need help with this

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 10% of its customers to NCJ and 25% to Dash, NCJ loses 15% of its customers to GTT and 20% to Dash, and Dash loses 25% of its customers to GTT and 5% 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?

Answer 1

Hi Amee!

With complex, coupled systems like this, we can "eyeball" some main trends:

GTT and Dash "play catch" with each other at 25%.

NCJ loses 35% while getting only 5% from Dash and only 10% from GTT -- NCJ is the loser with Dash getting 20 of the 35% loss or 60% of NCJ's loss...

Change in NCJ STOPS when 0.35 loss = 0.05 Dash + 0.10 GTT.

Start with Dash = GTT of similar size ...

0.35 NCJ = 0.15 GTT, thus GTT is about 2.3 the size of NCJ ...

100% market= GTT + Dash + NCJ= (2.3+2.3+1) NCJ's= 5.6 NCJ -- has about 18%

Start with GTT 40, Dash 42, NCJ 18 ... GTT loses 35% or 14pts while gaining 2.7 NCJ + 10.5 Dash = -1 pt

GTT 39, Dash 43, NCJ 18 ... GTT loses 13.6 pts while gaining 2.7 NCJ + 10.75 Dash = ~0 ;)

Dash loses 30% or 13 pts while gaining 3.6 NCJ + 9.75 = gain 0.35 pts - close!

NCJ loses 35% of 18 or 6.3 pts while gaining 3.9 GTT + 2.1 Dash= lose 0.3 pts

Approx. answer ===> GTT 39-, Dash 43+, NCJ 18- ... Best wishes