To solve the problem, let's go through the step-by-step calculations involved.
Step 1: Identify the prices and quantities for both years.
The prices for the items in 3005 are:
- Item1: [tex]$10
- Item2: $[/tex]20
- Item3: [tex]$30
The prices for the items in 3006 are:
- Item1: $[/tex]12
- Item2: [tex]$22
- Item3: $[/tex]35
Assume the quantities are the same in each year:
- Item1: 1 unit
- Item2: 1 unit
- Item3: 1 unit
Step 2: Calculate the total expenditure in each year.
Expenditure in 3005:
- For Item1: [tex]$10 1 = $[/tex]10
- For Item2: [tex]$20 1 = $[/tex]20
- For Item3: [tex]$30 1 = $[/tex]30
Total expenditure in 3005: [tex]$10 + $[/tex]20 + [tex]$30 = $[/tex]60
Expenditure in 3006:
- For Item1: [tex]$12 1 = $[/tex]12
- For Item2: [tex]$22 1 = $[/tex]22
- For Item3: [tex]$35 1 = $[/tex]35
Total expenditure in 3006: [tex]$12 + $[/tex]22 + [tex]$35 = $[/tex]69
Step 3: Calculate the CPI for 3006 using 3005 as the base year.
The formula for CPI is:
[tex]\[ \text{CPI in 3006} = \left( \frac{\text{Total Expenditure in 3006}}{\text{Total Expenditure in 3005}} \right) \times 100 \][/tex]
Plugging in the values:
[tex]\[ \text{CPI in 3006} = \left( \frac{69}{60} \right) \times 100 = 115.0 \][/tex]
Step 4: Calculate the inflation rate in 3006 using the CPI.
The formula for the inflation rate is:
[tex]\[ \text{Inflation Rate} = \left( \frac{\text{CPI in 3006} - \text{CPI in 3005}}{\text{CPI in 3005}} \right) \times 100 \][/tex]
Since the CPI in the base year is always 100:
[tex]\[ \text{Inflation Rate} = \left( \frac{115.0 - 100}{100} \right) \times 100 = 15.0\% \][/tex]
So, the CPI in 3006 using the 3005 CPI market basket is 115.0.
The inflation rate in 3006 using the 3005 CPI market basket is 15.0 percent.
