How to compute the consumer price index ?

The Consumer Price Index (CPI) is a measure of the average change over time in the prices paid by urban consumers for a market basket of consumer goods and services. Here is how you can compute the CPI:

1. Select a base year: The first step in computing the CPI is to select a base year against which all other years will be compared. The base year is typically set to 100.

2. Determine the basket of goods and services: Identify the items that are typically purchased by consumers, such as food, housing, transportation, and healthcare. This basket of goods and services should represent the typical spending patterns of urban consumers.

3. Collect price data: Gather price data for each item in the basket of goods and services for the current year and the base year. The prices should be collected from a variety of sources, such as government agencies, retailers, and surveys.

4. Calculate the cost of the basket: Multiply the price of each item in the basket by the quantity purchased in the current year and the base year. Add up the total cost of the basket for both years.

5. Calculate the CPI: Divide the total cost of the basket in the current year by the total cost of the basket in the base year and multiply by 100. This will give you the CPI for the current year.

CPI = (Cost of basket in current year / Cost of basket in base year) x 100

6. Interpret the results: A CPI greater than 100 indicates that prices have increased since the base year, while a CPI less than 100 indicates that prices have decreased. The CPI can be used to measure inflation and track changes in the cost of living over time.

Steps to Compute the Consumer Price Index (CPI)

1. Identify the reference period: Determine the period (e.g., a month, quarter) for which the CPI will be calculated.

2. Select a representative sample of goods and services: Collect data on a basket of goods and services that represent the consumption patterns of urban consumers. This basket typically includes items such as food, housing, transportation, medical care, and entertainment.

3. Determine the price of each item in the basket: Collect price quotes for each item in the basket from a variety of retail outlets. This can be done in person, online, or through surveys.

4. Calculate the average price for each item in the basket: Compute the average price for each item by aggregating the price quotes collected. This can be done using a weighted average, where each price is weighted by the importance (share) of the item in the basket.

5. Construct an index number for each item: Divide the average price of an item in the current period by its average price in the base period (often set as 100). This generates an index number for each item.

6. Aggregate the index numbers into a single CPI: Multiply each index number by the share of the corresponding item in the basket. Sum the products to obtain the CPI. The CPI represents the overall change in the average price level of the basket of goods and services.

7. Adjust for inflation: The CPI is often used as a measure of inflation. To obtain the inflation rate, subtract the CPI of the base period from the CPI of the current period and divide the difference by the base period CPI. Multiply the result by 100 to express it as a percentage.

Formula:

```
CPI = Σ(wᵢ - pᵢ)
```

Where:

- CPI is the Consumer Price Index
- wᵢ is the weight (share) of item i in the basket
- pᵢ is the price index of item i

Example:

Suppose we have a basket of goods and services with the following weights and prices:

| Item | Weight (wᵢ) | Price Index (pᵢ) |
|---|---|---|
| Food | 0.3 | 110 |
| Housing | 0.4 | 120 |
| Transportation | 0.2 | 130 |
| Other | 0.1 | 140 |

Using the formula above, the CPI would be calculated as:

```
CPI = (0.3-110) + (0.4-120) + (0.2-130) + (0.1-140) = 122
```

This means that the overall price level has increased by 22% since the base period.