Concumers in a certain state can choose between three long-distance telephone se

Question

Concumers in a certain state can choose between three long-distance telephone services: GTT, NCJ, and Dash. Agressive marketing by all three companies results in continual shift of customers among the three services. Each year, GTT loses 10% of its customers to NCJ and 10% to Dash, NVJ loses 30% of its customers to GTT and 15 to Dash, and Dash loses 5% of its customers to GTT and 25% to NCJ. Asumming that these percentages remain valid over a long period of time, what is each company's expected market share in the long run?

Explanation / Answer

GTT and NJC will wither and die (0% share) and Dash will take over in about 50 years. On microsoft Excel -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)

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