ProbSet4Ans - AEM 331 Suggested Answers to Problem Set #4...

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AEM 331 Suggested Answers to Problem Set #4 1. a. Note that AC = 500/ Q + 20 is always falling as Q increases. So there are economies of scale for all levels of output. With a single-product natural monopolist, economies of scale are sufficient for subadditivity, so we can also say that the cost function is subadditive for all levels of output. b. P = MC Q = 100 – 20 = 80. π = 20*80 – (500 + 20*80) = –500. c. Price is equal to average cost implies P = AC 100 – Q = (500 + 20 Q )/ Q 100 Q Q 2 = 500 + 20 Q Q 2 – 80 Q + 500 = 0 Q = 7 or 73 (approximately). We can discard Q = 7 because AC is falling beneath the demand curve there 1 so total surplus is increasing there. Hence, average cost pricing involves Q = 73, P = 27. DWL = ½*(27 – 20)*(80 – 73) = 49/2. d. If the market demand curve is Q = 100 – P , then with N = 10 identical consumers each buying q units, we can say that N*q = 100 – P q = 10 – P /10 is the individual demand curve. Inverting we have P = 100 – 10 q . At P = MC = 20, each consumer is buying q = 8 units, so for an individual CS = ½*(100 – 20)*8 = 320. [Note: You could equivalently calculate the market CS = 3200 and divide by N = 10 to get individual CS .] Thus consumers would pay a fixed fee of no more than $320. To break even, however, the firm only needs to charge 500/ N = $50 per consumer. Because the usage price is set equal to marginal cost, there is zero DWL. 2. a. For “rich” consumers, P = MC 100 – 6.3 q R = 20 q R = 12.7 (approximately). For “poor” consumers, P = MC 100 – 80 q P = 20 q P = 1. Total output is Q = 6* q R + 4* q P = 80.2. With P = MC , the only surplus to worry about here is CS , so first we can just figure that for each rich consumer, CS R = ½*(100 – 20)*12.7 = 508, while for each poor consumer CS P = ½*(100 – 20)*1 = 40. Thus total surplus is TS = CS = 6* CS R + 4* CS P = 3208.
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This note was uploaded on 09/23/2009 for the course AEM 3310 taught by Professor Prince,j. during the Winter '08 term at Cornell University (Engineering School).

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ProbSet4Ans - AEM 331 Suggested Answers to Problem Set #4...

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