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Math  /  Data & Statistics

QuestionTaxes - End of Chapter Problem
The following tax proposal has income as the tax base. Calculate the marginal tax rate for an income of $5,000\$ 5,000 and an income of $40,000\$ 40,000. Then, calculate the percentage of income paid in taxes for an individual with a pre-tax income of $5,000\$ 5,000 and for an individual with a pre-tax income of $40,000\$ 40,000. Classify the tax as being proportional, progressive, or regressive. Round answers to two places after the decimal, where applicable.
Tax Proposal: Each individual who earns more than $10,000\$ 10,000 pays a lump sum tax of $10,000\$ 10,000. If the individual's income is less than $10,000\$ 10,000, that individual pays in taxes exactly what his or her income is. a. marginal tax rate; income is $5,000\$ 5,000 :
100 \% marginal tax rate; income is $40,000\$ 40,000 : □\square \% 10%10 \% \% percentage paid on an income of $40,000\$ 40,000 : 25 \% b. percentage paid on an income of $5,000\$ 5,000 :

Studdy Solution

STEP 1

1. The tax proposal applies to all individuals with the specified income levels.
2. For incomes less than \$10,000, the tax is equal to the income.
3. For incomes greater than \$10,000, a lump sum tax of \$10,000 is applied.
4. Marginal tax rate is defined as the tax rate on the next dollar of income.

STEP 2

1. Calculate the marginal tax rate for an income of \$5,000.
2. Calculate the marginal tax rate for an income of \$40,000.
3. Calculate the percentage of income paid in taxes for an income of \$5,000.
4. Calculate the percentage of income paid in taxes for an income of \$40,000.
5. Classify the tax system as proportional, progressive, or regressive.

STEP 3

For an income of \$5,000, the tax paid is equal to the income, which is \$5,000. Therefore, the marginal tax rate is:
Marginal Tax Rate=ΔTaxΔIncome=$5,000$5,000=100% \text{Marginal Tax Rate} = \frac{\Delta \text{Tax}}{\Delta \text{Income}} = \frac{\$5,000}{\$5,000} = 100\%

STEP 4

For an income of \$40,000, the tax paid is a lump sum of \$10,000. The marginal tax rate on the next dollar earned is:
Marginal Tax Rate=ΔTaxΔIncome=$0$1=0% \text{Marginal Tax Rate} = \frac{\Delta \text{Tax}}{\Delta \text{Income}} = \frac{\$0}{\$1} = 0\%

STEP 5

For an income of \$5,000, the percentage of income paid in taxes is:
Percentage Paid=Tax PaidIncome×100=$5,000$5,000×100=100% \text{Percentage Paid} = \frac{\text{Tax Paid}}{\text{Income}} \times 100 = \frac{\$5,000}{\$5,000} \times 100 = 100\%

STEP 6

For an income of \$40,000, the percentage of income paid in taxes is:
Percentage Paid=Tax PaidIncome×100=$10,000$40,000×100=25% \text{Percentage Paid} = \frac{\text{Tax Paid}}{\text{Income}} \times 100 = \frac{\$10,000}{\$40,000} \times 100 = 25\%

STEP 7

Classify the tax system: - For lower incomes (\$5,000), the tax rate is 100%, which is higher than for higher incomes (\$40,000) at 25%. - This indicates a regressive tax system, where the tax rate decreases as income increases.
The marginal tax rate for an income of \$5,000 is \(100\%\). The marginal tax rate for an income of \$40,000 is \(0\%\). The percentage of income paid in taxes for an income of \$5,000 is \(100\%\). The percentage of income paid in taxes for an income of \$40,000 is \(25\%\). The tax system is regressive.

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