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Quiz 22. Production externalities Ans

# Quiz 22. Production externalities Ans - a = 150(c What are...

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Shomu Banerjee ECON 201 EXTERNALITY QUIZ ANSWERS A honey farm is located next to an apple orchard. The honey producer’s cost function is c H ( h ) = ( h 2 /100) – a /5, where h is the quantity of honey produced and a is the quantity of apples produced—there is a positive externality here since apple production reduces the honey farm’s cost of production. The apple orchard’s cost function is c A ( a ) = ( a 2 /100) – h , which shows a similar positive externality since honey production reduces the apple producer’s cost. Each firm behaves as competitive producer in its market and maximizes its profits. (a) Suppose the price of honey is \$2 per unit. How much honey does the farm produce? The marginal cost of the honey producer is MC H = h /50. Set the price of \$2 equal to the marginal cost to get h * = 100. (b) Suppose the price of apples is \$3 per unit. How many apples does the orchard produce? The marginal cost of the apple producer is MC A = a /50. Set the price of \$3 equal to the marginal cost to get
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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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