Use Matlab code Q1. 4 supermarkets (A, B, C, D) working on advertisement to get

Question

Use Matlab code

Q1. 4 supermarkets (A, B, C, D) working on advertisement to get higher market share. After several months, it is found a stable transition was established as follows:

30% customers of A stay with A, 10% changes to B, 30% changes to C, and rest customers changes to D; 20% customers of B changes to A, 35% stays with B, none changes to C, and rest to D;

and both C and D keep all customers.

a.Prepare a transition matrix, and

b.Get the limit transition matrix.

c.If the market share begins with A=0.3, B=0.3, C=0.15, and D=0.25, please find the stable market share.

Can you please provide MATLAB code for this?

Explanation / Answer

a)

P = [0.3 0.1 0.3 0.3 ; 0.2 0.35 0 0.45; 0 0 1 0 ; 0 0 0 1];
>> P

P =

    0.3000    0.1000    0.3000    0.3000
    0.2000    0.3500         0        0.4500
         0         0      1.0000         0
         0         0             0            1.0000

b)

P^n when n tend to infinity

P^1000

ans =

         0         0    0.4483    0.5517
         0         0    0.1379    0.8621
         0         0    1.0000         0
         0         0         0   1.0000

c)

pi_0 = [0.3 0.3 0.15 0.25]

pi_0 =

    0.3000    0.3000    0.1500    0.2500

>> pi_0 * P^1000

ans =

         0         0    0.3259    0.6741

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