Question

Set up both the vector and state probabilites and the matrix of transition probabilities given the following: store 1 currently has 40% of market and store 2 has 60%. In each period store 1 customers have an 80% of returning and 20% to switching to store 2. IN each period store 2 has a 90% chance customers return and 10% to switch to store 1. Also find vector 2

Answer 1

We are given that the store 1 has 40% of market and store 2 has 60%, therefore the state probabilities here are given as:

p₁ = 0.4 and p₂ = 0.6

Therefore the vector here is given as: (0.4 0.6)

From the given conditions:  In each period store 1 customers have an 80% of returning and 20% to switching to store 2. IN each period store 2 has a 90% chance customers return and 10% to switch to store 1, the matrix of transition probabilities here is given as:

Now from the given vector 1 and transition probability matrix, the vector 2 is given as:

p₁ = 0.8*0.4 + 0.1*0.6 = 0.32 + 0.06 = 0.38
p₂ = 0.2*0.4 + 0.9*0.6 = 0.08 + 0.54 = 0.62

Therefore the vector 2 is given as: (0.38 0.62)