Question 14.7: Cupboards Manufacture Study (2) Refer to Example 14.6 for th......

1 Using the Laspeyres weighted average of quantity relatives method:
Table 14.11 summarises the three-step approach (similar to the weighted average of price relatives method) using Formula 14.14, where the base value is found using (p_0 \times q_0).

Step 1: Find the quantity relative for each item in the basket, (\frac{q_1}{q_2}\%). Use Formula 14.11

Step 2: Find the base period value of each item in the basket

The base period value for each item is found using (p_0 \times q_0) if the Laspeyres method is used, or using (p_1 \times q_0) if the Paasche method is used.

Step 3: Weight the quantity relative for each item by its importance in the basket

Multiply each item’s quantity relative by its own base period value. Then sum these weighted relatives over all items. Finally, divide this sum by the base period value of the basket.

Management Interpretation

The ‘Quantity relatives’ column in Table 14.11 shows that the joinery used 15.56% more cold glue in 2011 than in 2010. Usage of paint also increased by 25% from 2010 to 2011. However, wooden board usage dropped by 9.84% over this same period.

In terms of the base period values, wooden boards are the highest-valued item in the carpentry raw materials basket (R7 686 out of R10 223 = 75.2%), followed by paint (R1 952 out of R10 223 = 19.1%), with cold glue being the lowest-valued item (only R585 out of R10 223 = 5.7%).

The weighting of each individual item’s quantity relative by its respective base period weight is shown in the ‘Weighted quantity relatives’ column. Finally, to derive the composite quantity index, the sum of the weighted quantity relatives (1 004 600) is divided by the base value of the basket (10 223).

Thus the Laspeyres (quantity relatives) quantity index = \frac{1\ 004\ 600}{10\ 233} = 98.3 (using Formula 14.14).

This result is the same as for the Laspeyres (weighted aggregates) composite quantity index (Example 14.6, Solution 1).

2   Using the Paasche weighted average of quantity relatives method
Table 14.12 summarises the three-step approach (similar to 1 above) using Formula 14.15 where the base value is found by weights derived from current prices (p_1 \times q_0).

Thus the Paasche (quantity relatives) quantity index = \frac{1\ 175\ 000}{12\ 069} = 97.4.

This result is the same as for the Paasche (weighted aggregates) composite quantity index (Example 14.6, Solution 2).