Chapter 15, Problem 4NP

a.

To determine

To calculate: The average tax rate and the marginal tax rate of someone earning $\$16,000$ and for someone earning $\$30,000$

Answer to Problem 4NP

For the earning $\$16,000$ , the average tax rate is $12.5\%$ and the marginal tax rate is $25\%$ and for the earning $\$30,000$ , the average tax rate is $20\%$ and the marginal tax rate is $30\%$ .

Explanation of Solution

Given is the tax slab of individuals,

Below$\$8,000$	$0\%$
From$\$8,000$ to$\$20,000$	$25\%$
Above$\$20,000$	$30\%$

For calculation of average tax rate the formula is given here:

$\text{A=}\frac{\text{Tax}\text{paid}}{\text{Total}\text{Income}}\text{×100}$

For the person earning $\$16,000$ , the average tax rate will be:

$\begin{array}{l}\text{=}\frac{\text{0}\text{.25(\$16,000-\$8,000)}}{\text{\$16,000}}\times \text{100}\\ \text{=}\frac{\text{\$2000}}{\text{\$16000}}\text{×100}\\ \text{=12}\text{.50\%}\end{array}$

Since, the person is earning $\$16,000$ , hence, initial $\$8,000$ tax rate is $0\%$ or exempt, and above $\$8,000$ remaining $\$8,000$ is taxed at the rate of $25\%$ . Therefore, the marginal tax rate for the person is $25\%$ .

For the person earning $\$30,000$ , the average tax rate will be:

$\begin{array}{l}\text{=}\frac{\text{(0}\text{.25×\$12,000+0}\text{.30×\$10,000)}}{\text{\$30,000}}\text{×100}\\ \text{=}\frac{\text{\$6,000}}{\text{\$30,000}}\text{×100}\\ \text{=20\%}\end{array}$

Since, the person is earning $\$30,000$ , hence, up to $\$8,000$ tax rate is $0\%$ or exempt, and above $\$8,000$ , he is taxed at the rate of $25\%$ on $\$12,000\left(\$20,000-\$8,000\right)$ and $30\%$ on $\$10,000\left(\$30,000-\$20,000\right)$ . Therefore, the marginal tax rate for the person is $30\%$ .

Economics Concept Introduction

Introduction: The government gets the fund from the taxes and borrowings for expenditure purposes like government consumption, investment, national defense, public health, etc. Government changes these tax slabs time to time to give relief to the persons earning lower incomes or charge extra taxes sometimes from the taxpayers.

b.

To determine

To compute: The average tax rate and the marginal tax rate with revised data.

Answer to Problem 4NP

For the earning $\$16,000$ , the average tax rate is $12.5\%$ and the marginal tax rate is $20\%$ and for the earning $\$30,000$ , the average tax rate is $19.33\%$ and the marginal tax rate is $30\%$ .

Explanation of Solution

Given is the tax slab of individuals,

Below$\$6,000$	$0\%$
From$\$6,000$ to$\$20,000$	$20\%$
Above$\$20,000$	$30\%$

For calculation of average tax rate the formula is given here:

$\text{A=}\frac{\text{Tax}\text{paid}}{\text{Total}\text{Income}}\text{×100}$

For the person earning $\$16,000$ , the average tax rate will be:

$\begin{array}{l}\text{=}\frac{0.2(\$16,000-\$6,000)}{\$16,000}\times 100\\ \text{=}\frac{\text{\$2000}}{\text{\$16000}}\text{×100}\\ \text{=12}\text{.50\%}\end{array}$

Since, the person is earning $\$16,000$ , hence, initial $\$6,000$ tax rate is $0\%$ or exempt, and above $\$6,000$ remaining $\$10,000$ is taxed at the rate of $20\%$ . Therefore, the marginal tax rate for the person is $20\%$ .

For calculation of average tax rate the formula is given here:

$\text{A=}\frac{\text{Tax}\text{paid}}{\text{Total}\text{Income}}\text{×100}$

For the person earning $\$30,000$ , the average tax rate will be:

$\begin{array}{l}\text{=}\frac{\text{(0}\text{.25×\$14,000+0}\text{.30×\$10,000)}}{\text{\$30000}}\text{×100}\\ \text{=}\frac{\text{(\$2,800+\$3,000)}}{\text{\$30,000}}\text{×100}\\ \text{=}\frac{\text{\$5,800}}{\text{\$30,000}}\text{×100}\\ \text{=19}\text{.33\%}\end{array}$

Since, the person is earning $\$30,000$ , hence, initial $\$6,000$ tax rate is $0\%$ or exempt, and above $\$6,000$ remaining $\$14,000\left(\$20,000-\$6,000\right)$ is taxed at the rate of $20\%$ and $\$10,000\left(\$30,000-\$20,000\right)$ is taxed at $30\%$ Therefore, the marginal tax rate for the person is $30\%$ .

Economics Concept Introduction

Introduction: The government gets the fund from the taxes and borrowings for expenditure purposes like government consumption, investment, national defense, public health, etc. Government changes these tax slabs time to time to give relief to the persons earning lower incomes or charge extra taxes sometimes from the taxpayers.

c.

To determine

To describe: If the changes in tax rate affect the labor supply of the person, for the person earning $\$16,000$ and for the person earning $\$30,000$ .

Answer to Problem 4NP

The tax rate lowers in part (b) will not affect the labor supply of the person initially earning $\$16,000$ , but increase in the labor supply of the person initially earning $\$30,000$ , since he has saved money due to lower taxes.

Explanation of Solution

A change in the marginal tax rate does not change the average tax rate of the person earning $\$16,000$ , he is taxed at the rate of $12.5\%$ in both the cases. Hence, the labor supply of the person will remain constant, as he was unable to save anything due to change in slab rate. Whereas, for the person earning $\$30,000$ , there is no change in the marginal tax rate but his average tax rate earlier was $20\%$ and after the change in slab was $19.33\%.$ thus, the labor supply of the person will increase because he saved money due to lower average tax rate than before.

Economics Concept Introduction

Introduction: The government gets the fund from the taxes and borrowings for expenditure purposes like government consumption, investment, national defense, public health, etc. Government changes these tax slabs time to time to give relief to the persons earning lower incomes or charge extra taxes sometimes from the taxpayers.