Problem 2 Suppose we have a monopolist who sells goods in a market with 3 consumer...

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Problem 2 Suppose we have a monopolist who sells goods in a market with 3 consumer types, indexed by i = 1, 2, 3. Aggregate demand for each consumer type is: Q(P) = = 100-5P Q2(P) 30 P Q3(P) = 80 - 2P where Q(P) refers to the total quantity consumers by consumer type i when the price is P. The monopolist has constant marginal costs of $10 per unit sold. A. Suppose that the monopolist is unable to price discriminate, so it sets a single price for all consumers. What is the equilibrium price and monopolist profits? What are the type-specific equilibrium quantities? B. Now suppose that the monopolist can engage in third degree price discrimination by offering each consumer type a separate price. What are the optimal prices for each consumer type? What is the monopolist's total profits? C. Now suppose (for the rest of the problem) that third degree price discrimination is costly, such that the monopolist must incur a positive fixed cost F for every price it maintains. For instance, this could include administrative costs of maintaining different prices for different groups. Thus, the monopolist may want to engage in full (3 separate prices), partial (2 prices), or no (1 price) third degree price discrimination, where partial refers to having some consumer types have their own price and other consumer types pool together and have a single price. What is the range of values F could take such that the monopolist is still willing to set 3 separate prices? D. What is the range of values F could take such that the monopolist chooses to set 2 separate prices? In this range, what are the prices and to which consumer types do they apply to? E. What is the range of values F could take such that the monopolist chooses to sell at a single price? Problem 2 Suppose we have a monopolist who sells goods in a market with 3 consumer types, indexed by i = 1, 2, 3. Aggregate demand for each consumer type is: Q(P) = = 100-5P Q2(P) 30 P Q3(P) = 80 - 2P where Q(P) refers to the total quantity consumers by consumer type i when the price is P. The monopolist has constant marginal costs of $10 per unit sold. A. Suppose that the monopolist is unable to price discriminate, so it sets a single price for all consumers. What is the equilibrium price and monopolist profits? What are the type-specific equilibrium quantities? B. Now suppose that the monopolist can engage in third degree price discrimination by offering each consumer type a separate price. What are the optimal prices for each consumer type? What is the monopolist's total profits? C. Now suppose (for the rest of the problem) that third degree price discrimination is costly, such that the monopolist must incur a positive fixed cost F for every price it maintains. For instance, this could include administrative costs of maintaining different prices for different groups. Thus, the monopolist may want to engage in full (3 separate prices), partial (2 prices), or no (1 price) third degree price discrimination, where partial refers to having some consumer types have their own price and other consumer types pool together and have a single price. What is the range of values F could take such that the monopolist is still willing to set 3 separate prices? D. What is the range of values F could take such that the monopolist chooses to set 2 separate prices? In this range, what are the prices and to which consumer types do they apply to? E. What is the range of values F could take such that the monopolist chooses to sell at a single price?