Answer to Question #107106 in Macroeconomics for Sarai

Question

A hypothetical society has three income earners, and all three must pay income taxes. The taxable income of Smith is $40,000, the taxable income of Jones is $100,000, and the taxable income of Brown is $200,000.
a. How much tax revenue is raised under a proportional income tax when the tax rate is 10 percent? How much is raised if the tax rate is 15%?
b. A progressive tax system is installed with a rate of 5 % on an income of $0–$40,000, a rate of 8 % on income over $40,000 and under $100,000, and a rate of 15% on all income over $100,000. Will this system raise more or less tax revenue than a proportional tax rate of 10 %?

Answer 1

a) Tax Smith = 40000*10% = 4000

Tax Jones = 100000*10% = 10000

Tax Brown = 200000* 10% = 20000

Sum = 34000

Tax Smith = 40000*15% = 6000

Tax Jones = 100000*15% = 15000

Tax Brown = 200000* 15% = 30000

Sum = 51000

b) Tax Smith = 40000*5% = 2000

Tax Jones = 40000* 5% + 60000*8% = 2000 + 4800 = 6800

Tax Brown = 40000* 5% + 60000*8%+100000* 15% = 2000 + 4800 + 15000 = 21800

Sum = 30600

A progressive tax less then proportional tax (rate of 10 %)