Question

Each of the following tax proposals has income as the tax base. In each case, calculate the marginal tax rate for each level of income. Then calculate the percentage of income paid in taxes for an individual with a pre-tax income of \(\$ 5,000\) and for an individual with a pre-tax income of \(\$ 40,000 .\) Classify the tax as being proportional, progressive, or regressive. (Hint: You can calculate the marginal tax rate as the percentage of an additional \(\$ 1\) in income that is taxed away.)a. All income is taxed at \(20 \%\). b. All income up to \(\$ 10,000\) is tax-free. All income above \(\$ 10,000\) is taxed at a constant rate of \(20 \%\). c. All income between \(\$ 0\) and \(\$ 10,000\) is taxed at \(10 \%\). All income between \(\$ 10,000\) and \(\$ 20,000\) is taxed at \(20 \%\). All income higher than \(\$ 20,000\) is taxed at \(30 \%\). d. Each individual who earns more than \(\$ 10,000\) pays a lump-sum tax of \(\$ 10,000\). If the individual's income is less than \(\$ 10,000\), that individual pays in taxes exactly what his or her income is. e. Of the four tax policies, which is likely to cause the worst incentive problems? Explain.

Short answer

Answer: For Tax Proposal a, with constant rate of 20%, the marginal tax rate is 20% for both incomes. The percentage of income paid in taxes for $5,000 and $40,000 is both 20%. This tax is proportional. For Tax Proposal b, with 0% tax on income up to $10,000 and 20% on income above $10,000, the marginal tax rate is 0% for $5,000 and 20% for $40,000. The percentage of income paid in taxes for $5,000 is 0% and for $40,000 is 15%. This tax is progressive. For Tax Proposal c, with marginal tax rates of 10%, 20%, and 30% for different income brackets, the marginal tax rate is 10% for $5,000 and 30% for $40,000. The percentage of income paid in taxes for $5,000 is 10% and for $40,000 is 25%. This tax is progressive. For Tax Proposal d, with a marginal tax rate of 100% for incomes below $10,000 and 0% for incomes above $10,000, the marginal tax rate is 100% for $5,000 and 0% for $40,000. The percentage of income paid in taxes for $5,000 is 100% and for $40,000 is 25%. This tax is regressive. The tax policy with the worst incentive problems is Tax Proposal d, as it creates disincentives for low-income individuals to work and might increase inequality.

Step-by-step solution

Calculation for Tax Proposal a.

All income is taxed at a constant rate of \(20\%\). Therefore, the marginal tax rate is also \(20\%\).

Calculation for Tax Proposal b.

There are two income brackets here - income up to \(10,000 (tax-free), and income above \)10,000 (taxed at \(20\%)\). The marginal tax rate for income up to \(10,000 is \)0\%\(. For income above \)10,000, the marginal tax rate is \(20\%\).

Calculation for Tax Proposal c.

There are three income brackets - between \(0\) and \(10,000 (taxed at \)10\%)\(, between \)10,000\( and \)20,000 (taxed at \(20\%)\), and higher than \(20,000 (taxed at \)30\%)\(. The marginal tax rates are \)10\%\(, \)20\%\(, and \)30\%$ respectively for the three income brackets.

Calculation for Tax Proposal d.

For individuals earning more than \(10,000, they pay a lump-sum tax of \)10,000\(. Those with income below \)10,000 pay taxes equal to their income. The marginal tax rate is \(100\%\) for incomes below \(10,000 and \)0\%\( for incomes above \)10,000. #Phase 2: Calculating the Percentage of Income Paid in Taxes#

Calculating for Tax Proposal a.

With a pre-tax income of \(5,000, an individual would pay \)5,000 * 0.2 = \(1,000 in taxes. The percentage of income paid in taxes would be \)\frac{1,000}{5,000} * 100 = 20\%\(. For an individual with a pre-tax income of \)40,000, they would pay \(40,000 * 0.2 = \)8,000 in taxes. The percentage of income paid in taxes would be \(\frac{8,000}{40,000} * 100 = 20\%\). This tax is proportional.

Calculating for Tax Proposal b.

