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Homework 4Managerial EconomicsDue Tuesday, October 25, 2016Instructions: Show all of your work!!!!1) MonopolyConsider 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 priceand quantity.b) Calculate and draw a diagram that depicts consumer surplus, producer surplus, profits, and anydeadweight welfare loss from the monopolist.c) How does this compare to the socially efficient outcome? Draw a diagram to compare theequilibrium, consumer surplus, and producer surplus. 2) Monopolist as Price-DiscriminatorConsider 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 . Considerthe following three pricing scenarios.a) Calculate the profit-maximizing price and then the optimal quantity sold to each consumerunder uniform pricing, i.e. the monopolist charges the same price for both consumers. What arethe monopolist’s profits? (Hint: first you need to find the market demand curve comprised ofboth consumers. Use horizontal aggregation.)b) Now assume the monopolist can engage in 1st degree price discrimination. What will be themonopolist’s profits? Illustrate the outcome graphically.c) Now assume the monopolist can engage in 3rd degree price discrimination, i.e. the monopolistcan choose a different price for each consumer. Calculate the profit-maximizing prices andquantities consumed by each consumer. What are the monopolist’s profits? How do theseprofits compare with the above two cases?

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