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

Identify Tax Structure

George lives in Harmony, where income taxes are structured such that the first $10,000 of earnings are taxed at 10%, and any earnings above $10,000 are taxed at 50%.

Calculate Marginal Tax Rate

The marginal tax rate is the rate applied to the last dollar of income earned. Since George earned $20,000, the portion above $10,000 ($10,000) is taxed at 50%. Thus, his marginal tax rate is 50%.

Calculate Taxes on Earnings

George pays 10% on the first $10,000 of his income, which equals $1,000 in taxes. He pays 50% on the next $10,000 (from $10,000 to $20,000), which equals $5,000 in taxes. The total tax paid is $1,000 + $5,000 = $6,000.

Determine Average Tax Rate

The average tax rate is the total tax paid divided by the total earnings. George paid \(6,000 in taxes on \)20,000 in earnings, so his average tax rate is \( \frac{6,000}{20,000} = 0.3 \) or 30%.

Select Correct Answer Option

George's marginal tax rate is 50%, and his average tax rate is less than 50% (30%). Therefore, the correct answer is option b: 50 percent; less than 50 percent.

Key concepts

Average Tax Rate

The average tax rate is a simple yet essential concept in taxation. It tells you the portion of your income that goes to pay taxes on the entirety of your earnings. To find it, you divide the total tax payment by your total income.

For instance, imagine George, who has an income of $20,000 in Harmony. After calculating his total taxes of $6,000, he uses the formula:

• Average Tax Rate = Total Tax Paid / Total Income
• Average Tax Rate = $6,000 / $20,000
• = 0.3 or 30%

Thus, George's average tax rate is 30%. Keep in mind, it's the average amount taxed per dollar he earns, providing a holistic view of his tax burden.

Income Tax Structure

A country's income tax structure dictates how much citizens owe based on their earnings. In the country of Harmony where George lives, the tax structure is split into different brackets.

Harmony's approach imposes:

• 10% tax on the first $10,000 of income
• 50% tax on any income above $10,000

This means George pays varying tax rates on different portions of his income, reflecting how Harmony levies taxes efficiently by using different bands or brackets for income levels.

Progressive Taxation

Progressive taxation is a system where the tax rate increases as the taxable amount of an individual's income rises. This kind of tax system is aimed at higher earners paying a greater percentage of their income compared to lower earners.

In Harmony, the tax system applies:

• A lower rate of 10% on the initial $10,000 of income
• A higher rate of 50% on income over $10,000

This kind of structure ensures that individuals like George see their tax rate increase with their income, placing a larger tax responsibility on higher earnings. It aims to reduce income inequality by evenly distributing the tax burden.

Tax Calculation Methodology

Calculating taxes involves breaking down income and applying the respective tax rates from the income tax structure. Tax calculation essentially means knowing which portion of your income falls into which tax bracket, then applying the respective rates.

Using Harmony's tax structure, let's break down George's income:

• The first $10,000 is taxed at 10%, resulting in $1,000
• Any income over $10,000, here another $10,000, is taxed at 50%, resulting in $5,000

The total taxes of $6,000 ($1,000 + $5,000) determine what George owes. Calculating taxes is about carefully segmenting income according to the brackets applied and summing the taxes from each segment, ensuring accurate tax bills for all earners.