Question

Introduction

Imagine the country is made up of 100 households. The federal government needs to collect $1,200,000 in income taxes to be able to function. The population consists of six (6) groups:

Group A: 19 households that earn $15,000 each

Group B: 20 households that earn $29,000 each

Group C: 21 households that earn $53,000 each

Group D: 21 households that earn $84,000 each

Group E: 15 households that earn $132,000 each

Group F: 4 households that earn $300,000 each

This scenario is roughly proportional to the actual United States population and tax needs. We are going to determine new income tax rates.

Flat Tax

The first proposal we'll consider is a flat tax -- one where every income group is taxed at the same percentage rate.

What is the total income of our six groups (all 100 households)? $

What flat tax rate would be necessary in order to collect $1,200,000? % (round to one decimal place)

Modified Flat Tax

The second proposal we'll consider is a modified flat-tax plan, where everyone only pays taxes on any income over $20,000. So everyone in group A will pay no taxes. Everyone in group B will pay taxes on $9,000. Everyone in group C will only pay taxes on $33,000, etc.

What is the total taxable income for the whole population? $

What flat tax rate would be necessary in order to collect $1,200,000 in this modified system? % (round to one decimal place)

Summary of Flat Tax

Complete the following table:

		Flat Tax Plan		Modified Flat Tax Plan
Group	Income per Household	Income Tax per Household	Income After Taxes	Income Tax per Household	Income After Taxes
A	$15,000	$	$	$	$
B	$29,000	$	$	$	$
C	$53,000	$	$	$	$
D	$84,000	$	$	$	$
E	$132,000	$	$	$	$
F	$300,000	$	$	$	$

Progressive Tax

The third proposal we'll consider is a progressive tax, where lower income groups are taxed at a lower percent rate, and higher income groups are taxed at a higher percent rate. For simplicity, we're going to assume that a household is taxed at the same rate on all of their income.

Determine the tax rate necessary for group F to meet the country's financial need ($1,200,000). HINT - Perform your calculations for total tax collected using the given rates for groups A - E. Then determine how much more tax you NEED to collect. Use that figure to determine the tax rate needed for group F.

Group	Income per Household	Tax Rate (%)	Income Tax per Household	Total Tax Collected for All Households	Income After Taxes per Household
A	$15,000	4.2%	$	$	$
B	$29,000	10.3%	$	$	$
C	$53,000	10.8%	$	$	$
D	$84,000	13.6%	$	$	$
E	$132,000	18.2%	$	$	$
F	$300,000	%	$	$	$

Does your total tax collected add up to $1,200,000? Select an answer yes no

Effective Rate

Discretionary income is the income people have left over after paying for necessities like rent, food, transportation, etc. The cost of basic expenses does increase with income, since housing and car costs are higher, however usually not proportionally. For each income group, an estimate of their essential expenses has been given. Compute the effective tax rate for each plan, relative to discretionary income (divide the tax paid by the discretionary income). Please remember that you should move your decimal place two places to turn a decimal into a percent. 0.25 would be 25%. 1.15 would be 115%.

Group	Income per Household	Discretionary Income (Estimated)	Effective Rate (Flat Tax)	Effective Rate (Modified Flat)	Effective Rate (Progressive)
A	$15,000	$750	%	%	%
B	$29,000	$2,900	%	%	%
C	$53,000	$7,950	%	%	%
D	$84,000	$16,800	%	%	%
E	$132,000	$39,600	%	%	%
F	$300,000	$105,000	%	%	%

(Round to one decimal place for all effective rates.)

Conclusion

Which plan seems the most fair to you? Which plan seems the least fair to you? Why? Make sure to answer in complete sentences with full explanation. A quality answer should have a few sentences of explanation with mathematical reasoning.

Answer 1

	Flat Tax
	Group	Taxable Income
	A	285000	=19*15000
	B	580000	=20*29000
	C	1113000	=21*53000
	D	1764000	=21*84000
	E	1980000	=15*132000
	F	1200000	=4*300000
	Total	6922000
	% of Tax=Tax required/Total taxable income	17.3%	=1200000/6922000*100
	Modified flat Tax
	Group	Taxable Income
	A	0
	B	180000	=20*(29000-20000)
	C	693000	=21*(53000-20000)
	D	1344000	=21*(84000-20000)
	E	1680000	=15*(132000-20000)
	F	1120000	=4*(300000-20000)
	Total	5017000
	% of Tax=Tax required/Total taxable income	23.9%	=1200000/5017000*100
		a	b=a*17.3%	c=a-b	d=(a-20000)*23.9%	e=a-d
			Flat Tax Plan		Modified Flat Tax Plan
	Group	Income per Household	Income Tax per Household	Income After Taxes	Income Tax per Household	Income After Taxes
	A	$15,000	$2,600	$12,400	0	$15,000
	B	$29,000	$5,027	$23,973	2,153	$26,847
	C	$53,000	$9,188	$43,812	7,893	$45,107
	D	$84,000	$14,562	$69,438	15,308	$68,692
	E	$132,000	$22,884	$109,116	26,789	$105,211
	F	$300,000	$52,008	$247,992	66,972	$233,028
	Progressive Tax	a	b	c=a*b	d=c*Number of household	e=a-c
	Group	Income per Household	Tax Rate (%)	Income Tax per Household	Total Tax Collected for All Households	Income After Taxes per Household
	A	$15,000	4.2%	$630	$11,970	$14,370
	B	$29,000	10.3%	$2,987	$59,740	$26,013
	C	$53,000	10.8%	$5,724	$120,204	$47,276
	D	$84,000	13.6%	$11,424	$239,904	$72,576
	E	$132,000	18.2%	$24,024	$360,360	$107,976
	F	$300,000	34.0%	$101,956	$407,822	$198,045
					$1,200,000
	Tax % for Group F=(Tax collection required-(Tax collected for all household Group A to E))/Total taxable income for Group F	34.0%	=(1200000-(11970+59740+120204+239904+360360))/(300000*4)
	Yes Total tax add upto 1200,000