Suppose Johnson Dry Cleaning (J) has a 40% market share initially, while NorthCl

ID: 3263323 • Letter: S

Question

Suppose Johnson Dry Cleaning (J) has a 40% market share initially, while NorthClean (N) has a 60% market share. Use the weekly transition matrix

J N

Start 2 By 1 Matrix 1st Row 1st Column Upper J 2nd Row 1st Column Upper N EndMatrix

left bracket Start 2 By 2 Matrix 1st Row 1st Column 0.5 2nd Column 0.5 2nd Row 1st Column 0.74 2nd Column 0.26 EndMatrix right bracket

to find the market share of each firm after 3 weeks.

After 3 weeks, Johnson has_____% and NorthClean has_____%.

(Round your answers to the nearest whole percentage.)

J N

Ans:

Transition matrix,P=

Two step Transition matrix,P2=

3 step transition matrix,P3=

Intial distribution,a0=[0.4 0.6]

an=a0*Pn

a3=a0*P3

a3=[0.4*0.5912+0.6*6050 0.4*0.4088+0.6*0.3950]

a3=[0.5995 0.4005]

Hence,after 3 weeks distribution market share of Johnson will be 59.95% and NorthClean will be 40.05%

0.5 0.5 0.74 0.26

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