Question

2. Suppose that a tax system is set up as follows: Everyone gets to subtract $3,000 from their income and then pays the government 20 percent of the rest. Is this tax proportional, progressive, or regressive? Show your reasoning. (Hint: Calculate what households with incomes of $10,000 per year, $50,000 per year, and $100,000 per year would pay in taxes and what percentage of their total income their taxes represent.)

Answer 1

It is not a proportional tax as the rate of tax is not proportional to income.

Suppose, there are two individuals with income x and y with x>y. Both pay tax r after substraction.

So, the first individual will pay a tax of (x-3000)*r and the second one pays (y-3000)*r

The effective tax rate for first one is (x-3000)*r/x=(1-3000/x)*r and for the second one is (y-3000)*r/y=(1-3000/y)*r

Since x>y, we know 3000/x<3000/y and 1-3000/x>1-3000/y

So, it is a progressive taxation as the effective tax rate is higher for richer people.