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1. Taxes may be variously described as progressive, proportional, or regressive,

ID: 1196038 • Letter: 1

Question

1. Taxes may be variously described as progressive, proportional, or regressive, depending on how the percentage of income paid in tax changes as income rises.

A. You can show that a tax on consumption is regressive using the Keynesian consumption function. Suppose C = 1000 + .5YD, and the government collects 10% of all consumption expenditures in taxes. Calculate the taxes paid by the household earning YD = 1000 with the household earning YD = 10,000. Show that the consumption tax is regressive — show your math. (4 points)

B. A number of people have argued for a flat tax with each person getting a personal exemption of, say, $10,000, meaning that they pay zero tax on the first $10,000 of income and then 20% on all income above that. Is such a flat tax progressive, proportional, or regressive? Offer an example to demonstrate your answer. (4 points)

Explanation / Answer

(A)

C = 1,000 + 0.5YD

When YD = 1,000, C = 1,000 + (0.5 x 1,000) = 1,000 + 500 = 1,500

Tax = 10% x C = 10% x 1,500 = 150

Tax as % of YD = 150 / 1,000 = 15%

When YD = 10,000, C = 1,000 + (0.5 x 10,000) = 1,000 + 5,000 = 6,000

Tax = 10% x YD = 10% x 6,000 = 600

Tax as % of YD = 600 / 10,000 = 6%

So, as YD increases, tax rate decreases. The tax system is regressive.

(B)

This tax system is progressive. It can be proved using following example.

Let's consider 2 individuals: One has taxable income of $20,000 and the other has taxable income of $100,000.

Tax payable, individual 1 = 20% x $(20,000 - 10,000) = 20% x $10,000 = $2,000

Average Tax rate = $2,000 / $20,000 = 10%

Tax payable, individual 2 = 20% x $(100,000 - 10,000) = 20% x $90,000 = $18,000

Average tax rate = $18,000 / $100,000 = 18%

So, average tax rate increases with income, therefore tax system is progressive.