's actual payments to its suppliers; its payment to the monopolist includes a monopoly margin). Hint: The optimal input mix can be found by the simultaneous solution of two equations: the equality of the marginal product per dollar of the inputs and the production function equated to 9.63 units. b. Assume that the monopolist decides to vertically integrate forward into the competitive industry Z, thereby extending its monopoly to cover industry Z. What will be the least-cost combination of L and M and its true economic cost in producing the 9.63 units? Hint: The vertically integrated firm will "charge" itself the marginal cost for M when determining its input mix. c. What is the cost saving that the vertically integrated monopolist will obtain if it produces 9.63 units? That is, what is the saving compared to the cost found in part a? d. What makes this vertical integration profitable? Is it in society's interest if the monopolist holds its output fixed at 9.63 units after vertical integration? e. In fact, after the vertical monopolization of Z, the firm M - Z would have a constant marginal cost of $2. Given this fact, what is the profit-maximizing price Pz and output Z ? Draw a figure to illustrate the overall social benefits and costs of this vertical integration
