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Use the information in the table to calculate the Consumer Price Index (CPI) and the inflation rate. The base year is 1975. Round answers to two decimal places.

\begin{tabular}{|c|c|c|c|}
\hline Market basket & Quantity & 1975 prices & 1976 prices \\
\hline A dozen eggs & 29 & [tex]$\$[/tex] 1.10[tex]$ & $[/tex]\[tex]$ 1.70$[/tex] \\
\hline Calculator & 19 & [tex]$\$[/tex] 15.00[tex]$ & $[/tex]\[tex]$ 17.00$[/tex] \\
\hline Microwave oven & 9 & [tex]$\$[/tex] 180.00[tex]$ & $[/tex]\[tex]$ 230.00$[/tex] \\
\hline
\end{tabular}

1. What is the CPI for 1975?
[tex]$\square$[/tex]

2. What is the CPI for 1976?
[tex]$\square$[/tex]


Sagot :

To calculate the Consumer Price Index (CPI) and the inflation rate, let's follow these steps:

### 1. Calculate the total cost of the market basket for 1975 and 1976.

Given:
- Quantities:
- A dozen eggs = 29
- Calculator = 19
- Microwave oven = 9

- Prices in 1975:
- A dozen eggs = \[tex]$1.10 - Calculator = \$[/tex]15.00
- Microwave oven = \[tex]$180.00 - Prices in 1976: - A dozen eggs = \$[/tex]1.70
- Calculator = \[tex]$17.00 - Microwave oven = \$[/tex]230.00

Total Cost in 1975:
[tex]\[ \text{Total Cost (1975)} = (29 \times 1.10) + (19 \times 15.00) + (9 \times 180.00) = 31.90 + 285.00 + 1620.00 = 1936.90 \][/tex]

Total Cost in 1976:
[tex]\[ \text{Total Cost (1976)} = (29 \times 1.70) + (19 \times 17.00) + (9 \times 230.00) = 49.30 + 323.00 + 2070.00 = 2442.30 \][/tex]

### 2. Calculate the CPI for the base year (1975).
The CPI for the base year is always set to 100.

CPI (1975):
[tex]\[ \text{CPI (1975)} = 100 \][/tex]

### 3. Calculate the CPI for 1976.
The CPI for 1976 is calculated using the formula:
[tex]\[ \text{CPI (1976)} = \left( \frac{\text{Total Cost (1976)}}{\text{Total Cost (1975)}} \right) \times 100 \][/tex]

CPI (1976):
[tex]\[ \text{CPI (1976)} = \left( \frac{2442.30}{1936.90} \right) \times 100 = 126.09 \][/tex]

### 4. Determine the inflation rate from 1975 to 1976.
The inflation rate is calculated using the formula:
[tex]\[ \text{Inflation Rate} = \left( \frac{\text{CPI (1976)} - \text{CPI (1975)}}{\text{CPI (1975)}} \right) \times 100 \][/tex]

Inflation Rate:
[tex]\[ \text{Inflation Rate} = \left( \frac{126.09 - 100}{100} \right) \times 100 = 26.09\% \][/tex]

### Summary:
- CPI for 1975: 100
- CPI for 1976: 126.09
- Inflation Rate from 1975 to 1976: 26.09%
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