Business, 10.03.2020 00:52 dayday0

Externalities. Consider the case where Firm S is producing steel (s) and pollution (x), and firm F is producing fishery (f). Both are producing in a perfectly competitive market where the market price is ps = 40 for steel, pf = 20 for fish, and pollution is free of charge. The cost function for firm S is cS(s, x) = s 2 + (x − 10)2 , and the cost function for firm F is cF (f, x) = 2f 2 + x 2 . (a) Write down the profit maximization problem for both firms. (b) Solve for firm S, the optimal amount of (s, x) it will choose to produce, and for firm F, the optimal amount of f it will produce. (c) Calculate the profit of each firm based on your answer to part (b). (d) Suppose the two firms merged into one large firm L. Its cost function is the sum of the two individual cost functions cL(s, x, f) = cS(s, x) + cF (f, x) = s 2 + (x−10)2 + 2f 2 + x 2 . Write down the profit maximization problem for the merged firm L, and find the optimal amount of (s, x, f) it will produce. (e) Calculate the profit for the merged firm L based on your answer to part (d). Compared to your answer in part (c), does internalizing the externalities increase the total profit?

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Externalities. Consider the case where Firm S is producing steel (s) and pollution (x), and firm F i...

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