Please provide full solution for the following problems: I need full solution wi

Question

Please provide full solution for the following problems:

I need full solution with explanation or work shown. The answers are as follows:

1. There are two restaurants in a small town: M and B. A survey shows that 10% of M customers in this week will switch to B restaurant next week, and 30% of B customers will go to M next week. If the market share for M restaurant is currently 50% this week, what is the M restaurant's market share next week? What is the steady-state market share for these two restaurants? What is the mean first passage time from B to M?

Explanation / Answer

Answer :

a) If market share of M is 50% then market share of B is also 50%

Now 10% of M’s and 30% of B’s customer’s move to opposite restaurant hence,

M has now 50 – 5 + 15 = 60 customers,

Similarly B now has 50 – 15 + 5 = 40 customers.

Hence market share of M next week is 60%.

b) Now for steady state the rate of switch or migration should continue.

Therefore if we keep on continuing the same calculation we will get to the steady state market share.

Now, M has 60 customers and B has 40 and 10% and 30% customers migrate hence,

M has now 60 – 3 + 12 = 69 customers,

Similarly B now has 40 – 12 + 3 = 31 customers.

Again, doing the same calculation a couple of times we will get the steady state numbers which is M = 75% and B = 25%

c) The mean first passage time form B to M is 30% x 10 = 3.3

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