Assume that in a given country, tax revenues, T , depend on income, I , according to the formula
T=4000+.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?
Now let’s generalize the tax schedule in this problem to: 3
T= a+ tI
where a and t are numbers. 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.