The average price of a movie ticket in 1970 was $3.30. Calculate the cost of a movie ticket in 1995, using the Consumer Price Index of 38.8 in 1970 and 152.4 in 1995. Round to the nearest cent.
The Correct Answer and Explanation is:
To calculate the cost of a movie ticket in 1995, we can use the formula based on the Consumer Price Index (CPI), which helps adjust prices for inflation:
[
\text{Cost in 1995} = \text{Cost in 1970} \times \frac{\text{CPI in 1995}}{\text{CPI in 1970}}
]
Given:
- The average price of a movie ticket in 1970 was $3.30.
- The CPI in 1970 was 38.8.
- The CPI in 1995 was 152.4.
Step-by-Step Calculation:
- Substitute the values into the formula:
[
\text{Cost in 1995} = 3.30 \times \frac{152.4}{38.8}
] - Calculate the CPI ratio:
[
\frac{152.4}{38.8} = 3.93
] - Multiply the cost in 1970 by the CPI ratio:
[
3.30 \times 3.93 = 12.99
]
Thus, the cost of a movie ticket in 1995 would be approximately $12.99.
Explanation:
The Consumer Price Index (CPI) measures the average change in prices paid by consumers for goods and services over time. In this case, it helps us account for inflation when comparing the cost of the same item in different years.
In 1970, a movie ticket cost $3.30, and by 1995, inflation had caused the general price level to rise. The CPI in 1970 was 38.8, meaning that prices in 1970 were indexed to this number. By 1995, the CPI had increased to 152.4, showing that the overall price level had risen significantly.
By using the CPI values, we calculated the equivalent price of the movie ticket in 1995. This adjustment gives us a sense of how inflation affects the cost of everyday items like movie tickets. The result shows that what cost $3.30 in 1970 would cost $12.99 in 1995, reflecting the increase in prices over the 25-year period.
This calculation illustrates the importance of adjusting for inflation when comparing the value of money across different time periods.