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Suppose that in a fixed population of breakfast-food consumers, there are just three brands, $X$, $Y$, and $Z$ that share that market.
Suppose that each year,
${10\%}$ of the brand $X$ buyers shift to brand $Y$ and ${20\%}$ to brand $Z$ and
${20\%}$ of the brand $Y$ buyers shift to brand $X$ and ${20\%}$ to brand $Z$
${10\%}$ of the brand $Z$ buyers shift to brand $X$ and none to brand $Y$
Suppose that it is found that despite all this shifting, the market shares of these three brands are nevertheless unchanged from year to year. What are these market shares?[4]

Suppose that in a fixed population of breakfast-food consumers, there are just three brands, $X$, $Y$, and $Z$ that share that market.

${10\%}$ of the brand $X$ buyers shift to brand $Y$ and ${20\%}$ to brand $Z$ and

${20\%}$ of the brand $Y$ buyers shift to brand $X$ and ${20\%}$ to brand $Z$

${10\%}$ of the brand $Z$ buyers shift to brand $X$ and none to brand $Y$

Suppose that it is found that despite all this shifting, the market shares of these three brands are nevertheless unchanged from year to year. What are these market shares?

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