7.3.4. Method of Averaging relatives

When there is only one commodity, the price index is the ratio of the price of the commodity in the current period to that in the base period, usually expressed in percentage terms. The method of averaging relatives takes the average of these relatives when there are many commodities.

This chunk explains how the price index is calculated for a single commodity and when dealing with multiple commodities. For a single commodity, you find the price in the current period and the price in the base period. The price index is calculated as a percentage to express how much the price has changed compared to the base period. For multiple commodities, you average the price relatives instead of calculating each individually.

Imagine you have a fruit stand. If apples cost $2 last year and now cost$3, the price index for apples is calculated as (3/2) * 100 = 150%. If you sell bananas and oranges too, and their prices have changed as well, instead of calculating each fruit's percentage change separately, you would average the changes to get a better overall view of how your fruit prices are varying over time.

The price index number using price relatives is defined as P = Σ (P1i/P0i) × 100, where P1 is the price of the ith commodity in the current period and P0 is the price in the base period.

This formula summarizes how to calculate the price index using price relatives. P1 and P0 represent the current and base prices of multiple commodities. By taking the ratio of each current price to its respective base price and multiplying by 100, you get a clearer view of the overall change in prices across all commodities. Summing these individual ratios gives a comprehensive index number.

Think of a school where students' test scores are compared from one year to the next. If in one subject a student scored 80 last year and 90 this year, their relative performance has improved. You can use a similar method to calculate the overall performance of all students across various subjects by taking their scores, comparing them year-round, and summarizing it all in a single performance index.

The weighted price index is the weighted arithmetic mean of price relatives defined as ∑ (Wi × (P1i/P0i) × 100) / ∑ Wi, where W represents the weight assigned based on relative importance.

This part of the chunk discusses how to give more significance to certain items that might weigh more in total consumer expenditure. In this formula, each commodity's price relative is multiplied by its weight (importance) and added together. This sum is then divided by the total weights to derive a more meaningful index that reflects the actual significance of price changes in daily life.

Imagine a group of friends planning to buy groceries for a party. If one friend wants a lot of snacks (which might cost a lot), they should have a heavier influence on the total budget compared to another friend who just wants a few sodas. Therefore, prices for snacks would carry more 'weight' in the budget index than sodas, similar to calculating a weighted price index.

In general, the base period weight is preferred to the current period weight because calculating the weight every year is inconvenient. It also refers to the changing values of different baskets. They are strictly not comparable.

This chunk emphasizes the significance of using the base period's weights when calculating price indices. It suggests that it's more efficient and reliable to use the weightings from a consistent base period instead of recalculating them annually due to the potential difficulty and inconsistency it may introduce over time. By using a fixed basket of goods from the base period, the indices remain standardized and comparable over different time periods.

Consider a marathon race where athletes are timed. If a new method of timing is introduced every year, comparing times from different years becomes complicated and unfair because the stopwatch types vary. Using a consistent timing method (base period weight) allows for fair comparisons of performance across years.

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