Question 1035222
 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.
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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. 
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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.
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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.