In 1980 the price of a microwave oven was $450 and CPI was 82 . Today the price of a microwave overn is $100 and CPI is 259. Round to two decimal places. What is the 1980 price of a microwave oven measured in todays dollars? $___________
What is todays price of a microwave oven measured in 1980 dollars? $_______
The Correct Answer and Explanation is:
To calculate the equivalent price of a microwave oven from 1980 in today’s dollars and vice versa, we can use the Consumer Price Index (CPI) to adjust for inflation.
Step 1: Calculate the 1980 Price in Today’s Dollars
The formula to convert the price from a past year to today’s dollars is:
[
\text{Adjusted Price} = \text{Price in Base Year} \times \left(\frac{\text{CPI Today}}{\text{CPI Base Year}}\right)
]
For the microwave oven in 1980:
- Price in 1980: $450
- CPI in 1980: 82
- CPI Today: 259
Now plug these values into the formula:
[
\text{Adjusted Price} = 450 \times \left(\frac{259}{82}\right)
]
Calculating this gives:
[
\text{Adjusted Price} = 450 \times 3.15853658537 \approx 1421.34
]
Thus, the price of a microwave oven in 1980 measured in today’s dollars is $1,421.34.
Step 2: Calculate Today’s Price in 1980 Dollars
To convert today’s price back to 1980 dollars, we can rearrange the formula:
[
\text{Adjusted Price in Base Year} = \text{Price Today} \times \left(\frac{\text{CPI Base Year}}{\text{CPI Today}}\right)
]
For today’s price of the microwave:
- Price Today: $100
- CPI in 1980: 82
- CPI Today: 259
Now plug these values into the formula:
[
\text{Adjusted Price in 1980} = 100 \times \left(\frac{82}{259}\right)
]
Calculating this gives:
[
\text{Adjusted Price in 1980} = 100 \times 0.3162185809 \approx 31.62
]
Thus, the price of a microwave oven today measured in 1980 dollars is $31.62.
Summary of Results
- 1980 Price in Today’s Dollars: $1,421.34
- Today’s Price in 1980 Dollars: $31.62
These calculations illustrate how inflation affects purchasing power over time. The significant difference in values emphasizes the impact of inflation on the cost of goods, showing how prices can increase drastically while nominal prices may appear lower.