# Managerial Economics Chapter 2 Hirschey

5896 WordsOct 22, 201124 Pages
P2.6 Price and Total Revenue. 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…show more content…
Calculate the profit-maximizing activity level. B. Calculate the company's optimal profit, and optimal profit as a percentage of sales revenue (profit margin). P2.7 SOLUTION A. Set MR = MC and solve for Q to find the profit-maximizing activity level: MR = MC \$1,500 = \$500 + \$0.01Q 0.01Q = \$1,000 Q = 100,000 This is a profit maximum because profits are decreasing for Q > 100,000. B. The total revenue function for 21st Century Insurance is: TR = P × Q = \$1,500Q Then, total profit is π = TR - TC = \$1,500Q - \$41,000,000 - \$500Q - \$0.005Q2 = 1,500(100,000) - 41,000,000 - 500(100,000) - 0.005(100,0002) = \$9,000,000 TR = \$1,500(100,000) = \$150,000,000 or \$150 million Profit Margin = π/TR = \$9,000,000/\$150,000,000 = 0.06 or 6 percent P2.9 Average Cost Minimization. Giant Screen TV, Inc., is a Miami-based importer and distributor of 60-inch screen HDTVs for residential and commercial customers. Revenue and cost relations are as follows: TR = \$1,800Q - \$0.006Q2 MR = ∂TR/∂Q = \$1,800 - \$0.012Q TC = \$12,100,000 + \$800Q + \$0.004Q2 MC = ∂TC/∂Q = \$800 + \$0.008Q A. Calculate output, marginal cost, average cost, price, and profit at the average cost-minimizing activity level. B. Calculate these values at the profit-maximizing activity