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%
