Sherry was just rotated out as Microsoft's X-Box sales manager for the Canadian market. In Canada, the X-Box competes with Nintendo's GameCube. Based upon sales and price data from different cities, Sherry estimated the following demand equation for X-Box in Canada:
QXd = 100,000 - 300 PX + 200 PG
where QXd is annual units of X-Box sold in Canada, PX is the average wholesale price of X-Box in Canada, and PG is the average wholesale price of GameCube in Canada. During the previous year, Nintendo sold 82,300 units of GameCube in Canada at an average wholesale price of $200. In contrast, Microsoft sold 102,500 units of X-Box in Canada during the year under Sherry's leadership.
a. For last year, what is the own-price elasticity of demand for X-Box and what is the cross-price elasticity of demand for X-Box with respect to GameCube?
Annual compensation for sales managers equals 2% of the sales revenue they generate in their region. Taking Sherry's place is Winston. Winston has been in sales for Microsoft for three years and is keen on maximizing his take home pay.
b. Assuming that demand and market conditions remain the same for X-box in Canada, will Winston sell the same number of X-Box units this next year that Sherry did last year? If Winston chooses a different quantity, then how many will he sell and will he be able to claim a larger market share than Sherry did? Will he be able to claim a larger pay-check than Sherry? Given Winston's strategy, what is the own-price elasticity of demand for X-Box and what is the cross-price elasticity of demand for X-Box with respect to GameCube? (You can answer these questions without any knowledge of production costs.)
Assume it costs Microsoft $90 to produce, package, and ship an X-Box unit. A Senior Vice President at Microsoft argues that the compensation formula for sales managers is not best for the company and is stockholders. He points out that if Winston sold X-Box units at a price of $250, Microsoft would realize more profit.
c. Is the Senior Vice President right? At Microsoft, are the goals of maximum market share, maximum revenues, and maximum profit one in the same?