Homework 3 Managerial Economics Due Tuesday, June 25, 2019 Instructions: Show all of your work!!!! 𝟑 𝟐 1. A monopolist with total cost function 𝒄(𝑸) = 𝟓𝟎𝑸 + 𝑸𝟐 faces a market demand function of 𝑸𝑫 (𝑷) = 𝟏𝟓𝟎 − 𝟐𝑷. a) Identify and give an example of four sources of monopoly power. b) Calculate the monopolist’s profit-maximizing price and quantity sold, and the monopolist’s profits. 𝟏 𝟐 2. A monopolist with total cost function 𝒄(𝑸) = 𝟒 + 𝟑𝑸 + 𝑸𝟐 faces a market demand function of 𝑸𝑫 (𝑷) = 𝟔𝟎 − 𝟒𝑷. a) Calculate the monopolist’s profit-maximizing price and quantity sold, and the monopolist’s profits, if the monopolist engages in uniform pricing. b) Depict the standard monopoly outcome with a graph (you do not have to graph the functions given above, just the generic monopoly problem). 𝟏 𝟐 3. A monopolist with total cost function 𝒄(𝑸) = 𝟏𝟎 + 𝑸𝟐 faces a market with two distinct consumer groups with the first group having a demand function of 𝑸𝟏 (𝑷) = 𝟖𝟎 − 𝟓𝑷𝟏 and the second having a demand function of 𝑸𝟐 (𝑷) = 𝟒𝟎 − 𝟐𝑷𝟐 . a) Is this monopolist operating in the short run or the long run? Explain how you know. b) The monopolist can engage in third degree price discrimination, setting a different price for each market segment. Calculate the monopolist’s optimal prices charged to each market segment, the quantities consumed by each market segment, and the monopolist’s profits. c) Calculate the monopolist’s profit-maximizing price and quantity sold if the monopolist must now engage in uniform pricing. Find the monopolist’s profits in this scenario. (Hint: use horizontal aggregation to form the total market demand curve). Would the monopolist rather engage in this price discrimination or would they rather set a uniform price? 4. A monopolist with cost function 𝒄(𝑸) = 𝑸𝟐 faces a demand function of 𝑸𝑨 (𝑷) = 𝟓𝟎 − 𝑷𝑨 in market segment A and 𝑸𝑩 (𝑷) = 𝟗𝟎 − 𝟐𝑷𝑩 in market segment B. a. Suppose the monopolist engages in 3rd degree price discrimination. Calculate monopolist’s profit maximizing prices and quantities for each market. b. Suppose now the monopolist has to engage in uniform pricing. What is the monopolist’s profit-maximizing price they should set? How do their profits compare to the profits they earn in part (a) above? (Hint: use horizontal aggregation to form the total market demand curve). c. Suppose the monopolist can upgrade their plant so that the cost function becomes: 𝑐(𝑄𝐴 , 𝑄𝐵 ) = 3𝑄𝐴 2 + 𝑄𝐵 2 . How much should you be willing to pay to get this upgrade?
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