The prices of a pound of butter for several different years are shown below.
Calculate the price of a pound of butter in 2010 dollars. Enter results in the table below. Round answers to the nearest penny.
| Year | 1970 | 1980 | 1990 | 2000 | 2010 |
| --- | --- | --- | --- | --- | --- |
| Price of butter (lb) (unadjusted) | $1.33 | $1.80 | $2.11 | $2.43 | $2.78 |
| Price in 2010 dollars | $7.33 | $ | $3.46 | $ | 2.78 Enter an exact number. |
| | | | | | |
Inflation rates between the indicated years and 2010 are shown in the table below.
| Time span | 1970-2010 | 1980-2010 | 1990-2010 | 2000-2010 |
| --- | --- | --- | --- | --- |
| Inflation rate | 451% | 154% | 64% | 26% |
Answer (1)
Calculate the price of butter in 1980 in 2010 dollars: P 1980 , 2010 = 1.80 × ( 1 + 1.54 ) = $4.57 .
Calculate the price of butter in 2000 in 2010 dollars: P 2000 , 2010 = 2.43 × ( 1 + 0.26 ) = $3.06 .
Round each result to the nearest cent.
The price of butter in 1980 in 2010 dollars is $4.57 and the price of butter in 2000 in 2010 dollars is $3.06 .
Explanation
Understanding the Problem We are given the prices of butter in different years and the inflation rates between those years and 2010. We need to calculate the price of butter in 2010 dollars for the years 1980 and 2000.
Formula for 2010 Dollars To calculate the price of butter in 2010 dollars, we use the formula: P y , 2010 = P y × ( 1 + I y , 2010 ) where:
P y , 2010 is the price of butter in year y in 2010 dollars.
P y is the price of butter in year y .
I y , 2010 is the inflation rate from year y to 2010.
Calculating for 1980 For the year 1980:
P 1980 = $1.80
I 1980 , 2010 = 154% = 1.54 So, the price of butter in 1980 in 2010 dollars is: P 1980 , 2010 = 1.80 × ( 1 + 1.54 ) = 1.80 × 2.54 = $4.572 Rounding to the nearest cent, we get $4.57.
Calculating for 2000 For the year 2000:
P 2000 = $2.43
I 2000 , 2010 = 26% = 0.26 So, the price of butter in 2000 in 2010 dollars is: P 2000 , 2010 = 2.43 × ( 1 + 0.26 ) = 2.43 × 1.26 = $3.0618 Rounding to the nearest cent, we get $3.06.
Final Answer Therefore, the price of a pound of butter in 1980 in 2010 dollars is $4.57 , and the price of a pound of butter in 2000 in 2010 dollars is $3.06 .
Examples
Understanding inflation-adjusted prices is crucial in personal finance and economics. For instance, comparing the price of goods like butter across different years helps consumers and economists understand real price changes, accounting for the effects of inflation. This allows for more accurate comparisons of purchasing power and economic trends over time. For example, knowing the inflation-adjusted price of butter helps families budget effectively and understand whether they are truly spending more or less on this staple food compared to previous years. Similarly, economists use inflation-adjusted prices to analyze consumer behavior and make informed policy decisions.
