Question

The tax system in Taxilvania includes a negative income tax. For all incomes below \(\$ 10,000,\) individuals pay an income tax of \(-40 \%\) (that is, they receive a payment of \(40 \%\) of their income). For any income above the \(\$ 10,000\) threshold, the tax rate on that additional income is \(10 \% .\) For the first three scenarios below, calculate the amount of income tax to be paid and after-tax income. a. Lowani earns income of \(\$ 8,000\). b. Midram earns income of \(\$ 40,000\). c. Hi-Wan earns income of \(\$ 100,000\). d. Can you find a notch in this tax system? That is, can you find a situation where earning more pre-tax income actually results in less after-tax income?

Short answer

Answer: No, there is no notch in the described tax system.

Step-by-step solution

Determine tax rate

Since Lowani's income of \(8,000\) is below the \(10,000\) threshold, the tax rate is -\(40 \%\) (meaning they receive a payment of \(40 \%\) of their income).

Calculate income tax

To find Lowani's income tax, multiply their income by their tax rate: \(8,000 \times -0.40 = -\$3,200\).

Calculate after-tax income

To find Lowani's after-tax income, add their income tax to their original income: \(8,000 - (-3,200) = \$11,200\). #b. Calculate Midram's income tax and after-tax income#

Determine tax rate

Midram's income is above the \(10,000\) threshold, so we need to take into account both tax rates. The first \(10,000\) of their income will have a -\(40 \%\) tax rate, and the remaining \(30,000\) will have a \(10 \%\) tax rate.

Calculate income tax

Apply the tax rates to the respective taxable amounts: \((10,000 \times -0.40) + (30,000 \times 0.10) = -4,000 + 3,000 = -\$1,000\).

Calculate after-tax income

Add the income tax to the original income: \(40,000 - (-1,000) = \$41,000\). #c. Calculate Hi-Wan's income tax and after-tax income#

Determine tax rate

Hi-Wan's income also exceeds the \(10,000\) threshold so we apply both tax rates. The first \(10,000\) will have a -\(40 \%\) tax rate, and the remaining \(90,000\) will have a \(10 \%\) tax rate.

Calculate income tax

Apply the tax rates: \((10,000 \times -0.40) + (90,000 \times 0.10) = -4,000 + 9,000 = \$5,000\).

Calculate after-tax income

Add the income tax to the original income: \(100,000 - 5,000 = \$95,000\). #d. Identify a notch in the tax system#

Check for notches

A notch occurs if earning more pre-tax income results in less after-tax income. In the tax system described, the only point where this could occur is at the \(10,000\) income threshold, because the tax rate changes from -\(40 \%\) to \(10 \%\).

Investigate the threshold

Consider two incomes: \(10,000\) and \(10,001\). For a \(10,000\) income, the tax paid is \(-4,000\), so the after-tax income is \(14,000\). For a \(10,001\) income, \(10,000\) is taxed at -\(40 \%\) and \(1\) is taxed at \(10 \%\), resulting in a tax payment of \((-4,000 + 0.10\times1)=-3,999.90\) and an after-tax income of \(10,001 - (- 3,999.90) = \$14,000.90\).

Conclusion for a notch

We can see that earning slightly more pre-tax income does not result in less after-tax income. Therefore, there is no notch in the described tax system.

Key concepts

Negative Income Tax

The concept of a negative income tax is quite interesting. In a standard tax system, individuals pay a percentage of their income to the government. However, with a negative income tax, individuals receive payments from the government when their income falls below a certain threshold. This effectively acts as a subsidy or a form of financial assistance.

In Taxilvania, for instance, the negative income tax applies to incomes below $10,000. Individuals in this bracket receive a payment equal to 40% of their earned income. For example, if someone earns $8,000, they receive $3,200 from the government. Essentially, the negative income tax serves the purpose of ensuring that low-income individuals have sufficient funds to meet their basic needs. The concept encourages economic participation by providing a safety net.

After-Tax Income

After-tax income is the amount that remains once all taxes have been deducted from a person's gross earnings. This is essentially the money that an individual takes home and can use for daily expenses, savings, or other financial commitments.

Calculating after-tax income involves subtracting the income tax from the gross income. For someone whose income is less than $10,000 in Taxilvania, the after-tax income is effectively their income plus the negative tax they received. For higher earners, the after-tax income consists of their total earnings minus what they pay in taxes. This figure is crucial as it reflects the true economic benefit someone enjoys from their work after fulfilling tax obligations.

Income Threshold

An income threshold is a specific point of income at which the applicable tax rate changes. It divides different zones of tax treatment. In Taxilvania, the key threshold is at $10,000. This is a crucial divider between earning a negative income tax and paying a positive tax rate.

Understanding this threshold is important as it impacts the net benefit a person receives or pays. Below the $10,000 mark, individuals benefit from the negative income tax. Beyond that point, for any additional income, individuals start paying 10% of the excess as tax. Therefore, thresholds play a significant role in determining tax liabilities and benefits at different income levels. They are vital for both taxpayers and policymakers to consider when assessing the balance between taxation and income support.

Tax Rate Calculation

Tax rate calculation is the process of determining the percentage of income collected as tax or returned as a negative tax. In Taxilvania's system, calculating the tax involves applying different rates based on income levels compared to the set threshold.

For income up to $10,000, a negative tax rate of 40% applies, resulting in the government making a payment to the taxpayer. For income beyond $10,000, a positive tax rate of 10% is applied on the amount exceeding the threshold. For example, if someone earns $40,000:

• The first $10,000 has a -40% tax rate, resulting in a $4,000 refund.
• The remaining $30,000 is taxed at 10%, leading to $3,000 in taxes paid.

Understanding this calculation helps taxpayers anticipate their financial position after taxes and allows for effective financial planning.