Question 14.6: Cupboard Manufacturer Study (1) The data in Table 14.8 refer......
Cupboard Manufacturer Study (1)
The data in Table 14.8 refers to a basket of three carpentry items (cold glue, wooden boards and paint) used by a joinery company in the manufacture of cupboards for 2010 and 2011 respectively. The data was collected from the company’s financial records.
(See Excel file C14.4 – carpentry material.)
Management Questions
1 Using the Laspeyres weighted aggregates method, construct a composite quantity index for the average change in the quantity of carpentry materials used (cold glue, wooden boards, paint) between 2010 (as base period) and 2011.
2 Using the Paasche weighted aggregates method, construct a composite quantity index for the average change in the quantity of carpentry materials used (cold glue, wooden boards, paint) between 2010 (as base period) and 2011.
Table 14.8 Data on carpentry material usage for joinery company (2010–2011)
| Carpentry items | Year 2010 | Year 2011 | ||
| p_0 | q_0 | p_1 | q_1 | |
| Cold glue (1 ℓ) | R13 | 45 | R15 | 52 |
| Boards (m^2) | R63 | 122 | R77 | 110 |
| Paint (5 ℓ) | R122 | 16 | R125 | 20 |
1 Using the Laspeyres weighted aggregates method:
A three-step approach similar to that applied to the weighted aggregrates composite price index is used. Table 14.9 summarises the three-step approach based on Formula 14.12.
Step 1
The base period value is found using \sum{(q_0 \times q_0)} = R10 223. This means that in 2010 (base period), the joinery used R10 223 worth of raw materials (cold glue, boards and paint).
Step 2
The current period value is found using \sum{(q_0 \times q_1)} = R10 046. This means that in 2011 (current period), the joinery used R10 046 worth of raw materials (cold glue, boards and paint), assuming 2010 prices were paid.
Step 3
The composite quantity index is found by dividing the current period value by the base period value.
Thus the Laspeyres (weighted aggregates) quantity index \frac{10046}{10223} × 100 = 98.3 (using Formula 14.12).
Management Interpretation
If prices are held constant at 2010 (base period) levels, the composite quantity index stands at 98.3 in 2011. This means that the joinery company used 1.7% less of all raw materials, on average, from 2010 to 2011.
2 Using the Paasche weighted aggregates method:
The Paasche method holds prices constant at current period levels. The ‘weighted aggregates’ three-step approach is summarised in Table 14.10 on the next page and is based on Formula 14.13.
Thus Paasche (weighted aggregates) quantity index = \frac{11750}{12069} × 100 = 97.4 (using Formula 14.13).
Management Interpretation
If prices are held constant at 2011 (current period) levels, the composite quantity index stands at 97.4 in 2011. This means that the joinery company used 2.6% less of all raw materials, on average, from 2010 to 2011.
Table 14.9 Laspeyres (weighted aggregates) composite quantity index
| Carpentry raw material | p_0 | q_0 | p_1 | q_1 | Base value (p_0 \times q_0) | Current value (p_0 \times q_1) |
| Cold glue (1 ℓ) | 13 | 45 | 15 | 52 | 585 | 676 |
| Boards (m^2) | 63 | 122 | 77 | 110 | 7686 | 6930 |
| Paint (5 ℓ) | 122 | 16 | 125 | 20 | 1952 | 2440 |
| 10 223 | 10046 | |||||
| Laspeyres (weighted aggregates) quantity index | 98.3 | |||||
Table 14.10 Paasche (weighted aggregates) composite quantity index
| Carpentry raw material | p_0 | q_0 | p_1 | q_1 | Base value (p_1 \times q_0) | Current value (p_1 \times q_1) |
| Cold glue (1 ℓ) | 13 | 45 | 15 | 52 | 675 | 780 |
| Boards (m^2) | 63 | 122 | 77 | 110 | 9394 | 8470 |
| Paint (5 ℓ) | 122 | 16 | 125 | 20 | 2000 | 2500 |
| 12069 | 11750 | |||||
| Paasche (weighted aggregates) quantity index | 97.4 | |||||