EZ Sharp Industries, Inc., manufactures the Keen Edge™ line of diamond-abrasive cutlery sharpeners for home use. EZ Sharp holds a patent on its unique design and can earn substantial economic profit if it prices its Keen Edge™ products wisely. EZ Sharp sells two models of its Keen Edge™ sharpeners: the Classic, which is the entry-level model, and the Professional, which has a sonic sensor that controls the speed of the sharpening wheels.

Short-run production of sharpeners is subject to constant costs: AVC = SMC for both models. The constant costs of production at EZ Sharp Industries are estimated to be

$20 = AVCC = SMCC

$30 = AVCP = SMCP

where AVC C and SMC C are the constant costs for the Classic model and AVC P and SMC P are the constant costs for the Professional model. Total fixed costs each month are $10,000. The sole owner of EZ Sharp also manages the firm and makes all pricing decisions. The owner–manager believes in assuring himself a 200 percent profit margin by using the cost-plus pricing methodology to set prices for his two product lines. At 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.

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’s 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

QC = 6,000 − 75PC + 25PP

QP = 5,000 − 50PP + 25PC

Where QC and QP are the monthly quantities demanded of Classic and Professional models, respectively, and PC and PP are the prices of the Classic and Professional models, respectively. Andrews Consulting solved the demand equations simultaneously to get the following inverse demand functions, which is why Anderson gets paid the “big bucks”:

PC = 136 − 0.016QC − 0.008QP

PS = 168 − 0.008QC − 0.024QP

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?