Chapter 12, Problem 4PA

To determine

State income tax, federal payroll tax, federal income tax, average tax rate, marginal tax rate.

Explanation of Solution

State income tax amount can be calculated as follows:

$\begin{array}{c}\text{State income tax}=\text{Income}\times {\text{Tax rate}}_{\text{State}}\\ =\text{30,000}\times \text{0}\text{.04}\\ =\text{1,200}\end{array}$

State income tax is $1,200.

Federal payroll tax can be calculated as follows:

$\begin{array}{c}\text{Federal payroll tax}=\text{Income}\times {\text{Tax rate}}_{\text{Federal payroll}}\\ =\text{30,000}\times \text{0}\text{.153}\\ =\text{4,590}\end{array}$

Federal payroll tax is $4,590.

Federal income tax can be calculated as follows:

$\begin{array}{c}\text{Federal income tax}=\left(9,075\times {\text{Tax rate}}_{\text{Income range 0 to 9,075}}\right)+\left(\begin{array}{l}\left(\text{Income}-9,0785\right)\\ \times {\text{Tax rate}}_{\text{Income range 9,075 above}}\end{array}\right)\\ =\left(9,075\times 0.1\right)+\left(\left(30,000-9,075\right)\times 0.15\right)\\ =907.5+3,138.75\\ =4,046.25\end{array}$

The Federal income tax is $4,046.25.

Average tax rate can be calculated as follows:

$\begin{array}{c}\text{Average tax rate}=\frac{\text{State income tax + Federal payroll tax + Federal income tax}}{\text{Total income }}\\ =\frac{1,200+4,590+4,046.25}{30,000}\\ =\frac{9,836.25}{30,000}\\ =0.3278\end{array}$

The average tax rate is 32.78%.

Marginal tax rate is calculated as follows:

$\begin{array}{c}\text{Marginal tax rate = Total tax rate for the income above \$9,075}\\ =0.15+0.153+0.04\\ =0.343\\ =34.3\%\end{array}$

The marginal tax rate is 34.3%.

New state income tax amount can be calculated as follows:

$\begin{array}{c}\text{State income tax}=\text{Income}\times {\text{Tax rate}}_{\text{State}}\\ =\text{60,000}\times \text{0}\text{.04}\\ =\text{2,400}\end{array}$

The State income tax is $2,400.

Federal payroll tax can be calculated as follows:

$\begin{array}{c}\text{Federal payroll tax}=\text{Income}\times {\text{Tax rate}}_{\text{Federal payroll}}\\ =\text{60,000}\times \text{0}\text{.153}\\ =\text{9,180}\end{array}$

The Federal payroll tax is $9,180.

Federal income tax can be calculated as follows:

$\begin{array}{c}\text{Federal income tax}=\left(\begin{array}{l}\left(9,075\times {\text{Tax rate}}_{\text{Income range 0 to 9,075}}\right)+\left(\begin{array}{l}\left(\text{36,900}-9,075\right)\\ \times {\text{Tax rate}}_{\text{Income range 9,075 to 36,900}}\end{array}\right)\\ +\left(\left(\text{Income}-36,900\right)\times {\text{Tax rate}}_{\text{Income range above 36,900}}\right)\end{array}\right)\\ =\left(9,075\times 0.1\right)+\left(\left(36,900-9,075\right)\times 0.15\right)+\left(\left(60,000-36,900\right)\times 0.15\right)\\ =907.5+4,173.75+5,775\\ =10,856.25\end{array}$

The federal income tax is $410,856.25.

New average tax rate can be calculated as follows:

$\begin{array}{c}\text{Average tax rate = }\frac{\text{Total taxes}}{\text{Total income}}\\ =\frac{\text{State income tax + Federal payroll tax + Federal income tax}}{\text{Total income }}\\ =\frac{2400+9180+10856.25}{30000}\\ =\frac{22436.25}{30000}\\ =0.374\\ =37.4\%\end{array}$

The average tax rate is 37.4%.

New marginal tax rate can be calculated as follows:

$\begin{array}{c}\text{Marginal tax rate = Total tax rate for the income above \$9,075}\\ =0.15+0.153+0.04+0.25\\ =0.443\\ =44.3\%\end{array}$

The marginal tax rate is 44.3%.

Economics Concept Introduction

Concept introduction:

Marginal tax rate: Marginal tax rate is the rate by which the taxes increase from an additional dollar of income.

Average tax rate: Average tax rate is defined as the total amount of taxes paid divided by total income.