Econ 100A Ans to PS4 - Department of Economics University...

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Econ 100A-Spring 2007 Page 1 Problem Set 4 Answers D e p a r t m e n t o f E c o n o m i c s Spring 2007 University of California, Berkeley Prof. Woroch Economics 100A PROBLEM SET 4 ANSWER SHEET TRUE or FALSE or UNCERTAIN and EXPLAIN : For each statement below, decide whether it is true or false or cannot be determined given the information, and explain the reasoning behind your answer in a few sentences. When appropriate, provide a diagram. 1. If the generation of electricity is known to have a cost function given by C(Q) = 100 + Q 2 , where Q is measured in mega-watts per year, then the market for electricity is a natural monopoly. Uncertain. It will depend on the level of demand for the product. Assuming that we are examining a long-run cost function, MC(Q)=2Q and ATC(Q)=100/Q + 2Q. The marginal cost curve is upward sloping and the average total cost curve is U-shaped. Remember that a natural monopoly exists when one firm can produce the total quantity demanded at a lower cost than if several firms supplied the product: C(Q 1 + Q 2 ) < C(Q 1 ) + C(Q 2 ). Plugging in the cost into this inequality gives: 100 + (Q 1 + Q 2 ) 2 < 100 + (Q 1 ) 2 + 100 + (Q 2 ) 2 . Rearranging we have: (Q 1 ) 2 + 2Q 1 Q 2 + (Q 2 ) 2 < 100 + (Q 1 ) 2 + (Q 2 ) 2 . Simplifying gives: Q 1 Q 2 < 50. If total production is small then dividing it between two plants will raise cost. If total production is large, however, one plant will be more costly than two. What is happening is that two plants have high average costs because they duplicate the fixed costs of 100, but a single plant has high costs because of rapidly rising average costs. Which configuration has lower cost depends on scale of production. 2. When there is only fixed cost to production, and no variable cost, a monopolist will set price to maximize its revenue, even if that price is below the firm’s average total cost. True. The monopoly wants to maximize its profits, that is, the difference between the revenue and the cost of production. Given that cost of production is independent of the scale, the monopoly maximizes profits by maximizing its revenue. The price can be below the average total cost, as monopolists can loss money. In this case the monopoly would be minimizing this loss. Note that maximum revenue occurs where marginal revenue is zero, i.e., at the top of the revenue hill. 3. All consumers are worse off under perfect (first degree) price discrimination practiced by a monopolist compared to the case when the firm must set a single price. False. In the case of first degree price discrimination, the monopolist extracts the entire consumer surplus from every individual that buys its product. However, if the monopolist must set a single price, some consumers would find it too high and would not buy the product. Therefore, these consumers do not have any consumer surplus and are indifferent between both cases.
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Econ 100A Ans to PS4 - Department of Economics University...

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