By the end of this chapter, you will be able to:
These skills will help you make smart, data-driven decisions that are essential in any technical or business environment.
Compiled by: Jane Chebet
Index numbers are essential tools in procurement management for measuring changes in prices, quantities, or values of goods and services over time. They assist procurement professionals in Kenya to analyze inflation trends, evaluate supplier price variations, and make informed purchasing decisions. This chapter focuses on the formulae used to compute index numbers and practical computation methods, including Laspeyre's, Paasche's, Fisher's ideal, and Marshal reports, all critical for effective procurement analysis.
Index numbers quantify relative changes in economic variables such as prices or quantities between different time periods. In procurement management, they help track price fluctuations of goods and services, enabling cost control and budget planning. This section introduces the main formulae used to compute index numbers, laying a foundation for their application in procurement contexts.
The price index number expresses the relative change in the price level of a basket of goods between a base period and a current period. It is generally computed as the ratio of the current period price to the base period price, weighted by quantities or expenditures.
The general formula for a weighted price index number is:
$$ \text{Price Index} = \frac{\sum (p_{1} \times q)}{\sum (p_{0} \times q)} \times 100 $$
where \(p_1\) is the price in the current period, \(p_0\) is the price in the base period, and \(q\) is the quantity or weight.
Example 1: A county government procures stationery items. The price of pens increased from Ksh 50 to Ksh 60, with quantity 100 units. Calculate the price index for pens.
Given: \(p_0 = 50\), \(p_1 = 60\), \(q = 100\)
$$ \text{Price Index} = \frac{60 \times 100}{50 \times 100} \times 100 $$
$$ = \frac{6000}{5000} \times 100 $$
$$ = 1.2 \times 100 = 120 $$
Answer: 120 (Price increased by 20%)
Example 2: A hospital buys syringes. In the base year, the price was Ksh 30, and in the current year Ksh 33. Quantity purchased was 200 units. Calculate the price index.
Given: \(p_0 = 30\), \(p_1 = 33\), \(q = 200\)
$$ \text{Price Index} = \frac{33 \times 200}{30 \times 200} \times 100 $$
$$ = \frac{6600}{6000} \times 100 $$
$$ = 1.1 \times 100 = 110 $$
Answer: 110 (Price increased by 10%)
Example 3: A retail business procures three items: A, B, C. Prices and quantities for base and current periods are:
| Item | \(p_0\) (Ksh) | \(p_1\) (Ksh) | \(q\) (units) |
|---|---|---|---|
| A | 20 | 22 | 50 |
| B | 15 | 18 | 30 |
| C | 40 | 44 | 20 |
Calculate the overall price index.
Given:
$$ \sum (p_1 \times q) = (22 \times 50) + (18 \times 30) + (44 \times 20) = 1100 + 540 + 880 = 2520 $$
$$ \sum (p_0 \times q) = (20 \times 50) + (15 \times 30) + (40 \times 20) = 1000 + 450 + 800 = 2250 $$
$$ \text{Price Index} = \frac{2520}{2250} \times 100 = 1.12 \times 100 = 112 $$
Answer: 112 (Overall price increase of 12%)
Quantity index numbers measure changes in quantities purchased or supplied, holding prices constant. This is useful for procurement managers tracking consumption or supply trends.
The general formula for a weighted quantity index number is:
$$ \text{Quantity Index} = \frac{\sum (q_1 \times p)}{\sum (q_0 \times p)} \times 100 $$
where \(q_1\) is quantity in the current period, \(q_0\) is quantity in the base period, and \(p\) is the price used as weight.
Example 1: A SACCO procures office chairs. The quantity increased from 40 to 50 units, price per chair Ksh 2,000. Compute the quantity index.
Given: \(q_0 = 40\), \(q_1 = 50\), \(p = 2000\)
$$ \text{Quantity Index} = \frac{50 \times 2000}{40 \times 2000} \times 100 $$
$$ = \frac{100000}{80000} \times 100 $$
$$ = 1.25 \times 100 = 125 $$
Answer: 125 (Quantity increased by 25%)
Example 2: A cooperative procures fertilizers. Base quantity 100 bags, current quantity 90 bags, price per bag Ksh 3,500. Calculate quantity index.
Given: \(q_0 = 100\), \(q_1 = 90\), \(p = 3500\)
$$ \text{Quantity Index} = \frac{90 \times 3500}{100 \times 3500} \times 100 $$
$$ = \frac{315000}{350000} \times 100 $$
$$ = 0.9 \times 100 = 90 $$
Answer: 90 (Quantity decreased by 10%)
Example 3: A retail store procures three items with prices and quantities:
| Item | \(q_0\) (units) | \(q_1\) (units) | \(p\) (Ksh) |
|---|---|---|---|
| A | 30 | 36 | 150 |
| B | 50 | 45 | 100 |
| C | 20 | 25 | 200 |
Calculate the quantity index.
