MS 3053 Markov Process - Market Share Analysis Theory Markov process model are useful in studying the evolution of system over repeated trials. The repeated trials are often successive time periods where the state (or condition) of the system at any particular time cannot be determined with certainty. Hence, transition probabilities are used to describe the manner in which the system makes transition from one period to the next. Based on these transition probabilities, we can compute the probability of the system being in a particular state at a given time period or over the long run. Market Share Analysis Markov process models have been used to describe the probability that, given a consumer purchases Brand A in one period, he will stay with Brand A or switch to Brand B in the next period. In this course, we will specifically look at the marketing applications of this consumer switching behavior model. Based on the computation, we can find out the market share of a certain brand in a future time period and the overall market share over the long run. In the next lecture, we will consider an accounting application of Markov process that deals with the transitioning of accounts receivable dollars to different account-aging categories. Transition Probabilities As the name suggests, transition probabilities indicates how customers move or transit from a certain brand/preference in one period to another brand/preference in the next period. Because multiple brands/preferences are available to the customers, we need to use a matrix to summarize the switching behaviors. Example 1 (Switching soft drink preference) Suppose there are only two brands of soft drink (Coke vs. Pepsi) available to the customers. Please keep in mind that we can easily extend this analysis to include N brands of soft drink. According to a marketing research, 90% of people who has purchased Coke today will purchase Coke tomorrow. Therefore, there are 10% of people who has purchased Coke will buy Pepsi tomorrow. Likewise, 80% of Pepsi customers today will continue their same choice tomorrow and 20% of them will switch to Coke. Identify the transition probability matrix for this brand switching behavior. Let Brand 1 to denote Coke and Brand 2 to denote Pepsi. State Probabilities Although transition probabilities tell us the chances of retaining the same brand and switching to another brand, they do not provide any information regarding the market share in a given time period. Hence, we use state probabilities to describe the market shares in period n. The notation i(n) indicates the market share (i.e., the state probability) of Brand i in Period n. Like transition probabilities, state probabilities can be written in matrix format to include different brands/preferences in the entire market. 1 Leung/MS3053/Fall2012 Example 2 (Market share in a given period) Coke has 40% share and Pepsi has 60% share in period 1: Coke has 80% share and Pepsi has 20% share in period n: Everyone is buying Coke in the current period (now = period 0): Market Share in a Given Period With the transition and initial state probabilities, we can compute the market shares of various brands in a given time period. The computation involves matrix multiplication and can be summarized as follows: Example 3 (Market share in a certain period) From Example 1, we know that the transition probabilities are: Currently, 50% of customers are buying Coke and 50% are buying Pepsi. The initial/current state probabilities are: What are the predicted market shares for Coke and Pepsi in the next period (Period 1)? What are the predicted market shares for Coke and Pepsi in Period 2? 2 Leung/MS3053/Fall2012 Market Shares Over the Long Run In addition to predicting the market shares in a future time period, we can also estimate the overall market shares in the long run, that is, the steady state market shares when the entire market is in equilibrium. In the steady state, we should expect all market shares are in equilibrium and do not change from period to period. In other words, consumers will exhibit negligible to no preference changes. The switching from Brand A to Brand B by a group of people will exactly offset the switching from Brand B to Brand A by another group. Thus, the mathematical expression is: Example 4 (Market Share Over the Long Run) Compute the equilibrium market shares of Coke and Pepsi over the long run. Example 5 (Computer market with 3 Brands) Suppose there exists three computer brands in the market and consumers' brand switching behavior for each quarter can be summarized by the following matrix. What are the steady state (long run) market shares for these three computer brands? HP Dell Toshiba HP 0.8 0.1 0.1 Dell 0.1 0.7 0.2 Toshiba 0.1 0.3 0.6 3 Leung/MS3053/Fall2012 Please turn in the following problems. (Use the back of page if necessary) Exercise 6 (Shares for retail market) Suppose there are only two supermarket chains in SA area (HEB and Walmart) available to the local customers. According to a marketing research conducted in San Antonio, 90% of people who made purchases at HEB last month will purchase at HEB again in this month. Therefore, there are 10% of people who purchased at HEB will shop at Walmart in the following month. Likewise, 95% of Walmart customers in this month will continue to shop at Walmart next month and 5% of them will shop at HEB. Identify the transition probability matrix for this brand switching behavior. Let 1 be HEB and 2 be Walmart. In January, 40% of local customers shopped at HEB and 60% shopped at Walmart. The initial/current state probabilities are: What are the predicted market shares for HEB and Walmart in March? What are the steady state (equilibrium) market shares for the two chains over the long run? 4 Leung/MS3053/Fall2012