Unformatted text preview: a * = 150. (c) What are the profits of each producer? The honey producer’s total cost equals (100 2 /100) – 150/5 = $70; since its revenues equal $200, its profit is $130. The apple producer’s total cost equals (150 2 /100) – 100 = $125; since its revenues equal $450, its profit is $325. (d) Suppose the two firms merge. Solve for the quantity of honey and apples produced and the profit of the merged company. ( Hint : Write down the profit function of the merged firm and then differentiate with respect to h and a .) The profit of the merged firm is π = 3 a + 2 h – [( a 2 /100) – h ] – [( h 2 /100) – a /5]. Differentiate with respect to h and set equal to zero: 2 + 1 – h /50 = 0. Solving, we get h **= 150. Differentiate with respect to a and set equal to zero: 3 + (1/5) – a /50 = 0. Solving, we get a **= 160. Then π = $481, more than the combined profits of the two firms when they were separate (130+325=$455)....
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 Summer '07
 Dr.ShomuBanerjee
 Economics, Microeconomics, Externalities, producer, Honey

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