Assume that in a given country, tax revenues, T , depend on income, I , according to the formula T = − 4,000 + 0.2I Thus, for example, when a household has an income of $50,000, its tax burden is −4,000 ⫹

0.2 ⫻ 50,000, or $6,000. Is this a progressive tax schedule? [Hint: Compute average tax rates at several different levels of income.]

Now let’s generalize the tax schedule in this problem to:

T = a + tI where a and t are numbers. (For example, in the tax schedule above, a ⫽ −4,000 and t ⫽ 0.2.)

Write down a formula for the average tax rate as a function of the level of income. Show that the tax system is progressive if a is negative, and regressive if a is positive. [Hint: The average tax rate is T / I .]