Question

Suppose Country \(\mathrm{X}\) has the following tax structure: $$ \begin{array}{|c|c|} \hline \text { Net Income } & \text { Tax } \\ \hline \$ 10,000 & \$ 1,000 \\ \hline 20,000 & 3,000 \\ \hline 30,000 & 6,000 \\ \hline \end{array} $$ At each of the three income levels, what is the average tax rate and the marginal tax rate?

Short answer

The average tax rates for the three income levels are 10%, 15%, and 20%. The marginal tax rates for the three income levels are N/A, 20%, and 30%.

Step-by-step solution

Calculate the Average Tax Rate

Calculate the average tax rate at each income level. Use the formula: \( \text{Average Tax Rate} = \frac{\text{Tax}}{\text{Net Income}} \) For Net Income of $10,000: \( \text{Average Tax Rate} = \frac{1,000}{10,000} = 0.10 \) For Net Income of $20,000: \( \text{Average Tax Rate} = \frac{3,000}{20,000} = 0.15 \) For Net Income of $30,000: \( \text{Average Tax Rate} = \frac{6,000}{30,000} = 0.20 \) Now we have the average tax rates at the three income levels: 10%, 15%, and 20%.

Calculate the Marginal Tax Rate for Each Income Level

Calculate the marginal tax rate for each income level. Use the formula: \( \text{Marginal Tax Rate} = \frac{\text{Change in Tax}}{\text{Change in Net Income}} \) For the first income level of $10,000, there is no preceding level, so we cannot calculate the marginal tax rate. For the Net Income of \(20,000, compare to the previous income level of \)10,000: \( \text{Marginal Tax Rate} = \frac{3,000 - 1,000}{20,000 - 10,000} = \frac{2,000}{10,000} = 0.20 = \) 20% For the Net Income of \(30,000, compare to the previous income level of \)20,000: \( \text{Marginal Tax Rate} = \frac{6,000 - 3,000}{30,000 - 20,000} = \frac{3,000}{10,000} = 0.30 = 30% \) Now we have the marginal tax rates at the three income levels: Not Applicable (N/A), 20%, and 30%.

Present the Results

Now we can present the results for each income level in a new table: $$ \begin{array}{|c|c|c|c|} \hline \text { Net Income } & \text { Tax } & \text { Average Tax Rate } & \text { Marginal Tax Rate }\\\ \hline \$ 10,000 & \$ 1,000 & 10 \% & \text{N/A}\\\ \hline \$ 20,000 & \$ 3,000 & 15 \% & 20 \%\\\ \hline \$ 30,000 & \$ 6,000 & 20 \% & 30 \%\\\ \hline \end{array} $$ We have now calculated the average tax rate and the marginal tax rate at each of the three income levels in Country X.

Key concepts

Average Tax Rate

The average tax rate represents the percentage of your total income that goes to taxes. It's calculated by dividing the total tax paid by the net income. For instance, if you earn $10,000 and pay $1,000 in taxes, your average tax rate is 10%. Similarly, if you earn $20,000 and pay $3,000 in taxes, your average tax rate rises to 15%. Lasty, for an income of $30,000 with $6,000 paid in taxes, the average tax rate reaches 20%.
The average tax rate gives a straightforward picture of how much you contribute in taxes relative to your earnings. It’s especially helpful for gauging the tax burden individuals face at various income levels.

Marginal Tax Rate

The marginal tax rate is critical to understanding how additional income is taxed. This rate applies to the last dollar earned in a specific income bracket. To determine it, calculate the change in tax divided by the change in net income when moving between brackets.
For example, if your income jumps from $10,000 to $20,000, and your tax increases from $1,000 to $3,000, your marginal tax rate is 20%. If it increases again from $20,000 to $30,000 with your tax rising from $3,000 to $6,000, the marginal tax rate is 30%.
Understanding this concept helps individuals predict how their income growth may affect their tax situation. The marginal tax rate helps in planning because it indicates the tax rate you will face on any future earnings.

Income Levels

Income levels are crucial when analyzing tax responsibilities. They form the basis of calculating tax obligations and determining both average and marginal tax rates. Different income levels often fall into distinct tax brackets, where taxes are levied at varying rates.
For instance, in Country X, there are clear thresholds: $10,000, $20,000, and $30,000. Tax at each level increases as income rises. This tiered approach ensures those with higher earnings contribute more in taxes, aligning with progressive tax principles.
Understanding how income is categorized helps taxpayers plan their finances effectively, as they can anticipate changes in tax obligations with income adjustments.