mid2_2008fx - Answer Key Second Midterm Examination: Econ...

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Answer Key Second Midterm Examination: Econ 101 Richard Buddin Fall 2008 Please answer all questions. The questions are in no particular order. If you do not understand a question, you should skip it and return to it later in the exam. 1. Firm 1 and Firm 2 are two competitive firms located near one another. Firm 1 produces an output X, and Firm 2 produces an output Y. The cost functions for the two firms are C X =0.25X 2 +4X+0.3Y 2 for Firm 1 and C Y =0.3Y 2 +3Y-0.15X 2 for Firm 2. P X =$34 and P Y =$30. a) Discuss externalities in the context of this problem. What is the nature of the externalities and why might this lead to inefficiencies? b) If the two firms make their production decisions independently, what levels of output would maximize profit for each firm? What will be firm profits? c) If an entrepreneur buys both firms, what levels of output would maximize profits? What will be firm profits for the merged firm? Discuss why profits are different here than in part b. d) Suppose that the two firms remained separate, and the local government instituted a Pigouvian tax and subsidy policy to promote efficiency. What tax and subsidy should the government set for each firm? Answer: a) Increases in Y increase the costs of X, and this is a negative externality. Increases in X reduce the cost of Y, and this is a positive externality. These externalities are likely to cause inefficiencies, because Firm 1 and 2 will consider the effects of their production decision on their separate profitability. In a collective sense, however, they are not considering the costs & profits from a broader social perspective. b) X*=60, Y*=45. Profits for Firm 1 are 292.5 & profits for Firm 2 are 1147.5. The total is 1440. c) X*=150, and Y*=22.5. Firm 1 portion of profits are -1276.88, and Firm 2 portion of profits is 3830.625. The total is 2553.75. The profits increase, because the entrepreneur weighs the effects of output changes on overall profitability. This internalizes the externalities. d) The government should subsidize Firm 1 at the rate of $45 per unit of X produced and tax Firm 2 at the rate of $13.5 per unit of Y produces. These taxes will induce the firms to produce the efficient amounts that take account of the externalities.
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This note was uploaded on 12/08/2008 for the course ECON 101 taught by Professor Buddin during the Spring '08 term at UCLA.

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mid2_2008fx - Answer Key Second Midterm Examination: Econ...

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