Chapter 10, Problem 15QP

(a)

To determine

Identify the total tax revenue paid by the five workers.

Explanation of Solution

The tax revenue can be calculated by using the following formula:

$\text{Tax revenue}=\text{Taxable amount}\times \frac{\text{Tax rate}}{100}$                                               (1)

Since the tax rates is 15% for all income groups up to $50,000 and 30% for all income group above $50,000, the tax paid by the five workers is calculated as follows:

The income of worker A is $20,000. Substitute the value in Equation-1 to get the value of tax amount as follows:

$\begin{array}{c}{\text{Tax}}_{\text{A}}=\text{\$20,000}\times \frac{\text{15\%}}{100}\\ =\$3,000\end{array}$

Thus, worker A has to pay $3,000.

The income of worker B is $40,000. Substitute the value in Equation-1 to get the value of tax amount as follows:

$\begin{array}{c}{\text{Tax}}_{\text{B}}=\text{\$40,000}\times \frac{\text{15\%}}{100}\\ =\$6,000\end{array}$

Thus, worker B has to pay $6,000.

The income of worker C is $60,000. Thus, the tax paid up to $50,000 is calculated using Equation-1 as follows:

$\begin{array}{c}{\text{Tax}}_{\text{C}}=\text{\$50,000}\times \frac{\text{15\%}}{100}\\ =\$7,500\end{array}$

The tax for remaining amount $10,000 $\left(\$60,000-\$50,000\right)$ is calculated using Equation-1 as follows:

$\begin{array}{c}{\text{Tax}}_{\text{C}}=\text{\$10,000}\times \frac{\text{30\%}}{100}\\ =\$3,000\end{array}$

Thus, the total amount of tax paid by worker C is $10,500 $\left(\$7,500+\$3,000\right)$.

The income of worker D is $80,000. Thus, as shown above, the tax paid up to $50,000 is $7,500.

The tax for remaining amount $30,000 $\left(\$80,000-\$50,000\right)$ is calculated using Equation-1 as follows:

$\begin{array}{c}{\text{Tax}}_{\text{D}}=\text{\$30,000}\times \frac{\text{30\%}}{100}\\ =\$9,000\end{array}$

Thus, the total amount of tax paid by worker D is $16,500 $\left(\$7,500+\$9,000\right)$.

The income of worker E is $100,000. Thus, the tax paid up to $50,000 is $7,500.

The tax for remaining amount $50,000 $\left(\$100,000-\$50,000\right)$ is calculated using Equation-1 as follows:

$\begin{array}{c}{\text{Tax}}_{\text{E}}=\text{\$50,000}\times \frac{\text{30\%}}{100}\\ =\$15,000\end{array}$

Thus, the total amount of tax paid by worker E is $22,500 $\left(\$7,500+\$15,000\right)$.

The total tax revenue is equal to the sum total of each worker’s taxable amount. Thus, it is calculated as follows:

$\begin{array}{c}\text{Total tax revenue}={\text{Tax}}_{\text{A}}+{\text{Tax}}_{\text{B}}+{\text{Tax}}_{\text{C}}+{\text{Tax}}_{\text{D}}+{\text{Tax}}_{\text{E}}\\ =\$3,000+\$6,000+\$10,500+\$16,500+\$22,500\\ =\$58,500\end{array}$

Thus, the total tax revenue is $58,500.

The total income of the five workers is calculated as follows:

$\begin{array}{c}\text{Total income}={\text{Income}}_{\text{A}}+{\text{Income}}_{\text{B}}+{\text{Income}}_{\text{C}}+{\text{Income}}_{\text{D}}+{\text{Income}}_{\text{E}}\\ =\$20,000+\$40,000+\$60,000+\$80,000+\$100,000\\ =\$300,000\end{array}$

Thus, the total income is $300,000.

The percentage of tax revenue to the total income is calculated as follows:

$\begin{array}{c}\text{Percent of tax revenue}=\frac{\$58,500}{\$300,000}\times 100\\ =19.5\%\end{array}$

Thus, the total tax revenue is 19.5% of the total income.

(b)

To determine

Identify the tax revenue after the decline in income. 

