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##### A monopolist has to decide how to price its product in two markets

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**Question**

A monopolist has to decide how to price its product in two markets and how to allocate product output between them. The markets are separated geographically by a national border. Demand in the two markets is;Q1 = 35 ? 1/2 P1;Q2 = 55 ? 1/2 P2;(Prices are in dollars and quantities are in units sold.) The monopolist?s total cost is;TC = 25(Q1 + Q2).;What are the prices charged, total product shipped to each market, and total profits under the following two conditions;a.The border is opened to free trade;b.The border is closed to trade and the markets are separated (the firm can ship to both markets, but product sold in one market can not be resold in the other).;The market for an industrial chemical has a single dominant firm, Don?s Chemicals (DC), and many other smaller firms that form a competitive fringe. DC has recently begun behaving as a price leader, setting price in the market while the other smaller competitors follow. The market demand curve and competitive fringe supply curve are given below. Marginal cost for DC is $0.8 per gallon.;QM = 160 ? 30 P;QF = 80 + 20 P;where QM is the market quantity demanded and QF is the amount supplied by the competitive fringe. Quantities are measured in gallons per week, and price is measured as price per gallon.;Assuming the dominant firm wishes to maximize profits, determine the price and output that would prevail in the market under the conditions described above. Identify the amount supplied by the dominant firm as well as the amount supplied by the competitive fringe.;Market researchers have determined that the per capita annual market demand for gasoline can be written as a linear relationship in logarithms, as follows;ln QGt = 6.8 - 0.49 ln PGt + 0.38 ln INCt + 0.50 ln QGt-1;where ln is natural logarithm, QGt and QGt-1 are annual per capita number of gallons of gasoline purchased in year t and year t-1, respectively, PGt is price per gallon of gasoline in year t, and INCt is per capita income in year t.;(a) What are the short-run price and income elasticities for gasoline? Why?;(b) What is the speed of adjustment between years t-1 and t? Why?;(c) What are the long-run price and income elasticities for gasoline? Why?;Suppose that your firm is the only producer of a high-tech sports utility vehicle for the US market. Assume a constant marginal cost of $30,000 to produce each vehicle and no fixed costs of production.;a. The US demand for the vehicle is given as Q = 30,000 - 500P where price is in thousands of dollars. What quantity of vehicles should you produce, what price will you charge, and what profits will you make?;b. Now suppose that there is a fixed cost of production of $45 million. How would your answer change to part a)?;The rock band Aerosmith is coming to Boston to perform at Fenway Park, and you are in charge of pricing and selling the tickets (assume all seats are the same and you only need to set a single price). Independent of the number of seats sold, you must pay the administration of Fenway Park a fixed amount of $950,000 to cover security and cleaning costs, which represents the only cost. There are 38,000 seats in Fenway Park.;a. Based on historical data, you estimate the demand for this event to be;Q = 70 ? (0.4) P;where Q is in thousands of tickets and P is the price per ticket in dollars. What price P should you charge? How many tickets will you sell and what are your profits? (Don?t worry if there are empty seats, you can always give those seats away to worthy charities.);b. Shortly before the concert, Aerosmith?s first Greatest Hits album is released, with rave reviews about how the band has evolved rock music in a revolutionary way. Because of this, you now believe that demand will be given as;Q = 90 ? (0.4) P;where again Q is in thousands of tickets and P is the price per ticket in dollars. What price P should you charge? How many tickets will you sell and what are your profits? (Again, don?t worry if there are empty seats);c. Suppose with demand as in b), you have the option of adding some temporary seats on the grass field for a cost of $45 a seat (assume these seats have the same view as the other seats and tickets for them would sell for the same price). Would you add any seats? What price P would you charge? How many tickets would you sell and what would your profits be?;d. Suppose with the situation in c), that the City of Boston decides to charge you $45 per ticket sold. What price P should you charge? How many tickets will you sell and what are your profits?

Paper#18114 | Written in 18-Jul-2015

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