Chapter 1, Problem 16P

To determine

The required tax in cents per gallon.

Answer to Problem 16P

The total required tax in cents gallon to make additional $\$60$ million revenue is $0.6417\text{cent}/\text{gallon}$.

Explanation of Solution

Given:

The population is $17$ million.

Ownership is $1.1$ cars per person.

Average rate is $12,000\text{mi}/\text{year}$.

Average fuel economy is $\text{24}\text{mi}/\text{gal}$.

Additional revenue is $\$60\text{million}\text{per}\text{year}$.

Calculations:

Write the expression to calculate the total number of cars.

  $\text{Total}\text{cars}=\text{Population}\times \text{Average}\text{ownership}\text{cars}$ ....... (I)

Substitute $17,000,000$ for population and $1.1$ for average ownership cars in Equation (I).

  $\begin{array}{c}\text{Total}\text{cars}=17,000,000\times 1.1\\ =18,700,000\end{array}$

Write the expression to calculate the number of miles driven each year.

  $\text{Number}\text{of}\text{miles}\text{driven}\text{each}\text{year}=\text{Total}\text{cars}\times \text{Average}\text{miles}$ ....... (II)

Substitute $18,700,000$ for total cars and $\text{12,000}\text{mi}/\text{year}$ for average miles driven in each year in Equation (II).

  $\begin{array}{c}\text{Total}\text{average}\text{driven}\text{by}\text{all}\text{cars}=18,700,000\times \text{12,000}\text{mi}/\text{year}\\ =224,400\times {10}^6\text{mi}/\text{year}\end{array}$

Write the expression to calculate the number of gallons consumed each year.

  $\text{Gallon}\text{gasoline}=\frac{\text{Total}\text{average}\text{driven}\text{by}\text{all}\text{cars}}{\text{Average}\text{fuel}\text{economy}}$ ....... (III)

Substitute $224,400\times {10}^6\text{mi}/\text{year}$ for total average driven by all cars and $\text{24}\text{mi}/\text{gallon}$ average fuel economy in Equation (III).

  $\begin{array}{c}\text{Gallons}\text{of}\text{gasoline}=\frac{224,400\times {10}^6\text{mi}/\text{year}}{\text{24}\text{mi}/\text{gallon}}\\ =9350\times {10}^6\text{gallon}/\text{year}\end{array}$

Write the expression to calculate the total tax per gallon of gasoline.

  $\text{Total}\text{tax}=\frac{\text{additional}\text{fund}\text{per}\text{year}}{\text{Gallons}\text{of}\text{gasoline}}$ ....... (IV)

Substitute $9350\times {10}^6\text{gallons}/\text{year}$ for gallons of gasoline and $\$60\times {10}^6/\text{year}$ for additional fund per year in Equation (IV).

  $\begin{array}{c}\text{Total}\text{tax}=\frac{\$60\times {10}^6/\text{year}}{9350\times {10}^6\text{gallons}/\text{year}}\\ =\text{\$}0.006417/\text{gallon}\\ =\left(\text{\$}0.006417/\text{gallon}\times \frac{100\text{cent}}{\$1}\right)\\ =0.6417\text{cent}/\text{gallon}\end{array}$

Conclusion:

Therefore, the total required tax in cents gallon to make additional $\$60$ million revenue is $0.6417\text{cent}/\text{gallon}$.