EZ Sharp Industries, Inc., manufactures the Kleen Edge(TM) 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 Kleen Edge(TM) products wisely. EZ Sharp sells two models of its Kleen Edge(TM) 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:
$20.00 = AVCc = SMCc
$30.00 = AVCp = SMCp
Where
AVCc and SMCc are constant cost for the classic model and
AVCp and SMCp are 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% 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 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% 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. Andrew reports that production is efficient, but pricing can be improved. Andrews argues 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 Kleen Edge (TM) products. The estimated demands are:
Qc = 6,000 – 75Pc + 25 Pp
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 prices of 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 model?
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?