Question

Suppose George made $$\$ 20,000$$ last year and that he lives in the country of Harmony. The way Harmony levies income taxes, each citizen must pay 10 percent in taxes on their first $$\$ 10,000$$ in earnings and then 50 percent in taxes on anything else they might earn. So given that George earned $$\$ 20,000$$ last year, his marginal tax rate on the last dollar he earns will be _____ and his average tax rate for his entire income will be _____. a. 50 percent; 50 percent. b. 50 percent; less than 50 percent. c. 10 percent; 50 percent. d. 10 percent; less than 50 percent.

Short answer

b. 50 percent; less than 50 percent.

Step-by-step solution

Understand Tax Structure

Harmony implements a dual tax rate: 10% on the first $10,000 and 50% on income exceeding $10,000. With George earning $20,000, he will experience both tax rates.

Calculate Tax on First Portion of Income

Calculate the tax owed on the first $10,000. With a 10% tax rate, George pays 0.10 * $10,000 = $1,000.

Calculate Tax on Remaining Income

Calculate the tax on income exceeding $10,000. The remaining income is $20,000 - $10,000 = $10,000. At a 50% tax rate, George pays 0.50 * $10,000 = $5,000.

Determine Marginal Tax Rate

The marginal tax rate is the tax rate applied to the last dollar earned. Since George's last dollar falls in the above-$10,000 range, his marginal tax rate is 50%.

Calculate Total Tax Paid

Total taxes paid by George is the sum of the taxes from the first and second portions of his income: $1,000 + $5,000 = $6,000.

Calculate Average Tax Rate

The average tax rate is calculated by dividing total taxes paid by total income. George's average tax rate is \( \frac{\\(6,000}{\\)20,000} \times 100\% = 30\% \). This rate is less than 50%.

Select Correct Answer Based on Calculations

Based on a marginal tax rate of 50% and an average tax rate of 30% (less than 50%), the correct answer is b. 50 percent; less than 50 percent.

Key concepts

Average Tax Rate

The average tax rate is a critical concept in understanding personal income tax. It represents the proportion of total income paid in taxes. Unlike the marginal tax rate, which applies only to the last dollar earned, the average tax rate gives a broader picture by accounting for every dollar of taxable income.

To calculate the average tax rate, you divide the total taxes paid by the total income earned, then multiply by 100 to express it as a percentage. For George, who earned \(20,000 and paid \)6,000 in taxes, the formula would look like this: \[\frac{6,000}{20,000} \times 100\% = 30\%\]This tells us that, on average, George paid 30% of his income in taxes. This is lower than the higher marginal tax rate because the lower rate applied to part of his income, effectively reducing the overall rate.

Income Tax Structure

The income tax structure in any country is vital in determining how taxes will be applied to an individual’s earnings. In George's country, Harmony, there is a tiered system comprising two brackets.

• The first bracket taxes the initial $10,000 of income at 10%.
• Any income beyond $10,000 is taxed at a much higher rate of 50%.

This structure means that as income increases, a greater portion could be subjected to the higher tax rate. Such systems aim to ensure fairness, where higher earners contribute more to the state revenue. Tax structures like Harmony's help in reducing inequality by imposing heavier taxes on those with higher ability to pay. Understanding these structures helps in planning finances and anticipating tax liabilities.

Tax Calculation

Tax calculation requires careful attention to the specific rates applied to different income brackets. In George's case, his income is subjected to both tiers of Harmony’s tax system. Here's how the calculations are broken down:

• On the first $10,000: With a tax rate of 10%, George pays $1,000.


• For the remaining $10,000 (i.e., $20,000 total income minus the $10,000 taxed at 10%), with a tax rate of 50%, George pays $5,000.

The total tax paid is simply the sum of these two amounts, which is $6,000. Breaking down the calculations into manageable steps helps avoid errors and ensures clarity in understanding the tax obligation. Correct tax calculations are essential not only for compliance but also in effectively managing personal finances.

Step-by-Step Tax Problems

Solving tax problems step-by-step can demystify the complexities involved and assist in understanding the application of different rates. By approaching George’s tax issue in steps, we unravel the income components more easily.

The step-by-step approach involves understanding the tax structure, identifying the relevant income brackets, and applying the respective rates. For instance:

• Step 1: Recognize the dual tax structure (10% for the first $10,000 and 50% thereafter).


• Step 2: Calculate the tax for each segment of income.


• Step 3: Total the tax amounts to find the total tax paid.


• Step 4: Compute the average tax rate as the total tax divided by the total income.
• Step 5: Determine the marginal tax rate by observing the rate applied to the highest dollar earned.

This methodical breakdown not only helps solve the current problem but also builds skills for tackling more complex taxation scenarios in future exercises.