Question

7. Let's do some taxes. The following table are the 2020 tax brackets for single tax filers. Tax rate 10% 12% 22% 24% 32% 35% 37% Amount $0 to $9,700 $9,701 to $39,475 $39,476 to $84.200 $84,201 to $160,725 $160,726 to $204,100 $204,101 to $510,300 $510,301 or more a) For example, if you make $54,000 in 2020, the first $9,700 is taxed at 10%, the next amount from $9,701 to $39,475 is taxed at 12%, and finally, the amount from $39,476 to $54,000 is taxed at 22% (there are also deductions and credits, but let's ignore those for now). What is the total amount of tax you would need to pay? b) Write the tax rates as a 7-dimensional vector ū (0.1,0.12, 0.22, 0.24, 0.32, 0.35,0.37). Represent the amount of tax you need to pay as a dot product ū. ū. What is the value of the vector ū that corresponds to the calculation you made in part a)? c) Our current system is a "progressive tax system,” since tax rates increase as income increases. Flat tax proposals have also been proposed. Under the flat tax system, suppose all income is taxed at 17%, regardless of your income. How much would you have to make in 2020 in order to pay the same amount of tax under both systems? 2 d) If you make less than your answer in part c), which system do you pay more tax under?

Answer 1

a)

Tax Rate	Slab	Amount	Tax on Amount
10%	$0 to $9,700	9,700	970
12%	$9,701 to $39,475	29,775	3,573
22%	$39,476 to $84,200	14,525	3,196
24%	$84,201 to $160,725	-	-
32%	$160,726 to $204,100	-	-
35%	$204,101 to $510,300	-	-
37%	$510,301 and more	-	-
		54,000	7,739
	Tax to be paid		7,739

b) (0.1,9700), (0.12,29775), (0.22,14525), (0.24,0), (0.32,0), (0.35,0), (0.37,0)

      970+3573+3196+0+0+0+0=7739

c)

Particulars	Amount	Rate	Tax
Tax to be paid on flat tax system	54,000	17%	9,180
Tax to be paid on progressive tax system	54,000	slab rate	7,739

d) In the given case tax is lower in progressive tax system. But if we are high net worth individual it is more beneficial if its flat tax rate system. More income means income taxed at a higher rate in progressive system