Taylor\'s and Sower\'s are two stores that do alterations of garments. Neither s

Question

Taylor's and Sower's are two stores that do alterations of garments. Neither store has achieved 100% customer loyaty: 45 % of Taylor's customers take their next job to Sower's, and 25 % of Sower's customers take their next job to Taylor's. Currently, 60 % of people take their jobs to Sower's. What will the market distribution be two jobs from now? Give answer to 4 decimal places.

and Sower's are two stores that do alterations of garments. Neither store has achieved 100% customer loyaty: 45 of Taylor's customers take their next job to ower's, and 25% of Sower's customers take their next job to Taylor's. Currently, 60% of people take their jobs to Sower's. What will the market distribution be two jobs fr ow? Give answer to 4 decimal places. [S T Number Number]

Explanation / Answer

Let name Taylor and Sower as T and S respectively.

Here we have to calculate the terms in infinity time

so lets say at stable level P(S) = P'(S) and P(T) = P'(T)

so P'(S) = P'(T) * 0.45 + P'(S) * 0.75...(i) [ as there is saturation so no change]

P'(T) = P'(T) * 0.55 + P'(S) * 0.25.......(ii)

P'(T) * 0.45 = P'(S) * 0.25

P'(T) / P'(S) = 0.25/0.45 = 5/9

so

P'(T)/(P'(T) + P'(S)) = 5/(5 + 9)

P'(T) = 5/14 = 0.3571 as P'(T) + P'(S) = 1

P'(S) = 1 - 5/14 = 9/14 = 0.6429

S0, for Sower's market share will be = 64.29%

and for taylor's market hare will be = 35.71%

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