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Predicting market shares

Over any given month, Dress-Rite loses 10% of its customers to Fashion, Inc., and 20% of its market to Luxury Living. But Fashion, Inc., loses 5% of its market to Dress-Rite and 10% of its market to Luxury Living each month; and Luxury Living loses 5% of its market to Fashion, Inc., and 5% of its market to Dress-Rite. At the present time, each of these clothing stores has an equal share of the market.

a. What do you think the market shares will be next month?
b. What will they be in three months?

Problem 16-18
The cellular Phone industry is very competitive. Two companies in the greater Lubbock area, Horizon and Local Cellular, are constantly battling each other in an attempt to control the market. Each company has a one-year service agreement. At the end of each year, some customers will renew, while some will switch to the other company. Horizon customers tend to be loyal, and 80% renew, while 20% switch. About 70% of the Local Cellular customers renew with them and about 30% switch to Horizon. If there are currently 100,000 Horizon customers this year, and 80,000 Local Cellular customers, how many would we expect each company to have next year?

Note: Please review the PowerPoint Slides using the link below for the next two problems:
http://wps.prenhall.com/bp_render_qam_9/0,11119,2557610-,00.html

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I would do the second problem first....it uses the same method as the first problem, but is much simpler.

Over any given month, Dress-Rite loses 10% of its customers to Fashion, Inc., and 20% of its market to Luxury Living. But Fashion, Inc., loses 5% of its market to Dress-Rite and 10% of its market to Luxury Living each month; and Luxury Living loses 5% of its market to Fashion, Inc., and 5% of its market to Dress-Rite. At the present time, each of these clothing stores has an equal share of the market.

a. What do you think the market shares will be next month?
b. What will they be in three ...

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