Given:
$$ \sum (q_1 \times p) = (36 \times 150) + (45 \times 100) + (25 \times 200) = 5400 + 4500 + 5000 = 14900 $$
$$ \sum (q_0 \times p) = (30 \times 150) + (50 \times 100) + (20 \times 200) = 4500 + 5000 + 4000 = 13500 $$
$$ \text{Quantity Index} = \frac{14900}{13500} \times 100 = 1.1037 \times 100 = 110.37 $$
Answer: 110.37 (Quantity increased by 10.37%)
Value index numbers express the change in total value (price × quantity) of goods or services between periods. This is significant in procurement to assess expenditure changes.
The formula is:
$$ \text{Value Index} = \frac{\sum (p_1 \times q_1)}{\sum (p_0 \times q_0)} \times 100 $$
where \(p_1, q_1\) are current period price and quantity, and \(p_0, q_0\) are base period price and quantity.
Example 1: A university procures textbooks. Base period: price Ksh 1,000, quantity 500. Current period: price Ksh 1,100, quantity 550. Calculate value index.
Given: \(p_0=1000\), \(q_0=500\), \(p_1=1100\), \(q_1=550\)
$$ \text{Value Index} = \frac{1100 \times 550}{1000 \times 500} \times 100 $$
$$ = \frac{605000}{500000} \times 100 $$
$$ = 1.21 \times 100 = 121 $$
Answer: 121 (Value increased by 21%)
Example 2: A hotel procures food supplies. Base: price Ksh 300, quantity 1000; current: price Ksh 280, quantity 1100. Calculate value index.
Given: \(p_0=300\), \(q_0=1000\), \(p_1=280\), \(q_1=1100\)
$$ \text{Value Index} = \frac{280 \times 1100}{300 \times 1000} \times 100 $$
$$ = \frac{308000}{300000} \times 100 $$
$$ = 1.0267 \times 100 = 102.67 $$
Answer: 102.67 (Value increased by 2.67%)
Example 3: A bank procures office equipment:
| Item | \(p_0\) (Ksh) | \(q_0\) | \(p_1\) (Ksh) | \(q_1\) |
|---|---|---|---|---|
| Printer | 20,000 | 5 | 22,000 | 6 |
| Scanner | 15,000 | 3 | 15,500 | 4 |
| Laptop | 50,000 | 2 | 48,000 | 3 |
Calculate value index.
Given:
$$ \sum (p_1 \times q_1) = (22000 \times 6) + (15500 \times 4) + (48000 \times 3) = 132000 + 62000 + 144000 = 338000 $$
$$ \sum (p_0 \times q_0) = (20000 \times 5) + (15000 \times 3) + (50000 \times 2) = 100000 + 45000 + 100000 = 245000 $$
$$ \text{Value Index} = \frac{338000}{245000} \times 100 = 1.3796 \times 100 = 137.96 $$
Answer: 137.96 (Value increased by 37.96%)
A retail store has two products. Product A price changed from Ksh 80 to Ksh 88, quantity 150 units; Product B price changed from Ksh 120 to Ksh 132, quantity 100 units. Calculate the price index using base period quantities. (5 marks)
A hospital's procurement of gloves changed from 500 boxes to 550 boxes, price per box Ksh 400. Calculate the quantity index. (5 marks)
A school buys three types of books. Base period prices and quantities: (Ksh 500, 100), (Ksh 800, 50), (Ksh 200, 200). Current period prices and quantities: (Ksh 550, 110), (Ksh 850, 45), (Ksh 210, 210). Calculate the value index. (7 marks)
Create a free account to open more of this chapter.
Free: practical guides, quick cards, workplace scenarios and more.
Create a free accountThis chapter introduced the fundamental formulae used to compute index numbers, which are essential tools in measuring changes in economic and business variables over time. It detailed the computation methods for four key types of index numbers: Laspeyre's, Paasche's, Fisher's ideal, and Marshal reports, explaining how each method incorporates different weights and base periods. The chapter emphasized the calculation procedures for Laspeyre's and Paasche's indices, highlighting their respective use of base and current period quantities. Fisher's ideal index was presented as a geometric mean of Laspeyre's and Paasche's indices, providing a balanced measure. Marshal reports were discussed to show practical summarization of price and quantity changes. Finally, the chapter explored the application of these index numbers in decision making, demonstrating how they assist managers and policymakers in analyzing trends, adjusting budgets, and formulating economic strategies. This comprehensive coverage equips students with both the theoretical and practical skills to effectively use index numbers in various professional contexts.
In January 2023, the price of a procurement item was Ksh 250. In January 2024, the price rose to Ksh 275. Calculate the price index number using January 2023 as the base year. (2 marks)
A procurement manager records quantities and prices of three items in two years as follows:
| Item | Quantity (Base Year) | Price (Base Year Ksh) | Price (Current Year Ksh) |
|---|---|---|---|
| A | 100 | 50 | 55 |
| B | 200 | 20 | 22 |
| C | 150 | 30 | 33 |
Calculate the Laspeyre’s price index number for the current year using the base year quantities. (3 marks)
At the start of this chapter we promised you would be able to:
Tick each one you can genuinely do.
So, are you there yet?
You're competent when you can confidently do 50% or more of what this chapter promised.
Sign in to record how you're doing.