How to calculate CPI
Question: Calculate the CPI based on the following table.
| Survey Year | Base Year | This Year | |
|---|---|---|---|
| Px | $3 | $4 | $6 |
| Py | $6 | $8 | $12 |
| Qx | 10 | 8 | 12 |
| Qy | 5 | 6 | 10 |
To compute the cost of each basket (of goods X and Y) in the current year and base year...
...we'll use the following formula:
Remember: we want to take quantities from the survey year, not from today or base year.
The Quantity of x and y is always taken from the survey year (this is to ensure we have the same basket of goods we are comparing every year).
Therefore, we'll plug in 10 for Qx...
| Survey Year | Base Year | This Year | |
|---|---|---|---|
| Px | $3 | $4 | $6 |
| Py | $6 | $8 | $12 |
| Qx | 10 | 8 | 12 |
| Qy | 5 | 6 | 10 |
...and 5 for Qy.
| Survey Year | Base Year | This Year | |
|---|---|---|---|
| Px | $3 | $4 | $6 |
| Py | $6 | $8 | $12 |
| Qx | 10 | 8 | 12 |
| Qy | 5 | 6 | 10 |
The price for pencils (Px) today is $6...
| Survey Year | Base Year | This Year | |
|---|---|---|---|
| Px | $3 | $4 | $6 |
| Py | $6 | $8 | $12 |
| Qx | 10 | 8 | 12 |
| Qy | 5 | 6 | 10 |
...and the price for notebooks (Py) today is $12.
| Survey Year | Base Year | This Year | |
|---|---|---|---|
| Px | $3 | $4 | $6 |
| Py | $6 | $8 | $12 |
| Qx | 10 | 8 | 12 |
| Qy | 5 | 6 | 10 |
The prices of x and y in the numerator are based on today's prices.
The price for pencils (Px) in the base year was $4...
| Survey Year | Base Year | This Year | |
|---|---|---|---|
| Px | $3 | $4 | $6 |
| Py | $6 | $8 | $12 |
| Qx | 10 | 8 | 12 |
| Qy | 5 | 6 | 10 |
...and the price for notebooks (Py) in the base year is $8.
| Survey Year | Base Year | This Year | |
|---|---|---|---|
| Px | $3 | $4 | $6 |
| Py | $6 | $8 | $12 |
| Qx | 10 | 8 | 12 |
| Qy | 5 | 6 | 10 |
The prices of x and y in the denominator are based on the base year's prices.
From here, we can solve for a CPI of 150!