Explanation of Solution

Since the salaries fall by 25%, the new income of worker A is $15,000 $\left(20,000\times 25/100\right)$. Substitute the value in Equation-1 to get the value of new tax amount as follows:

$\begin{array}{c}{\text{Tax}}_{\text{A}}=\text{\$15,000}\times \frac{\text{15\%}}{100}\\ =\$2,250\end{array}$

Thus, worker A has to pay $2,250.

The new income of worker B is $30,000 $\left(40,000\times 25/100\right)$. Substitute the value in Equation-1 to get the value of new tax amount as follows:

$\begin{array}{c}{\text{Tax}}_{\text{B}}=\text{\$30,000}\times \frac{\text{15\%}}{100}\\ =\$4,500\end{array}$

Thus, worker B has to pay $4,500.

The new income of worker C is $45,000$\left(60,000\times 25/100\right)$. Substitute the value in Equation-1 to get the value of new tax amount as follows:

$\begin{array}{c}{\text{Tax}}_{\text{C}}=\text{\$45,000}\times \frac{\text{15\%}}{100}\\ =\$6,750\end{array}$

Thus, worker C has to pay $6,750.

The new income of worker D is $60,000$\left(80,000\times 25/100\right)$. Thus, the tax paid up to $50,000 is calculated using Equation-1 as follows:

$\begin{array}{c}{\text{Tax}}_{\text{D}}=\text{\$50,000}\times \frac{\text{15\%}}{100}\\ =\$7,500\end{array}$

The tax for remaining amount $10,000 $\left(\$60,000-\$50,000\right)$ is calculated using Equation-1 as follows:

$\begin{array}{c}{\text{Tax}}_{\text{D}}=\text{\$10,000}\times \frac{\text{30\%}}{100}\\ =\$3,000\end{array}$

Thus, the total of tax paid by worker D is $10,500 $\left(\$7,500+\$3,000\right)$.

The new income of worker E is $75,000$\left(100,000\times 25/100\right)$. Thus, the tax paid up to $50,000 is $7,500.

The tax for remaining amount $25,000 $\left(\$75,000-\$50,000\right)$ is calculated using Equation-1 as follows:

$\begin{array}{c}{\text{Tax}}_{\text{E}}=\text{\$25,000}\times \frac{\text{30\%}}{100}\\ =\$7,500\end{array}$

Thus, the total tax amount paid by worker E is $15,000 $\left(\$7,500+\$7,500\right)$.

The total tax revenue is calculated as follows:

$\begin{array}{c}\text{Total tax revenue}={\text{Tax}}_{\text{A}}+{\text{Tax}}_{\text{B}}+{\text{Tax}}_{\text{C}}+{\text{Tax}}_{\text{D}}+{\text{Tax}}_{\text{E}}\\ =\$2,250+\$4,500+\$6,750+\$10,500+\$15,000\\ =\$39,000\end{array}$

Thus, the total tax revenue is $39,000.

The total income of the five workers after the decline of salaries is calculated as follows:

$\begin{array}{c}\text{Total income}={\text{Income}}_{\text{A}}+{\text{Income}}_{\text{B}}+{\text{Income}}_{\text{C}}+{\text{Income}}_{\text{D}}+{\text{Income}}_{\text{E}}\\ =\$15,000+\$30,000+\$45,000+\$60,000+\$75,000\\ =\$225,000\end{array}$

Thus, the total income is $225,000.

The percentage of tax revenue to the total income is calculated as follows:

$\begin{array}{c}\text{Percent of tax revenue}=\frac{\$39,000}{\$225,000}\times 100\\ =17.33\%\end{array}$

Thus, the total tax revenue is 17.33% of the total income.

(c)

To determine

Explain the progressive tax structure as an automatic stabilizer.

Explanation of Solution

Option ‘a’ and option ‘b’ show that as income falls, the tax revenue also follows it. Therefore, a progressive tax structure declines the percentage of tax revenue when income declines. Thus, the progressive tax system act as an automatic stabilizer.

Economics Concept Introduction

Progressive tax: The progressive tax system is a tax collecting system where the tax rate increases as tax base increases.