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Firm 1 produces output x with a cost function c1(x) = x2 + 10. Firm 2 produces output y with a cost function c2(y, x) = y2 + x. Thus, the more that firm 1 produces, the greater are firm 2's costs. Both firms face competitive product markets. The competitive price of x is $20 and the competitive price of y is $40. No new firms can enter the industry and the old ones must remain. The efficient Pigouvian tax on the x good is
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