6.F. Income Tax Vs. Sales Tax

6.f. Income Tax vs. Sales Tax

Suppose that you must pay $100 in tax, but the government gives you a choice of paying the $100 either as a sales tax on some good or as an income tax. Since your tax payment would be $100 either way, it might seem that you would not care which kind of tax you pay. But we can use indifference curves and budget lines to show that you would always prefer a $100 income tax to a $100 sales tax.

The consumer in figure 6.f.1 initially locates at point A, on the untaxed budget line. A sales tax on good x will make x more expensive, thus rotating the budget line to the left as shown, and leaving the consumer at point B on the ‘after sales tax’ budget line, consuming xB units of x and yB units of y. To see how much tax the consumer is paying, imagine that he had tried to consume xB units of x before the tax was imposed. He would have been able to locate at point D, consuming xB units of x and yD units of y. Thus, we can think of the tax as taking away (yD -yB) units of y from the consumer. Assume that this amounts to 100 units of y, or $100, assuming the price of y is $1.

Now return the consumer to point A, and imagine that a $100 income tax is imposed instead of the $100 sales tax. A $100 income tax would shift the ‘untaxed’ budget line down by $100, but the slope of the budget line would be unaffected, since the income tax does not affect relative prices of x and y. We have already asserted that point B is $100 below point D, so the ‘after income tax’ budget line must pass through point B.

Notice that the ‘after income tax’ budget line cuts through the indifference curve at point B, making a higher indifference curve attainable at point C. Point B marked the highest indifference curve reachable on the ‘after sales tax’ budget line, while point C marks the highest indifference curve reachable on the ‘after income tax’ budget line. Since point C is preferred to point B, the consumer prefers the $100 income tax to the $100 sales tax.