Consumers in a certain state choose between three long distance telephone servic

Question

Consumers in a certain state choose between three long distance telephone services. GTT, NCJ, and Dash. Aggressive marketing by all three companies results in a continual shift of customers among the three services. Each year, GTT loses 25% of its customers to NCJ and 5% to Dash, NCJ loses 10% of its customers to GTT and 25% to Dash, and Dash loses 5% of its customers to GTT and 30% to NCJ. Assuming that these percentages remain valid over a long period of time, what is each company's expected market share in the long run? So GTT expected market share is ... Dash expected share is.. NCJ expected share is...

Explanation / Answer

long answer short: GTT and NJC will wither and die (0% share) and Dash will take over in about 50 years how-to guide: to illustrate this nicely as a trend graph a theoretical case, the most efficient way to generate the data is using a spreadsheet, if you are proficient with Microsoft Excel for example -make six columns, on for the current # of customers and net change for that year, for each company -to make this simple, I gave each company a 33.3% share to start with, 100 customers each; note: this is with the assumption that they start off with equal shares, use this unless otherwise specified -to find the net change for each company, GTT for example: = -0.4 * [GTT current customers] + 0.15 * [NJC current customers] ; since GTT loses a total of 40% of its business, but NJC loses 15% to GTT, giving GTT a net loss of 25 customers using the above starting data -the other companies can be done in a similar fashion, then add the net change to the current year to get the next year's customer distribution, and repeat (calculate change as a percent of current customers, and calculate for next year) -after about 30 years, the trend will be plenty abundant, I'll leave the analysis write-up up to you, by 50 years Dash will own the market (note that customer #s are integers, some accuracy will be lost in rounding, but can't display 0.8 customers realistically) -enjoy

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