Managerial Economics

Consider a monopolist with a cost function of () = 4 + 2. Suppose the market demand function is = 24 ? 2. a) Under uniform pricing (i.e. the basic monopoly problem), find the monopolist’s optimal price and quantity. b) Calculate and draw a diagram that depicts consumer surplus, producer surplus, profits, and any deadweight welfare loss from the monopolist. c) How does this compare to the socially efficient outcome? Draw a diagram to compare the equilibrium, consumer surplus, and producer surplus. 2) Monopolist as Price-Discriminator Consider a monopolist who has a cost function of () = 10. This monopolist faces two consumers, the first having demand 1 (1 ) = 60 ? 1 and the second having demand 2 (2 ) = 50 ? 2 . Consider the following three pricing scenarios. a) Calculate the profit-maximizing price and then the optimal quantity sold to each consumer under uniform pricing, i.e. the monopolist charges the same price for both consumers. What are the monopolist’s profits? (Hint: first you need to find the market demand curve comprised of both consumers. Use horizontal aggregation.) b) Now assume the monopolist can engage in 1st degree price discrimination. What will be the monopolist’s profits? Illustrate the outcome graphically. c) Now assume the monopolist can engage in 3rd degree price discrimination, i.e. the monopolist can choose a different price for each consumer. Calculate the profit-maximizing prices and quantities consumed by each consumer. What are the monopolist’s profits? How do these profits compare with the above two cases?

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