EZ Sharp industries Inc manufactures the Keen Edge line of diamond abrasive cutlery sharpeners for home use. Dia Sharp holds a patent on ist 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 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 AVCc and SMCc are the constant costs for the Classic model and AVCp and SMCp are the constant cost each month are $10,000. The sole owner of EZ Sharp also manages the firm and makes all pricing decisons. The owner -manager believes in assuming himself a 200 percent profit margin by using the cost-plun 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 unites of Professional model per month.
a. Using the cost-plus techinque, compute the prices the owner charges for the Classic and the Professional models, based on his requried 200 perfec profit margin.
b. How much profit is EZ sharp earning each month using the cost-plus prices in part a?
The owner 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 Consutling to recommend ways for EZ Sharp to increase it profits. Andrews reports that production is efficient, but pricing can be improved. Andrews argures that the cost-plus pricing technique is not working well and presents a new pricing plan based on optimal pricing techniques(ie MR=MC rule)
To implement teh MR=MC methodology, Andrews undertakes a statisical study to estimate the demands for two Keen Edge products. The estimated demands are
Qc = 6000 - 75Pc + 25Pp
Qp = 5000 - 50Pp + 25 Pc
where Qc and Qp are the monthly quantities demanded of Classic and Professional models respectively and Pc and Pp are the prices of Classic and Professional models respectively. Andrews Consulting solved the demand equations simultaneously to get the following inverse demand funcations which is why Andrews gets paid the big bucks
Pc = 136 - 0.016Qc - 0.008Qp
Ps = 168 - 0.008Qc - 0.024Q
c. Find the two marginal revenue function for the Classic and Professional models.
d. Det each marginal reveue function in part c equal to the appropriate cost and solve for the profit maximizing quantities.
e. Using the results for part d, what prices will Andrews Consulting recommend for each of the models.
f. When the owner sees the price recommened by Andrews , he brags abou how close his simple cost-plus pricing method had come tho their suggested price. Compute the profit EZ Sharp can earn using the consultants' prices in part d. Is there any reason for the owner to bray about his cost-plus pricing skills?