Chapter 9 Project

Market Share Matrix

Assume you are the sales and marketing director for Joe's Java, a coffee shop located on a crowded city street corner. There are two competing coffee shops on this block—Buck's Café and Tweak's Coffee. The management has asked you to develop a marketing campaign to increase your market share from $25\%$ to at least $35\%$ within $6$ months. With the resulting plan to meet this goal, you predict that each month

1. you will retain $93\%$ of your customers, $4\%$ will go to Buck's Café, and $3\%$ will go to Tweak's Coffee;

2. Buck's Café will retain $91\%$ of their customers, $6\%$ will come to Joe's Java, and $3\%$ will go to Tweak's Coffee; and

3. Tweak's Coffee will retain $92\%$ of their customers, $3\%$ will come to Joe's Java and $5\%$ will go to Buck's Café.

The current percentage of the market is shown in this matrix:

$x_0=\left[\begin{array}{c}0.25\\ 0.45\\ 0.30\end{array}\right]\begin{array}{c}\mathit{\text{Joe's}}\\ \mathit{\text{Buck's}}\\ \mathit{\text{Tweak's}}\end{array}$

After one month the shares of the coffee shops are

$x_1=P{x}_0=\left[\begin{array}{ccc}0.93& 0.06& 0.03\\ 0.04& 0.91& 0.05\\ 0.03& 0.03& 0.92\end{array}\right]\left[\begin{array}{c}0.25\\ 0.45\\ 0.30\end{array}\right]=\left[\begin{array}{c}0.2685\\ 0.4345\\ 0.2970\end{array}\right]$

1. Construct a table that lists the market share for all of the coffee shops at the end of each of the first $6$ months.

2. Will your campaign be successful based on this model? (Will you reach $35\%$ market share in $6$ months?)

3. What actions do you think Buck's Café and Tweak's Coffee will take as your market share changes?

4. What effect could their actions have on the market?