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.