Question

Mr. Errol makes deliveries by bicycle for a living and earns \(\$ 200\) a week. He is currently taxed at a rate of \(20 \% .\) Be cause of his superior work record, his boss gave Mr. Errol a \$10 raise in pay. Mr. Errol is excited, but does not realize that this raise in pay puts him in a \(25 \%\) tax bracket. a) How much of an increase in take-home salary does this raise amount to? b) Discuss Mr. Errol's marginal tax rate.

Short answer

After calculating the original and new after-tax salaries, we find that Mr. Errol's increase in take-home salary is \( \$7.50 \). His marginal tax rate after the raise is \( 25\% \), as the additional \$10 he earns is taxed at the higher 25% bracket. As a result, he will take home only $7.50 from the \$10 raise in his salary due to the increased tax rate.

Step-by-step solution

(Step 1: Calculate Mr. Errol's original after-tax salary.)

Mr. Errol earns \(200 a week and is taxed at a rate of \)20\%$. To calculate his after-tax salary, multiply his weekly salary by the tax rate and subtract the result from the weekly salary amount. Original after-tax salary = \(200 - (200 * \frac{20}{100})\) #a) Calculate the new salary with the raise and new tax rate#

(Step 2: Calculate Mr. Errol's new salary with raise and tax rate.)

Mr. Errol received a \(10 raise. So his new weekly salary is \)210. Now, we need to calculate his new after-tax salary with the new tax rate of \(25\%\). New after-tax salary = \(210 - (210 * \frac{25}{100} )\) #a) Calculate the increase in take-home salary#

(Step 3: Calculate the increase in take-home salary.)

To find the increase in take-home salary, subtract the original after-tax salary from the new after-tax salary. Increase in take-home salary = (New after-tax salary) - (Original after-tax salary) #b) Discuss the new marginal tax rate#

(Step 4: Discuss Mr. Errol's marginal tax rate.)

The marginal tax rate is the tax rate that applies to the last dollar of income earned. In this case, we will calculate Mr. Errol's marginal tax rate by finding the difference in total taxes paid before and after the raise and dividing it by the raise in salary ($10). Marginal tax rate = \(\frac{(\text{Taxes Paid- Before }-\text{Taxes Paid - After})}{\text{Raise in Salary}, 10}\) Next, we will discuss Mr. Errol's marginal tax rate by analyzing the calculated marginal tax rate.

Key concepts

Tax Brackets

Understanding tax brackets is essential for comprehending how your income is taxed. In simple terms, tax brackets determine the rate at which your income is taxed. These brackets kick in at different levels of income. As your income increases, so does the percentage of tax you pay on that additional income. Mr. Errol initially falls in the 20% tax bracket, meaning any earnings up to a certain threshold are taxed at this rate.

However, with Mr. Errol's $10 raise, he moves to a new tax bracket of 25%. This means that extra earnings beyond the previous threshold are now taxed more heavily. It’s important to note that only the additional income—such as Mr. Errol’s $10 raise—is taxed at the higher rate, not his entire income.

Tax brackets are structured in such a way to maintain a progressive tax system, where individuals with higher incomes pay a higher percentage of tax on their earnings. This system aims to ensure fairness and equity in taxation.

After-Tax Salary

After-tax salary is the amount of money you take home after all the taxes are deducted. Calculating the after-tax salary requires you to know the percentage of tax that applies to your income. For Mr. Errol, his initial weekly salary was \(200, which was taxed at a rate of 20%.

To find his original after-tax salary, you calculate:

• Tax Deduction: \( 200 \times \frac{20}{100} = 40 \)
• After-Tax Salary: \( 200 - 40 = 160 \)

With a \)10 raise, his salary increased to $210, and he entered the 25% tax bracket. His new after-tax salary calculation is:

• Tax Deduction: \( 210 \times \frac{25}{100} = 52.5 \)
• After-Tax Salary: \( 210 - 52.5 = 157.5 \)

The after-tax salary gives a clear picture of what Mr. Errol actually earns each week and allows him to understand the true impact of his wage increase.

Income Tax Calculation

Income tax calculation is an essential skill for understanding how changes in income affect your take-home pay. The calculation starts by determining the tax amount based on the income and the applicable tax bracket.

For example, Mr. Errol initially calculated tax on his \(200 income using the 20% rate. The calculated tax was \)40, resulting in a take-home pay of \(160. After his raise, his income of \)210 was subjected to a 25% tax, leading to a tax of \(52.5.

To calculate the increase in take-home salary, subtract the original after-tax amount from the new after-tax amount:

• Increase: \( 157.5 - 160 = -2.5 \)

Interestingly, Mr. Errol discovered that instead of increasing, his take-home pay actually decreased by \)2.50 per week due to the higher tax rate. This calculation reveals how critical it is to understand income tax structures and the effect of tax brackets on take-home salary.