Major league baseball teams have imposed what is commonly called a “luxury tax” on themselves. A team is subject to the tax if its payroll exceeds a specified level. The annual threshold for for the luxury tax is $189 million for 2014-16. A team that exceeds the threshold must pay 17.5% to 50% of the amount by which its payroll is above the threshold, where the “tax rate” depends on the number of years the team is over. This question looks at why teams might subject themselves to this tax.
a. Suppose there are two major league baseball teams, Team 1 and Team 2. They will both choose to offer either high salaries to players or low salaries. They will make their decisions simultaneously. If both choose low each will earn $500; if both choose high each will earn $400. If one chooses high and the other chooses low, the team that chooses high will attract the best players and will earn $600, but the team that chooses low will earn just $300. Show that high is a dominant strategy but that both teams would be better off if both chose low.
b. Under a 1922 Supreme Court decision, major league baseball is not subject to many antitrust laws. Suppose these two teams agree to a “luxury tax.” Under this luxury tax, a team that chooses high must pay a tax of $250. Find the new equilibrium in this game.
c. Some people might argue that the luxury tax in baseball is not an important determinant of major league salaries. As evidence, they show that team payrolls rarely exceed the threshold level and so teams rarely pay the tax. What does you answer to this question suggest about logic of this claim?