ASRJC Tutorial 3 Q6

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]