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HW6 Solutions

# HW6 Solutions - Homework 8 Consider the following demand...

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Homework 8 Consider the following demand curve: P = 24 – Q d , which implies that MR= 24 – 2Q d. Now consider a Monopoly with TC and MC given, respectively, by TC = Q 2 + 36, MC = 2*Q, where Q is the quantity supplied by the monopolist. a. Consider a single price monopoly. What is the optimal monopoly price and quantity? What is the economic profit of the monopoly? In general, a single pricing firm chooses quantity so that MC = MR (whenever price is above the average variable cost in the short run and above the average total cost in the long run). In a perfectly competitive market, MR = P, but this will not be the case for a monopolist that faces a downward sloping demand curve. Here : MR = MC implies, 24 – 2Q = 2Q 4Q = 24 Q M * = 6 P M * = 24 – 6 = 18 P M * = 18 Profit = M = TR – TC = 18*6 – (6 2 + 36) = 108 – 72 = 36 > 0 . b. What quantity would a perfectly competitive industry (with the same costs and facing the same demand) produce? P = MC implies 24 - Q = 2Q 3Q = 24 Q PC = 8 P PC = 16 Profit = PC = TR – TC = 8*16 – (8 2 + 36) = 128 – 100 = 28 .

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Remark: profits are higher as well. c. Producer surplus is the area below the price and above the MC curve (note that profits equal producer surplus minus fixed costs). Graphically show the consumer under a monopolistic environment. Answer: See attached pictures
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HW6 Solutions - Homework 8 Consider the following demand...

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