sp11-hwk1-ans

sp11-hwk1-ans - Managerial Economics Homework #1 Spring...

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Managerial Economics Homework #1 Spring 2011 Suggested Answers 1. The Portland Sea Dogs, the AA affiliate of the Boston Red Sox major league baseball team, have enjoyed a surge in popularity. During a recent home stand, suppose the club offered \$5 off the \$12 regular price of reserved seats, and sales spurted from 3,200 to 5,200 tickets per game. A. Derive the function that describes the price/output relation with price expressed as a function of quantity (tickets sold). Also express tickets sold as a function of price. B. Use the information derived in part A to calculate total revenues at prices in \$1 increments from \$5 to \$15 per ticket. What is the revenue-maximizing ticket price? If variable costs are negligible, is this amount also the profit-maximizing ticket price? SOLUTION A. When a linear demand curve is written as: P = a + bQ a is the intercept and b is the slope coefficient. Because 3,200 seats were sold at a regular price of \$12 per game, and 5,200 seats were sold at the discount price of \$7, two points on the firm’s linear demand curve are identified. Given this information, it is possible to identify the linear demand curve by solving the system of two equations with two unknowns, a and b : 12 = a + b (3,200) minus 7 = a + b (5,200) 5 = -2,000 b b = -0.0025 By substitution, if b = -0.0025, then: 12 = a + b (3,200) 12 = a - 0.0025(3,200) 12 = a - 8 a = 20

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With price expressed as a function of quantity, the reserved seat demand curve can be written: P = \$20 - \$0.0025Q Similarly, the number of tickets sold (quantity) can be expressed as a function of price: P = \$20 - \$0.0025Q 0.0025Q = \$20 - P Q = 8,000 – 400P This simple linear characterization of the firm’s demand curve can be used to profitably guide production, pricing and promotion decisions. B. The Portland Sea Dogs could use the estimated linear market demand curve to estimate the quantity demanded during the same marketing period for ticket prices in the range from \$5 to \$15 per ticket, using \$1 increments: Price Quantity TR=P×Q \$5 6,000 30,000 6 5,600 33,600 7 5,200 36,400 8 4,800 38,400 9 4,400 39,600 10 4,000 40,000 11 3,600 39,600 12 3,200 38,400 13 2,800 36,400 14 2,400 33,600 15 2,000 30,000 From the table, the revenue-maximizing ticket price is \$10. This is also the profit- maximizing ticket price if variable costs and, hence, marginal costs are negligible. The pricing promotion resulted in declining revenues, and the \$7 price results in an activity level that is above the revenue-maximizing output. Because the marginal
cost of fan attendance cannot be less than zero, the profit-maximizing price cannot be less than the revenue-maximizing price of \$10. 2. 21st Century Insurance offers mail-order automobile insurance to preferred-risk drivers in the

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This note was uploaded on 10/15/2011 for the course QM QM101 taught by Professor Huyduong during the Winter '11 term at RMIT Vietnam.

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sp11-hwk1-ans - Managerial Economics Homework #1 Spring...

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