Question

Imagine the country is made up of 100 households. The federal government needs to collect $800,000 in income taxes to be able to function. The population consists of 6 groups:

Group A: 20 households that earn $12,000 each Group B: 20 households that earn $29,000 each
Group C: 20 households that earn $50,000 each
Group D: 20 households that earn $79,000 each
Group E: 15 households that earn $129,000 each
Group F: 5 households that earn $295,000 each
This scenario is roughly proportional to the actual United States population and tax needs. We are going to determine new income tax rates.
The first proposal we'll consider is a flat tax - one where every income group is taxed at the same percentage tax rate.
1) Determine the total income for the population (all 100 people together)
2) Determine what flat tax rate would be necessary to collect enough money.
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 only on $9,000.
3) Determine the total taxable income for the whole population
4) Determine what flat tax rate would be necessary to collect enough money in this modified system

Answer 1

The total income for the population is $5,810,000, requiring a flat tax rate of 13.77% to meet the federal government's tax need. Under a modified flat-tax plan, the total taxable income is $4,970,000, which necessitates a tax rate of 16.10%.

Step-by-step explanation:

To determine the total income for the population and the necessary flat tax rate to collect $800,000, we must first calculate the total income:

• Group A: 20 households x $12,000 = $240,000
• Group B: 20 households x $29,000 = $580,000
• Group C: 20 households x $50,000 = $1,000,000
• Group D: 20 households x $79,000 = $1,580,000
• Group E: 15 households x $129,000 = $1,935,000
• Group F: 5 households x $295,000 = $1,475,000

Total income = $5,810,000

To collect $800,000 with a flat tax, we use the formula tax revenue needed / total income = flat tax rate, which gives:

Flat tax rate = $800,000 / $5,810,000 = 0.1377 or 13.77%

For the modified flat-tax plan where income is only taxed over $20,000:

• Group A contributes nothing as their income is at the threshold.
• Group B: 20 households x ($29,000 - $20,000) = $180,000
• Group C: 20 households x ($50,000 - $20,000) = $600,000
• Group D: 20 households x ($79,000 - $20,000) = $1,180,000
• Group E: 15 households x ($129,000 - $20,000) = $1,635,000
• Group F: 5 households x ($295,000 - $20,000) = $1,375,000

Total taxable income = $4,970,000

Modified flat tax rate = $800,000 / $4,970,000 = 0.1610 or 16.10%