Chapter 20, Problem 17E

Many factors influence the retail price of gasoline. The following table shows the average retail price for a gallon of regular grade gasoline for each year from 2011 through 2014 (U.S. Energy Information Administration website, April 2015).

Year	Average Price ($)
2011	3.521
2012	3.618
2013	3.505
2014	3.358

1. a. Use 2011 as the base year and develop a price index for the retail price of a gallon of regular grade gasoline over this four-year period.
2. b. Use 2012 as the base year and develop a price index for the retail price of a gallon of regular grade gasoline over this four-year period.

To determine

Find the price index for the retail price of a gallon of regular grade gasoline over this four-year period by using 2011 as the base year.

Answer to Problem 17E

The price indexes for the retail price of a gallon of regular grade gasoline over this four-year period by using 2011 as the base year are,

Year	Average Price ($)	$\text{Price relative in Period }t$
2011	3.521	100
2012	3.618	102.8
2013	3.505	99.5
2014	3.358	95.4

Explanation of Solution

Calculation:

The data shows the average retail price for a gallon of regular grade gasoline for each year from 2011 to 2014.

The price indexes for the retail price of a gallon of regular grade gasoline over this four-year period by using 2011 as the base year are obtained below:

Year	Average Price ($)	$\text{Price relative in Period }t=\frac{\text{Price in period }t}{\text{Base period price}}\left(100\right)$
2011	3.521	$\frac{\text{3}\text{.521}}{\text{3}\text{.521}}\left(100\right)=100$
2012	3.618	$\frac{\text{3}\text{.618}}{\text{3}\text{.521}}\left(100\right)=102.8$
2013	3.505	$\frac{\text{3}\text{.505}}{\text{3}\text{.521}}\left(100\right)=99.5$
2014	3.358	$\frac{\text{3}\text{.358}}{\text{3}\text{.521}}\left(100\right)=95.4$

To determine

Find the price index for the retail price of a gallon of regular grade gasoline over this four-year period by using 2012 as the base year.

Answer to Problem 17E

The price indexes for the retail price of a gallon of regular grade gasoline over this four-year period by using 2012 as the base year are,

Year	Average Price ($)	$\text{Price relative in Period }t$
2011	3.521	97.3
2012	3.618	100
2013	3.505	96.9
2014	3.358	92.8

Explanation of Solution

Calculation:

The price indexes for the retail price of a gallon of regular grade gasoline over this four-year period by using 2012 as the base year are obtained below:

Year	Average Price ($)	$\text{Price relative in Period }t=\frac{\text{Price in period }t}{\text{Base period price}}\left(100\right)$
2011	3.521	$\frac{\text{3}\text{.521}}{\text{3}\text{.618}}\left(100\right)=97.3$
2012	3.618	$\frac{\text{3}\text{.618}}{\text{3}\text{.618}}\left(100\right)=100$
2013	3.505	$\frac{\text{3}\text{.505}}{\text{3}\text{.618}}\left(100\right)=96.9$
2014	3.358	$\frac{\text{3}\text{.358}}{\text{3}\text{.618}}\left(100\right)=92.8$