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)