Question

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

• Group A: 19 households that earn $13,000 each
• Group B: 20 households that earn $33,000 each
• Group C: 20 households that earn $52,000 each
• Group D: 19 households that earn $81,000 each
• Group E: 18 households that earn $135,000 each
• Group F: 4 households that earn $301,000 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 $1,100,000? % (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 $13,000. Everyone in group C will only pay taxes on $32,000, etc.

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

What flat tax rate would be necessary in order to collect $1,100,000 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	$13,000	$	$	$	$
B	$33,000	$	$	$	$
C	$52,000	$	$	$	$
D	$81,000	$	$	$	$
E	$135,000	$	$	$	$
F	$301,000	$	$	$	$

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 ($1,100,000). 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	$13,000	4.5%	$	$	$
B	$33,000	8.3%	$	$	$
C	$52,000	10.6%	$	$	$
D	$81,000	14.3%	$	$	$
E	$135,000	13.6%	$	$	$
F	$301,000	%	$	$	$

Does your total tax collected add up to $1,100,000? 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	$13,000	$650	%	%	%
B	$33,000	$3,300	%	%	%
C	$52,000	$7,800	%	%	%
D	$81,000	$16,200	%	%	%
E	$135,000	$40,500	%	%	%
F	$301,000	$105,350	%	%	%

(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.

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Formats

Answer 1

Flat Tax :

Group	No. Of households	Income	Total Income
Group A	19	$   13,000	$     247,000
Group B	20	$   33,000	$     660,000
Group C	20	$   52,000	$ 1,040,000
Group D	19	$   81,000	$ 1,539,000
Group E	18	$ 135,000	$ 2,430,000
Group F	4	$ 301,000	$ 1,204,000
	100		$ 7,120,000

Flat tax rate would be necessary in order to collect $1,100,000 = $1,100,000 / $7,120,000 * 100 = 15.40%

Modified Flat Tax :
Group	No. Of households	Income	Income over $20,000 (Taxable Income)	Total Taxable Income
Group A	19	$   13,000	$                           -	$                -
Group B	20	$   33,000	$                 13,000	$     260,000
Group C	20	$   52,000	$                 32,000	$     640,000
Group D	19	$   81,000	$                 61,000	$ 1,159,000
Group E	18	$ 135,000	$               115,000	$ 2,070,000
Group F	4	$ 301,000	$               281,000	$ 1,124,000
	100			$ 5,253,000

Flat tax rate would be necessary in order to collect $1,100,000 in the modified syatem = $1,100,000 / $5,253,000 * 100 = 20.9%

Summary of Flat Tax
		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	$         13,000	$                  2,002	$            10,998	$                                 -	$       10,998
B	$         33,000	$                  5,082	$            27,918	$                          2,717	$       25,201
C	$         52,000	$                  8,008	$            43,992	$                          6,688	$       37,304
D	$         81,000	$                12,474	$            68,526	$                       12,749	$       55,777
E	$       135,000	$                20,790	$         114,210	$                       24,035	$       90,175
F	$       301,000	$                46,354	$         254,646	$                       58,729	$     195,917

Progressive Tax :

Group	No. Of households	Income per Household	Tax Rate (%)	Income Tax per household	Total Tax collected for all Households	Income after taxes per Household
A	19	$       13,000	4.5%	$                     585	$                 11,115	$          12,415
B	20	$       33,000	8.3%	$                 2,739	$                 54,780	$          30,261
C	20	$       52,000	10.6%	$                 5,512	$               110,240	$          46,488
D	19	$       81,000	14.3%	$               11,583	$               220,077	$          69,417
E	18	$    135,000	13.6%	$               18,360	$               330,480	$        116,640
F	4	$    301,000	31.0%	$               93,310	$               373,240	$        207,690

Total Tax collected excluding group F = $726,692

Required Tax Collection = $1,100,000

Required Tax Collection from Group F = $373,308 ($1,100,000 - $726,692)

Total Income of Group F = $301,000 * 4 = $1,204,000

Tax Rate of Group F = $373,308 / $1,204,000 = 31.0%

Effective Rate :

Group	Income per Household	Discretionary Income (Estimated)	Income Tax per household (Flat Tax)	Effective Rate (Flat Tax)	Income Tax per household (Modified Flat)	Effective Rate (Modified Flat)	Income Tax per household (Progressive)	Effective Rate (Progressive)
A	$       13,000	$               650	2002	308.0%	$                        -	0.0%	$                       585	90.0%
B	$       33,000	$            3,300	5082	154.0%	$                 2,717	82.3%	$                   2,739	83.0%
C	$       52,000	$            7,800	8008	102.7%	$                 6,688	85.7%	$                   5,512	70.7%
D	$       81,000	$         16,200	12474	77.0%	$               12,749	78.7%	$                 11,583	71.5%
E	$    135,000	$         40,500	20790	51.3%	$               24,035	59.3%	$                 18,360	45.3%
F	$    301,000	$       105,350	46354	44.0%	$               58,729	55.7%	$                 93,310	88.6%

The most fair method seems is progressive tax. From the above table we can see that in progressive tax higher income group pays higher percentage of tax and lower income group pays lower income tax.

The least fair method is flat tax method. In flat tax method we can see that the person of low income group as well as of high income group pays same percentage of tax. In the above table, we can see that the people in Group A has discretionary income of Only $650, but they have to pay income tax of $ 2,002. So, logically they cannot pay that much amount of tax.