Exam 14: Markov Analysis

Given the following vector of state probabilities and the accompanying matrix of transition probabilities,find the next period vector of state probabilities. (0.4 0.4 0.2)

Table 14-1 The following data consists of a matrix of transition probabilities (P)of three competing companies,and the initial market share π(0).Assume that each state represents a company (Company 1,Company 2,Company 3,respectively)and the transition probabilities represent changes from one month to the next. P = π(0)= (0.3,0.6,0.1) -Using the data in Table 14-1,determine Company 1's estimated market share in the next period.

Markov analysis is a technique that deals with the probabilities of future occurrences by analyzing currently known probabilities.

There is a 30% chance that any current client of company A will switch to company B this year.There is a 20% chance that any client of company B will switch to company A this year.If these probabilities are stable over the years,and if company A has 1000 clients and company B has 1000 clients,in the long run (assuming the probabilities do not change),what will the market shares be?

If we want to use Markov analysis to study market shares for competitive businesses,

In Markov analysis,the row elements of the transition matrix must sum to 1.