Respuesta :
CPI stands for consumer price index. The actual price of the cast-iron pan is 12. 5% higher than the expected price.
What is CPI?
CPI stands for consumer price index. It is the measure of the weighted average of prices of an item(goods and services) over a period of time. It is given by the formula,
[tex]CPI_t=\dfrac{C_t}{C_0} \times 100[/tex]
where [tex]C_t[/tex] is the current market price and [tex]C_o[/tex] is the base year price,
As it is given that the price of the cast-iron pan was $28.35 in 1983, while it is $52.95 today, also, the CPI for the cast iron pan is given to be 166, therefore, the expected price of the cast iron pan can be written as,
[tex]CPI_t=\dfrac{C_t}{C_0} \times 100[/tex]
Substitute the values in the formula we will get,
[tex]166=\dfrac{C_t}{28.35} \times 100\\\\C_t=\dfrac{166 \times 28.35}{100}\\\\C_t = \$47.061[/tex]
Thus, the expected price of the cast iron pan is $47.061.
Now, the percent relation of the actual price of a cast-iron pan to the expected price can be written as,
[tex]\rm Percentage\ change = \dfrac{Actual\ cost- Expected\ cost}{Expected\ cost} \times 100[/tex]
Substitute the value of the expected price and the actual price,
[tex]\rm Percentage\ change = \dfrac{\$52.95-\$47.061}{\$47.061}\times 100 \\\\\rm Percentage\ change = 0.12513 \times 100\\\\\rm Percentage\ change = 12.513\%[/tex]
Hence, the actual price is 12. 5% higher than the expected price.
Learn more about CPI:
https://brainly.com/question/5992428
Answer:
✅ D. The actual price is 12.5% higher than the expected price.
