7.3.1. Example 1: Calculation of simple aggregative price index

In the following sections, the principles of constructing an index number will be illustrated through price index numbers. The formula for a simple aggregative price index is:

P = ΣP₁ × 100 / ΣP₀,

where P₁ and P₀ indicate the price of the commodity in the current period and base period respectively.

The simple aggregative price index is a way of measuring how prices change over time for a set of items. This formula essentially compares the current prices of these items to their prices in a base period, allowing us to see overall price changes. If we were to take a basket of goods and look at how their prices have increased or decreased, this formula tells us the average change expressed as a percentage.

Imagine you went to the grocery store today and noted the prices of some items. If you compare these prices to the prices five years ago, you will get a sense of how much prices have risen. For instance, if a loaf of bread cost $1 five years ago and now costs$1.50, using our formula helps us calculate the overall price increase for all items in your cart.

Using data from example 1, the simple aggregative price index is calculated as follows:

P = (4+6+5+3) / (2+5+4+2) × 100 = 138.5.

Here, price is said to have risen by 38.5 percent.

In this example, we sum the current prices of four commodities (4+6+5+3) which gives us 18. Then, we sum the base period prices for the same commodities (2+5+4+2) which gives us 13. We then divide the sum of the current prices by the sum of the base prices and multiply by 100 to convert it to a percentage. The result, 138.5, tells us that there has been an overall price increase of 38.5%.

Think of it like measuring your growth over the years by comparing your height at different ages. Just as you’d compare your current height to what it was when you were younger, we compare current prices to past prices to see how much they’ve changed. If you grew from 4 feet to 5.5 feet, that’s a noticeable increase, just like our price index shows a significant rise.

Do you know that such an index is of limited use? The reason is that the units of measurement of prices of various commodities are not the same. It is unweighted, because the relative importance of the items has not been properly reflected.

The limitation of the simple aggregative price index is that it treats all commodities as equal, without considering how much of our budget is spent on each item. For instance, if you spend most of your money on food, a rise in food prices will affect you more than a rise in the price of jewelry, even if both items have the same percentage increase. This makes the index less accurate in reflecting the real cost of living.

Imagine if you were tracking the overall price of a meal at a restaurant but included drinks, appetizers, and desserts equally, regardless of how much you typically spend on each. If the dessert price goes up significantly but you hardly ever buy desserts, that inflation won’t impact you like the price of your main dish that you buy regularly. This example shows how unequal weighting can misrepresent your true spending experience.

There are two methods of constructing an index number: It can be computed by the aggregative method and by the method of averaging relatives.

An index number becomes a weighted index when the relative importance of items is taken care of.

Weighted index numbers account for the different levels of importance of various items. This means that instead of treating all items equally, we consider how much they contribute to overall spending. For instance, if food makes up a large part of a household's expenses, it should carry more weight in the index than a luxury item that is rarely purchased.

Think about how you allocate your allowance. If you spend 60% of it on food, 20% on clothing, and the rest on entertainment, a change in food prices should be more impactful in your calculations of how much your costs have risen compared to clothing or entertainment. Thus, a weighted index provides a clearer picture of the economic reality.

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