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(b) Consider the Hotelling linear city model. Two firms, 1 and 2, supply a good. The marginal and fixed costs are zero. The firms are located at the extremes of a line of unit length. A continuum of consumers are indexed by x, capturing their preference for a firm, x E [0,1]. Each consumer can demand at most one unit of the good. Their evaluation of the good is 10. The consumers unit transport cost is t 2 0 per unit travelled. Firms compete by setting prices. As a result of the previous assumptions, the utility of consumer x if buying from firm 1 is: U, (x) = 10 - tx - P and if buying from firm 2 is: U2(x) = 10 -t(1 - x) - P2. i) Derive the Nash equilibrium for this game. [7 marks] ii) Assume that in part (a) c = 0. Compare the equilibrium properties (price, market shares, profits) of the two games, and discuss the managerial implications of the findings. [6 marks]Homework for Chapter 1 1: Problem # 2 in the text (Chapter II) NOTE: PLEASE USE THE ATTACHED EXCEL FILE TITLED "Homework for Chapter 11_Excel" TO SOLVE THE FOLLOWING PROBLEM. Black Diamond, Inc., a manufacturer of carbon and graphite products for the aerospace and transportation industries, is considering several funding alternatives for an investment project. To finance the project, the company can sell 1,000 15- year bonds with a $1,000 face value, 7% coupon rate. The bonds require an average discount of $50 per bond and flotation costs of $40 per bond when being sold. The company can also sell 5,000 shares of preferred stock that will pay a $2 dividend per share at a price of $40 per share. The cost of issuing and selling preferred stocks is expected to be $5 per share. To calculate the cost of common stock, the company uses the dividend discount model. The firm just paid a dividend of $3 per common share. The company expects this dividend to grow at a constant rate of 3% per year indefinitely. The flotation costs for issuing new common shares are 7%. The company plans to sell 10,000 shares at a price of $50 per share. The company's tax rate is 40%. a) Calculate the company's after-tax cost of long-term debt. b) Calculate the Company's cost of preferred equity. c) Calculate the company's cost of common equity. d) Calculate the company's weighted average cost of capital. e) What is the company's weighted average cost of capital without flotation costs?Problems For problems 1, 2, 3, and 4 consider a market must at least be covering their vari- containing four identical firms, each of which able costs. Identify the constraint that makes an identical product. The inverse demand y must satisfy for this to be the case. for this product is P = 100 - Q. where P is b. Assume that firms 1 and 2 merge and price and O is aggregate output. The production that all firms continue to act as Cournot costs for firms 1, 2, and 3 are identical and given competitors after the merger. Confirm by C(q;) = 20q;; (i = 1, 2, 3), where q; is the that this merger is unprofitable. output of firm i. This means that for each of c. Now assume that firms 1 and 4 merge. these firms, variable costs are constant at $20 Can this merger be profitable if y is per unit. The production costs for firm 4 are positive so that firm 4 is a high-cost C(q4) = (20 + y)q4, where y is some constant. firm? What has happened to the profits Note that if y > 0, then firm 4 is a high-cost of firm 2 as a result of this merger? firm, while if y qi- costs of F in addition to the variable costs 1=1 noted above. When two firms merge the 1. Assume that the firms each choose their merged firm has fixed costs of bF where outputs to maximize profits given that they 1
0. Derive a condition on b, F, put for each firm, the product price, and and y for this merger to be profitable. the profits of the four firms. For this to Give an intuitive interpretation of this be a "true" equilibrium, all of the firms condition
