Question

Suppose brands A and B have consumer loyalties of .7 and .8 , meaning that a customer who buys A one week will with probability .7 buy it again the next week, or try the other brand with .3. What is the limiting market share for each of these products?

Answer 1

The question asks for the limiting market share of two brands based on given loyalty probabilities, which involves setting up and solving a model of brand switching.

Step-by-step explanation:

The question involves calculating the limiting market share for brands A and B using their given consumer loyalty probabilities. To find the limiting market share, we can use a model of brand switching where each brand's market share in the next period depends on its current share and the loyalty rates. Specifically, suppose x is the market share of brand A and 1 - x is the market share of brand B. Then the market share of A in the next period is x × 0.7 (since 70% of current A customers will stick with A) plus (1 - x) × 0.2 (since 20% of B customers will switch to A). Solving this for x when the market share does not change from one period to the next gives us the limiting market share. Similarly, we can do this for brand B to find its limiting market share. However, without additional information, the limiting market share can't be calculated precisely in this message.