Quantitative Analysis for Management, 13/e

14.3 Predicting Future Market Shares

One of the purposes of Markov analysis is to predict the future. Given the vector of state probabilities and the matrix of transition probabilities, it is not very difficult to determine the state probabilities at a future date. With this type of analysis, we are able to compute the probability that a person will be shopping at one of the grocery stores in the future. Because this probability is equivalent to market share, it is possible to determine future market shares for American Food Store, Food Mart, and Atlas Foods. When the current period is 0, calculating the state probabilities for the next period (period 1) can be accomplished as follows:

$$\pi \left(1\right)=\pi \left(0\right)P$$ (14-3)

Computing future market shares.

Furthermore, ...