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

Question

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]

Accepted Answer

Market shares of $X,Y,Z$ are $26\frac23\%$, $6\frac23\%$, and $66\frac23\%$ respectively

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