Bahari Household Basket: A Laspeyres Index and the Real Wage Dispute
A trade union and an employer are in a wage dispute. An employee earned KSh 45,000 a month in 2022 and KSh 54,000 in 2024. The union claims a 25% increase on the 2024 wage; the employer says the worker is already '20% better off'. A household basket based on 2022 quantities was compiled:
| Item | 2022 price (KSh) | 2024 price (KSh) | 2022 quantity |
|---|---|---|---|
| Maize flour (2 kg) | 50 | 65 | 20 |
| Milk (litre) | 40 | 50 | 15 |
| Transport (trip) | 30 | 36 | 25 |
| Rent (room/month) | 2,000 | 2,400 | 1 |
Both parties have asked for an independent calculation before the next negotiating meeting.
1. Compute the Laspeyres price index for 2024 with 2022 as the base year, and interpret the result.
Read the worked answer
| Item | P0Q0 | P1Q0 |
|---|---|---|
| Maize flour | 50 × 20 = 1,000 | 65 × 20 = 1,300 |
| Milk | 40 × 15 = 600 | 50 × 15 = 750 |
| Transport | 30 × 25 = 750 | 36 × 25 = 900 |
| Rent | 2,000 × 1 = 2,000 | 2,400 × 1 = 2,400 |
| Total | 4,350 | 5,350 |
Index = (ΣP1Q0 ÷ ΣP0Q0) × 100 = (5,350 ÷ 4,350) × 100 = 122.99.
The same basket that cost KSh 4,350 in 2022 cost KSh 5,350 in 2024 - a rise of about 23%. Note that rent carries 2,000/4,350 = 46% of the basket weight, so the index is dominated by housing.
2. Using the index, compute the employee's real wage in 2024 in 2022 prices, and the nominal wage that would be needed in 2024 to restore 2022 purchasing power. Which of the two parties' positions is supported?
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Real wage 2024 = 54,000 × (100 ÷ 122.99) = KSh 43,907 in 2022 prices.
Change in real wage = (43,907 ÷ 45,000) − 1 = −2.43%. The employee is worse off in real terms, by roughly KSh 1,093 a month.
Wage needed to restore 2022 purchasing power: 45,000 × 1.2299 = KSh 55,346, i.e. a shortfall of 55,346 − 54,000 = KSh 1,346 on the current wage, or a 22.99% rise on the 2022 wage.
Assessment: the employer is wrong - the 20% nominal rise is less than the 23% rise in prices, so real pay has fallen. The union is broadly right on the arithmetic, but its claim of 25% on the 2024 wage would take pay well beyond mere restoration; the cost-of-living case supports about 2.5% on the current wage (KSh 55,346), and any amount above that must be argued on productivity or comparability grounds, not on the index.
3. The employer disputes the index, arguing that workers simply switched from expensive items. Critically evaluate the use of this index as a measure of the employee's cost of living.
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Strengths: it is transparent, reproducible, uses a fixed basket so it measures pure price change and base-period quantities are readily observed.
Weaknesses relevant to this dispute:
- Substitution bias (upward bias): the Laspeyres form holds 2022 quantities fixed. When maize flour rose 30%, households bought more of cheaper substitutes; the index ignores that and overstates the cost of maintaining the same standard of living. The employer's point has some force.
- Weight sensitivity: rent is 46% of the basket. A single rent survey error, or a worker living in a cheaper area, swings the index sharply. A worker who owns a home has a very different inflation experience from the index.
- Aggregation: one county-wide basket cannot represent every household; income group, family size and location all matter.
- Quality and coverage: it ignores quality change, new goods, and informal-market prices where many workers actually buy.
Conclusion: the index is a reasonable starting point and clearly refutes the '20% better off' claim, but it should be treated as a range rather than a precise figure. A defensible settlement uses the index to establish the restoration figure (about KSh 55,346) and negotiates any productivity element separately.