Managerial Economics Chapter 2 Hirschey

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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
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