By the end of this chapter, you will be able to:
Mastering these skills will help you analyze data effectively and contribute to better business decisions in your trade.
Use index numbers to measure changes in economic and business variables over time or between different locations, which is crucial for human resource professionals monitoring salary adjustments, cost of living, and wage negotiations. This chapter focuses on the key formulae and methods for computing index numbers that accurately reflect price or quantity changes relevant to HR contexts in Kenya. Understanding how to compute and interpret Lapser's, Paasche's, Fisher's ideal, and Marshal's index numbers enables HR practitioners to make informed decisions on compensation and benefits aligned with economic realities.
Index numbers quantify relative changes in a variable such as prices, wages, or quantities over time by comparing a current period with a base period. There are several formulae used to compute index numbers, each with different weighting schemes reflecting the importance of items in the index basket. These formulae form the foundation for understanding price and quantity movements relevant to HR salary adjustments and budgeting.
A price index number measures the relative change in prices of a basket of goods and services between two periods. Its general formula is:
$$ \text{Price Index} = \frac{\text{Price in current period}}{\text{Price in base period}} \times 100 $$
This basic formula is adapted in various methods to include weighting based on quantities or expenditures.
Example 1: Calculate the price index of an item whose price was Ksh 120 in the base year and Ksh 150 in the current year.
Given: Base price = Ksh 120, Current price = Ksh 150
$$ \text{Price Index} = \frac{150}{120} \times 100 $$
$$ = 1.25 \times 100 $$
$$ = 125 $$
Answer: 125 (Price increased by 25%)
Example 2: A commodity's price increased from Ksh 80 to Ksh 96. Find the price index.
Given: Base price = Ksh 80, Current price = Ksh 96
$$ \text{Price Index} = \frac{96}{80} \times 100 $$
$$ = 1.2 \times 100 $$
$$ = 120 $$
Answer: 120 (Price increased by 20%)
Quantity index number measures changes in quantities of goods or services consumed or produced between two periods. The general formula is:
$$ \text{Quantity Index} = \frac{\text{Quantity in current period}}{\text{Quantity in base period}} \times 100 $$
This helps HR professionals analyze trends in employee benefits usage or training hours over time.
Example 1: Quantity of training hours increased from 100 hours to 140 hours. Calculate the quantity index.
Given: Base quantity = 100 hours, Current quantity = 140 hours
$$ \text{Quantity Index} = \frac{140}{100} \times 100 $$
$$ = 1.4 \times 100 $$
$$ = 140 $$
Answer: 140 (Training hours increased by 40%)
Example 2: Number of employees attending health check-ups decreased from 200 to 180. Calculate the quantity index.
Given: Base quantity = 200, Current quantity = 180
$$ \text{Quantity Index} = \frac{180}{200} \times 100 $$
$$ = 0.9 \times 100 $$
$$ = 90 $$
Answer: 90 (Decrease of 10%)
Weighted index numbers assign weights to items based on their relative importance, such as expenditure or quantity. The general formula is:
$$ \text{Weighted Index} = \frac{\sum (P_n \times Q_b)}{\sum (P_b \times Q_b)} \times 100 $$
Where \(P_n\) is price in the current period, \(P_b\) price in base period, and \(Q_b\) quantity in base period.
Example 1: Two commodities have prices and quantities as below:
| Commodity | Base Price (Ksh) | Current Price (Ksh) | Base Quantity |
|---|---|---|---|
| A | 50 | 60 | 10 |
| B | 30 | 33 | 20 |
Calculate the weighted price index.
Given:
$$ \sum (P_n \times Q_b) = (60 \times 10) + (33 \times 20) = 600 + 660 = 1260 $$
$$ \sum (P_b \times Q_b) = (50 \times 10) + (30 \times 20) = 500 + 600 = 1100 $$
$$ \text{Weighted Price Index} = \frac{1260}{1100} \times 100 = 114.55 $$
Answer: 114.55 (Prices increased by 14.55%)
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Create a free accountThis chapter covered the essential formulae used for computing various types of index numbers, providing the foundation for understanding their calculation and interpretation. It explored the computation of index numbers through different methods, including Laspeyres, Paasche, Fisher's ideal, and Marshall indexes, each with distinct approaches to weighting and data use. The chapter emphasized the step-by-step calculation processes for these indexes, highlighting their relevance and differences in practical applications. Additionally, it discussed how index numbers serve as vital tools in decision making by summarizing complex data trends, aiding businesses and organizations in analyzing price changes, inflation, and economic performance. Trainees were encouraged to engage in practical work to reinforce their understanding and application of these concepts. Overall, the chapter integrated theory and practice to equip students with both the computational skills and analytical insight necessary for using index numbers effectively in business contexts.
A Human Resource manager wants to calculate the Laspeyres index for employee training costs. The base year training cost per employee was Ksh 15,000, and the current year cost is Ksh 18,000. The number of employees trained in the base year was 120. Calculate the Laspeyres index. (2 marks)
The number of employees in three departments in the base year were 50, 30, and 20 respectively. In the current year, their average monthly salaries are Ksh 40,000, Ksh 50,000, and Ksh 60,000 respectively. Calculate the Paasche index for salaries using current year quantities. (3 marks)
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