Consumers in a certian state can choose between three long-distance telephone se

Question

Consumers in a certian state can choose between three long-distance telephone services: GTT, NCJ, 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 20% to DASH, NCJ loses 15% of its customers to GTT and 20% to DASH, and DASH loses 10% of it customers to GTT and 5% to NCJ. Assuming that these percentages reain valid over a long period of time, what is each company's expected market share in the long run?

Explanation / Answer

....... GTT NCJ Dash
GTT 0.55 0.25 0.20
NCJ 0.15 0.65 0.20
Dash 0.10 0.05 0.85

for steady state,
0.55p +0.15q + 0.10r = p
0.25p +0.65q + 0.05r = q
0.20p +0.20q + 0.85r = r
p+q+r = 1

which yields

[ 0.202 0.226 0.571 ]

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.