Question 14.3: Toiletries Usage Study (2) Refer to the problem scenario of ......

Using the Paasche weighted aggregates method:
The same three steps in calculating the weighted aggregates composite price index are used.

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, but consuming current period quantities. It is found by multiplying each item’s base period price with its current period quantity (p_0 \times q_1) and then summing over all items in the basket.

Base period value = \sum{(p_0 \times q_1)}          14.6

In the example, the base period value is:

(1.95 × 40) + (14.65 × 18) + (6.29 × 16) = 442.34

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

Using Paasche, the current period value of a basket is the current cost of the basket of items based on current prices and current consumption. It is found by multiplying each item’s current period price with its current period quantity (p_1 \times q_1) and then summing over all items in the basket.

Current period value = \sum{(p_1 \times q_1)}          14.7

In the example, the current period value is:

(2.1 × 40) + (15.95 × 18) + (6.74 × 16) = 478.94

Step 3: Calculate the composite price index

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

Paasche (weighted aggregates) price index = \frac{\sum{(p_1 \times q_1)}}{\sum{(p_0 \times q_1)}} × 100%          14.8

Thus the Paasche (weighted aggregates) price index is:

\frac{478.94}{442.34} × 100 = 108.3

The calculations for these three steps are summarised in Table 14.4.

Management Interpretation

For this basket of toiletry items that is based on the quantity of items consumed in 2011 (i.e. the current period), the base period value is R442.34 and the current period value is R478.94. This means that in 2010, a typical two-person household in Tshwane spent R442.34 on the toiletries basket, while a year later, in 2011, they spent R478.94 on the same basket. Overall, the average price of this basket of toiletries has increased by 8.3% from 2010 to 2011, while holding quantities consumed constant at 2011 levels.