With a pre-tax income of \(5,000, an individual would pay no taxes, because the income is below \)10,000. The percentage of income paid in taxes is \(0\%\). For an individual with a pre-tax income of \(40,000, they would pay taxes on \)30,000 (income above \(10,000), which is \)30,000 * 0.2 = \(6,000. The percentage of income paid in taxes would be \)\frac{6,000}{40,000} * 100 = 15\%$. This tax is progressive.

Calculating for Tax Proposal c.

With a pre-tax income of \(5,000, an individual would pay \)5,000 * 0.1 = \(500 in taxes. The percentage of income paid in taxes would be \)\frac{500}{5,000} * 100 = 10\%\(. For an individual with a pre-tax income of \)40,000, they would pay taxes as follows: \(10,000 * 0.1 = \)1,000 for the first bracket, and \(30,000 * 0.3 = \)9,000 for the third bracket. The total taxes paid would be \(1,000 + \)9,000 = \(10,000. The percentage of income paid in taxes would be \)\frac{10,000}{40,000} * 100 = 25\%$. This tax is progressive.

Calculating for Tax Proposal d.

With a pre-tax income of \(5,000, an individual would pay \)5,000 in taxes. The percentage of income paid in taxes would be \(\frac{5,000}{5,000} * 100 = 100\%\). For an individual with a pre-tax income of \(40,000, they would pay a lump-sum tax of \)10,000. The percentage of income paid in taxes would be \(\frac{10,000}{40,000} * 100 = 25\%\). This tax is regressive.

Tax Policy with Worst Incentive Problems

Tax proposal d is likely to cause the worst incentive problems. For individuals earning below \(10,000, the tax rate is \)100\%\(, which might disincentivize them from working. On the other hand, people with income above \)10,000 have no marginal tax rate, incentivizing them to earn more without paying additional taxes. This might lead to work disincentives for low-income individuals and increased inequality.

Key concepts

Marginal Tax Rate

The concept of the marginal tax rate is fundamental to understanding how tax systems affect individuals. The marginal tax rate refers to the percentage of tax applied to an additional \\(1\\) of income. This rate helps determine how much of each additional dollar earned is paid in taxes. For instance, if the marginal tax rate is \20\%\, then for every extra dollar of income earned, \20\%

• Marginal tax rates can vary across different income brackets.
• The rate is crucial for understanding the effects on individuals' incentive to earn extra income.
• In some tax systems, the marginal tax rate can increase as income rises, indicating a progressive taxation method.

Understanding marginal tax rates aids in analyzing how tax policies might influence work and earning decisions.

Progressive Tax

A progressive tax system assigns higher tax rates to higher income levels. This ensures that individuals with higher incomes contribute a larger proportion of their income compared to those with lower incomes. The principle behind progressive taxation is equity, aiming to reduce income disparity within society. In progressive systems:

• Tax rates increase with higher income brackets.
• Individuals with lower incomes pay a smaller percentage of their income in taxes.
• The marginal tax rate rises as one moves to higher income levels, supporting the idea of "taxing according to ability to pay."

Such tax systems aim to ease the financial burden on those earning less by shifting more responsibility to those who can afford it.

Regressive Tax

A regressive tax structure sees lower-income earners paying a larger percentage of their income compared to higher-income earners. This means a heavier tax burden relative to income is placed on those who earn less. Regressive taxes challenge the principle of equity since:

• Lower-income individuals pay a higher percentage of their income in taxes.
• This approach can exacerbate income inequality.
• Lump-sum taxes, where a fixed amount is required, are inherently regressive.

Regressive taxation may discourage economic activity among lower-income individuals due to the high relative cost, thus potentially stifling economic mobility.

Proportional Tax

A proportional tax, often referred to as a "flat tax," imposes the same tax rate across all income levels. This means everyone pays the same percentage of their income as tax, regardless of their total earnings. The defining attribute of proportional taxes is consistency:

• The tax rate remains constant, irrespective of income bracket.
• Both high and low earners pay the same tax rate, maintaining a neutral stance towards income equality.
• This can simplify tax calculations and collection procedures.

Proportional taxes aim to provide fairness by treating all taxpayers equally, yet they do not adjust for what one can afford, which can be a point of contention regarding economic inequality.