SOLUTION: hi everyone please help me with these.. suppose three companies: A, B, C dominates the market for a certain product and are competing against each other for a large share of the m

Question 1035222: hi everyone please help me with these..
suppose three companies: A, B, C dominates the market for a certain product and are competing against each other for a large share of the market. currently comapany A has 2/9 of the market, comapany B has 4/9 of the market and company C has 1/3 of the market. the market survey indicates that every 6 months company A retains 3/4 of its customer and loss 1/6 to company B and 1/12 to company C. company B retains 1/2 of its customer and loss 1/3 to company A and 1/6 to company C. company C retains 3/8 of its customer and loss 1/4 to company A and 3/8 to company B. find the share of the market that each company will have.
1. one year later
2. in the long run
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
three companies: A, B, C dominates the market for a certain product and are competing against each other for a large share of the market.
---------
currently company A has 2/9 of the market, company B has 4/9 of the market and company C has 1/3 of the market.
------------------------------------
the market survey indicates that every 6 months
company A retains 3/4 of its customer and losses 1/6 to company B and 1/12 to company C.
company B retains 1/2 of its customer and losses 1/3 to company A and 1/6 to company C.
company C retains 3/8 of its customer and losses 1/4 to company A and 3/8 to company B. find the share of the market that each company will have.
=======
1. one year later:
A = 2[((3/4)-(1/6)-(1/12))(2/9) +(1/3)(4/9) +(1/4)(1/3)]
B = 2[((1/2) -(1/3)-(1/6))(4/9) +(1/6)(2/9) +(3/8)(1/3)]
C = 2[((3/8) -(1/4)-(3/8))(1/3) +(1/12)(2/9)+(1/6)(4/9)]
2. in the long run
Compare the answers you get for A,B,C to the fraction
they had at the beginning of the year. See a decrease
or an increase?? That's what will happen each year.
I'll leave that to you.
Cheers,
Stan H.
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