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# Chapter6 - Chptr 6 Homework Answers P6.3 Revenue vs Profit...

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1 Chptr 6 Homework Answers P6.3 Revenue vs. Profit Maximization. The Best Buy Company, Inc., is a leading specialty retailer of consumer electronics, personal computers, entertainment software and appliances. The Company operates retail stores and commercial Web sites, the best known of which is bestbuy.com. Recently, this site offered a Sony 600- Watt Home Theater with combination 600-total-watt surround sound receiver, 5-disc DVD player with DVD, CD, CD-R/RW and MP3 playback and digital AM/FM tuner plus matching 6-speaker set including subwoofer. At a price of \$1,100, weekly sales totaled 2,500 units. After a \$100 online rebate was offered, weekly sales jumped to 5,000 units. Using these two price-output combinations, the relevant linear demand and marginal revenue curves can be estimated as: P = \$1,200 - \$0.04Q and MR = \$1,200 - \$0.08Q A. Calculate the revenue-maximizing price-output combination and revenue level. If Best Buy = s marginal cost per unit is \$800, calculate profits at this activity level assuming TC = MC Η Q. B. Calculate the profit-maximizing price-output combination. Also calculate revenues and profits at the profit-maximizing activity level. P6.3 SOLUTION A. To find the revenue-maximizing price-output rental rate, set MR = 0, and solve for Q. Because TR = P Η Q = (\$1,200 - \$0.04Q)Q = \$1,200Q - \$0.04Q 2 MR = Μ TR/ Μ Q MR = \$1,200 - \$0.08Q = 0 0.08Q = 1,200 Q = 15,000

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2 At Q = 15,000, P = \$1,200 - \$0.04(15,000) = \$600 Total revenue at a price of \$600 is: TR = P Η Q = \$600 Η 15,000 = \$9 million per week π = TR - TC = \$1,200Q - \$0.04Q 2 - \$800Q = \$1,200(15,000) - \$0.04(15,000 2 ) - \$800(15,000) = -\$3 million per week (loss) ( Note: Μ 2 TR/ Μ Q 2 < 0. This is a revenue-maximizing output level because total revenue is decreasing for output beyond Q > 15,000 units.) B. To find the profit-maximizing output level analytically, set MR = MC, or set M π = 0, and solve for Q. Because MR = MC \$1,200 - \$0.08Q = \$800 0.08Q = 400 Q = 5,000 At Q = 5,000, P = \$1,200 - \$0.04(5,000) = \$1,000