Question 14.2: Toiletries Usage Study (1) The data in Table 14.2 shows the ......

Using the Laspeyres weighted aggregates method:

Step 1: Find the base period value for the basket of items

The base period value is what the basket of items would have cost in the base period. It is found by multiplying each item’s base period price with its base period quantity (p_0 \times q_0) and then summing over all items in the basket.

Base period value = \sum{(p_0 \times q_0)}          14.3

In the example, the base period value is:

(1.95 × 37) + (14.65 × 24) + (6.29 × 14) = R511.8

Step 2: Find the current period value for the basket of items

Using Laspeyres, the current period value is the cost of the basket of items in the current period paying current prices (p_1), but consuming base period quantities (q_0). The current period value is found by multiplying each item’s current period price with its base period quantity (p_1 \times q_0) and then summing over all items in the basket.

Current period value = \sum{(p_1 \times q_0)}          14.4

In the example, the current period value is:

(2.10 × 37) + (15.95 × 24) + (6.74 × 14) = R554.86

Step 3: Calculate the composite price index

Divide the current period value by the base period value to derive the composite price index.

Laspeyres (weighted aggregates) price index = \frac{\sum{(p_1 \times q_0)}}{\sum{(p_0 \times q_0)}} × 100%        14.5

Thus the Laspeyres (weighted aggregates) price index is:

\frac{554.86}{511.81} × 100 = 108.4

The calculations for these three steps are summarised in Table 14.3.

Management Interpretation

For this basket of toiletry items, the base period value is R511.81 and the current period value is R554.86. This means that in 2010, a typical two-person household in Tshwane spent R511.81 on the toiletries basket, while a year later, in 2011, they spent R554.86 on the same basket. Overall, the average price of this basket of toiletries has increased by 8.4% from 2010 to 2011, while holding quantities consumed constant at 2010 levels.