these prices, EZ Sharp is selling 3,750 units of the Classic model per month and 2,000 units of the Professional model per month. $30 AVC P SMC P $20 AVC C SMC C 10 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0 20 30 40 50 60 70 80 90 100 Quantity (thousands of units) Price and cost (dollars) MC MR B MR S 120 D S D B 110 C H A P T E R 14 Advanced Pricing Techniques 619 P R I C E , L A M O N I C A 2 7 2 9 B U
a. Using the cost-plus technique, compute the prices the owner-manager charges for the Classic and the Professional models, based on his required 200 percent profit margin. b. How much profit is EZ Sharp earning each month using the cost-plus prices in part a ? The owner–manager is ready to sell the firm, but he knows the value of the firm will increase if he can increase the monthly profit somehow. He decides to hire Andrews Consulting to recommend ways for EZ Sharp to increase its profits. Andrews reports that production is efficient, but pricing can be improved. Andrews argues that the cost- plus pricing technique is not working well for EZ Sharp and presents a new pricing plan based on optimal pricing techniques (i.e., the MR MC rule). To implement the MR MC methodology, Andrews undertakes a statistical study to estimate the demands for two Keen Edge™ products. The estimated demands are where Q C and Q P are the monthly quantities demanded of Classic and Professional models, respectively, and P C and P P are the prices of the Classic and Professional mod- els, respectively. Andrews Consulting solved the demand equations simultaneously to get the following inverse demand functions, which is why Anderson gets paid the “big bucks”: c. Find the two marginal revenue functions for the Classic and Professional model sharpeners. d. Set each marginal revenue function in part c equal to the appropriate cost and solve for the profit-maximizing quantities. e. Using the results from part d , what prices will Andrews Consulting recommend for each of the models? f. When the owner–manager sees the prices recommended by Andrews Consulting, he brags about how close his simple cost-plus pricing method had come to their suggested prices. Compute the profit EZ Sharp can earn using the consultants’ prices in part d. Is there any reason for the owner–manager to brag about his cost- plus pricing skills? 8. Although there is relatively little difference in the cost of producing hardcover and pa- perback books, these books sell for very different prices. Explain this pricing behavior. 9. The Wall Street Journal once reported on dating services, noting that the fees were $300 for men and $250 for women. The owner of the service said that the difference in fees was to compensate for inequalities in pay scales for men and women. Can you suggest any alternative reasons for this difference?