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The table shows the cost of a fixed basket of goods that a typical urban consumer would buy in the economy of Kindleberger. The base period for the consumer price index (CPI) is the year 2010. Please specify answers to two decimal places.

\begin{tabular}{|l|c|}
\hline
Year & Cost of a basket of goods \\
\hline
2010 & \[tex]$6,150.00 \\
\hline
2021 & \$[/tex]6,500.00 \\
\hline
2022 & \[tex]$5,725.00 \\
\hline
\end{tabular}

1. What is the CPI for 2010?

CPI for 2010: $[/tex]\square[tex]$

2. What is the CPI for 2021?

CPI for 2021: $[/tex]\square$


Sagot :

To find the Consumer Price Index (CPI) for the years 2010 and 2021, we will use the following formula:

[tex]\[ \text{CPI in a given year} = \left( \frac{\text{Cost of the basket in the given year}}{\text{Cost of the basket in the base year}} \right) \times 100 \][/tex]

Here, the base year is 2010, and the cost of the basket in the base year is [tex]$6,150.00. ### CPI for 2010: Since 2010 is the base year, the cost of the basket in 2010 is used as the denominator and numerator in the formula: \[ \text{CPI for 2010} = \left( \frac{6,150.00}{6,150.00} \right) \times 100 \] Simplifying this: \[ \text{CPI for 2010} = 1 \times 100 = 100.00 \] So, the CPI for 2010 is 100.00. ### CPI for 2021: To find the CPI for 2021, we use the cost of the basket in 2021, which is $[/tex]6,500.00, and compare it to the base year cost:

[tex]\[ \text{CPI for 2021} = \left( \frac{6,500.00}{6,150.00} \right) \times 100 \][/tex]

Calculating this:

[tex]\[ \text{CPI for 2021} = \left( \frac{6,500.00}{6,150.00} \right) \times 100 \approx 1.0569 \times 100 = 105.69 \][/tex]

So, the CPI for 2021 is 105.69.

Therefore, the final CPIs are:
- CPI for 2010: 100.00
- CPI for 2021: 105.69