The three market leaders in homeowners insurance in Missouri are State Farm, American Family Insurance Group, and Allstate. Based on data from 2007, two relationships between the Missouri homeowners insurance percentage market shares are found to be x=1+y+zz=16−0.2w,
where x, y, z, and w are, respectively, the percentages of the market held by State Farm, American Family, Allstate, and other companies. Given that the four groups account for the entire market, obtain a third equation relating x, y, z, and w, and solve the associated system of three linear equations to show how the market shares of State Farm, American Family, and Allstate depend on the share held by other companies. Which of the three companies’ market share is most impacted by the share held by other companies?
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