OSU Econ 462: Managerial Economics – A monopolist has an (inverse) demand curve for its product

OSU Econ 462: Managerial EconomicsProblem Set #3DUE: In-Class, Mon., May 23.1. A monopolist has an (inverse) demand curve for its product of P = 30 – 6Q (where Q is inmillions of units). Its total cost curve is: TC = 14 + 3Q + 3Q2. Find the profit maximizinglevel of output, the profit maximizing price and the monopolist’s profits.2. Suppose you have 8 customers for a good that only you produce. For simplicity, assumethat the total and marginal cost of producing the good is zero. Each customer has adifferent willingness to pay for the good and these are listed below:CustomerABCDEFGHWillingness to pay$109876543a. Suppose that you cannot tell these customers apart and have to act as a simplemonopolist: What is the optimal price and quantity pair? What is the total profit?b. Suppose instead you can act as a perfect price discriminator: What is the optimalpricing scheme? What is the total profit?c. Suppose you can only tell if a customer is one of the top four customers or one of thebottom four customers: What is the optimal pricing scheme? What is the totalprofit?3. A firm that produces cars sells three types: a low quality car for $12,000, a mediumquality car for $18,000 and a high quality car for $26,000. Is this evidence of this firmpracticing price discrimination? Explain.4. A monopolist produces a single good from the utilization of two plants, plant 1 and plant2. It faces an inverse demand curve of: P = 1100 – 2Q, where Q is total quantityproduced, thus Q = q1 + q2. q1 = quantity produced in plant 1 and q2 = quantity producedin plant two. Plant 1 is an older plant and has a marginal cost of production equal to10q1. Plant 2 is newer and its marginal cost of production is 5q2. How much should thismonopolist produce in total and how much will each plant be producing at the profitmaximizing level of output?5. A university has determined that its students fall into two categories when it comes toroom and board demand. University planners call these two types, Sleepers and Eaters.The reservation prices for a dormitory room and the basic meal plan of the two types areas follows:Dorm RoomMeal PlanSleepers$5,500$2,500Eaters$3,000$6,000Currently, the university offers students the option of selecting just the dorm room at$3,000, just the meal plan at $2,500, or both for a total price of $5,500. An economicconsultant advises the university to stop offering the two goods separately and, instead, tosell them only as a single, combined room and board package. Explain the consultant’sstrategy and determine what price the university should set for the combined product.6. In the early 1970s, the six largest manufacturers of ready-to-eat breakfast cereals had 95percent of the market. Over the preceding twenty years, these same manufacturersintroduced over eighty new varieties of cereals. How would you evaluate this strategyfrom the standpoint of the Hotelling spatial model described in the lecture?