Building a price index: the basket and the significance of weights

Overview

Weights in a price index determined.

What you need to know

Answer each one before you reveal it.

Questions from this subtopic

Each one with the model answer underneath.

1. 1

   Why must a price index be weighted rather than being a simple average of price changes?

   Model answer

   An unweighted average treats a rise in the price of a rarely bought item as equally important as a rise in the price of something households buy constantly. If postage stamps double while the cost of housing is unchanged, a simple average would record substantial inflation although almost no household is meaningfully worse off. Weighting each category by its share of total household spending ensures that a price change affects the index in proportion to how much of household budgets it actually touches.

2. 2

   How are the weights in a price index determined?

   Model answer

   They are derived from a large survey of household expenditure, which records what households actually spend across categories of goods and services. Each category's weight is its share of total spending, so a category absorbing a fifth of household budgets receives a weight of 20 out of 100, or 200 out of 1,000. The weights are revised annually so that the index continues to reflect current spending patterns rather than those of a past era.

3. 3

   A household spends £400 a month on food, £600 on housing, £200 on transport and £800 on other items. Calculate the weights out of 1,000.

   Model answer

   Total spending is 400 plus 600 plus 200 plus 800, which is £2,000. Each weight is the category's spending divided by the total, multiplied by 1,000. Food is 400 divided by 2,000, multiplied by 1,000, which is 200. Housing is 300, transport is 100 and other items are 400. The weights sum to 1,000, which is the arithmetic check that they have been computed correctly.

4. 4

   Using weights of food 200, housing 300, transport 100 and other 400 out of 1,000, and price indices of 110, 105, 120 and 102 respectively, calculate the overall price index and the rate of inflation.

   Model answer

   Multiply each weight by its index and sum: food is 200 times 110, which is 22,000; housing is 300 times 105, which is 31,500; transport is 100 times 120, which is 12,000; other is 400 times 102, which is 40,800. The total is 106,300. Divide by the sum of the weights, 1,000, to give an overall index of 106.3. Since the base index was 100, the inflation rate is 6.3 per cent.

5. 5

   A price index uses weights out of 100 of food 20, housing 30, transport 15, energy 10, clothing 5 and other 20, with price indices of 105, 108, 102, 130, 98 and 104. Calculate the overall index and the inflation rate.

   Model answer

   The weighted products are 20 times 105 equals 2,100; 30 times 108 equals 3,240; 15 times 102 equals 1,530; 10 times 130 equals 1,300; 5 times 98 equals 490; and 20 times 104 equals 2,080. These sum to 10,740. Dividing by the total weight of 100 gives an overall index of 107.4, so inflation is 7.4 per cent. Notice that energy rose by 30 per cent and clothing fell by 2 per cent, yet the overall figure is far closer to the middle of the range because each is scaled by its weight.

6. 6

   Using the same six price indices of 105, 108, 102, 130, 98 and 104, but weights of food 10, housing 20, transport 10, energy 30, clothing 10 and other 20, calculate the overall index and explain what the comparison demonstrates.

   Model answer

   The weighted products are 10 times 105 equals 1,050; 20 times 108 equals 2,160; 10 times 102 equals 1,020; 30 times 130 equals 3,900; 10 times 98 equals 980; and 20 times 104 equals 2,080. The sum is 11,190, and dividing by 100 gives an overall index of 111.9, so inflation is 11.9 per cent. Every price is identical to the previous calculation, yet the rate is 4.5 percentage points higher purely because energy, the fastest-rising category, now carries three times the weight. This demonstrates that the weights are not a technicality but a determinant of the answer.

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