Chapter 7: Index Numbers

Q11Written answer

What is the difference between a price index and a quantity index?

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ANSWER A price index measures and permits comparison of the change in the prices of a specified set of goods between two periods (e.g. CPI, WPI). A quantity (volume) index measures the change in the physical volume of goods — production, construction or employment — rather than their prices (e.g. the Index of Industrial Production). In short, a price index reflects price change while a quantity index reflects change in physical output.

Q12Written answer

Is the change in any price reflected in a price index number?

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ANSWER No. A price index is based only on a selected, representative basket of items. A price change is reflected in the index only if that commodity is included in the basket. If an item is not in the basket, a change in its price does not affect the index. Moreover, the impact of an included item depends on its weight, so a price change in a low-weight item has only a small effect.

Q13Written answer

Can the CPI for urban non-manual employees represent the changes in the cost of living of the President of India?

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ANSWER No. The CPI for urban non-manual employees is built from the consumption basket and spending pattern of ordinary urban non-manual workers. The President of India has an entirely different lifestyle and basket of goods and services, so this index cannot represent the change in the President’s cost of living. An index represents only the group for whose typical basket it is constructed.

Q14Written answer

The monthly per capita expenditure incurred by workers for an industrial centre during 1980 and 2005 on the following items are given below. The weights of these items are 75, 10, 5, 6 and 4 respectively. Prepare a weighted index number for cost of living for 2005 with 1980 as the base.

Items	Price in 1980	Price in 2005
Food	100	200
Clothing	20	25
Fuel & lighting	15	20
House rent	30	40
Misc	35	65

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ANSWER Use the weighted index of price relatives: CPI = ΣWR / ΣW, where R = (P₁/P₀) × 100.

Item	Weight W	P₀ (1980)	P₁ (2005)	R = (P₁/P₀)×100	WR
Food	75	100	200	200.00	15000.00
Clothing	10	20	25	125.00	1250.00
Fuel & lighting	5	15	20	133.33	666.67
House rent	6	30	40	133.33	800.00
Misc	4	35	65	185.71	742.86
Total	100				18459.53

CPI = ΣWR / ΣW = 18459.53 / 100 = 184.6 (approx.). Interpretation: the cost of living in 2005 is about 184.6, i.e. it has risen by roughly 84.6 per cent compared with 1980.

Q15Written answer

Read the following table carefully and give your comments.

INDEX OF INDUSTRIAL PRODUCTION BASE 1993–94

Industry	Weight in %	1996–97	2003–2004
General index	100	130.8	189.0
Mining and quarrying	10.73	118.2	146.9
Manufacturing	79.58	133.6	196.6
Electricity	10.69	122.0	172.6

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ANSWER With 1993–94 as base (= 100), industrial production rose in every sub-sector and overall in both years, with much higher levels in 2003–04 than in 1996–97. General index: rose from 130.8 (a 30.8% rise over the base) in 1996–97 to 189.0 (an 89% rise) in 2003–04, showing strong growth in industrial output over the decade. Manufacturing carries by far the largest weight (79.58%) and grew the most — from 133.6 to 196.6 — so it is the main driver of the rise in the general index. Electricity (weight 10.69%) grew from 122.0 to 172.6, and mining and quarrying (weight 10.73%) grew the least, from 118.2 to 146.9. Comment: overall industrial production improved substantially between 1996–97 and 2003–04; manufacturing, having the highest weight and highest growth, contributed the most to this rise, while mining lagged behind. This reflects healthy industrial expansion in the economy during the period.

Q16Written answer

Try to list the important items of consumption in your family.

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ANSWER This is an activity, so answers will vary; list the items your own family actually buys regularly. A model list of important items of consumption is: Food: cereals (rice, wheat/flour), pulses (dal), edible oil, milk and milk products, vegetables, fruits, sugar, salt, spices, eggs/fish/meat. Fuel & light: LPG/cooking gas, electricity, petrol/diesel. Clothing & footwear. Housing: house rent or maintenance. Education: school/tuition fees, books, stationery. Health: medicines, doctor’s fees. Transport & communication: bus/auto fare, mobile recharge, internet. Miscellaneous: toiletries, cleaning items, recreation. Food usually takes the largest share of the family budget. (Use your family’s real items.)

Q17Written answer

If the salary of a person in the base year is Rs 4,000 per annum and the current year salary is Rs 6,000, by how much should his salary be raised to maintain the same standard of living if the CPI is 400?

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ANSWER Step 1 – salary needed to keep the base-year standard of living: multiply the base salary by CPI/100. Required salary = Rs 4,000 × (400 / 100) = Rs 4,000 × 4 = Rs 16,000. Step 2 – compare with the current salary: the person already earns Rs 6,000, so the additional rise needed = 16,000 − 6,000 = Rs 10,000. Conclusion: to maintain the same standard of living the salary should be raised by Rs 10,000 (i.e. to Rs 16,000 per annum).

Q18Written answer

The consumer price index for June, 2005 was 125. The food index was 120 and that of other items 135. What is the percentage of the total weight given to food?

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ANSWER Let the weight (proportion) of food = w, so the weight of other items = (1 − w). The overall CPI is the weighted average of the two indices: 125 = 120w + 135(1 − w) 125 = 120w + 135 − 135w ⇒ 125 − 135 = −15w ⇒ −10 = −15w w = 10 / 15 = 0.6667 Percentage weight given to food = 66.67% (about two-thirds); the weight of other items is 33.33%.

Q19Written answer

An enquiry into the budgets of the middle class families in a certain city gave the following information; What is the cost of living index during the year 2004 as compared with 1995?

Expenses on items	Food	Fuel	Clothing	Rent	Misc.
	35%	10%	20%	15%	20%
Price (in Rs) in 2004	1500	250	750	300	400
Price (in Rs) in 1995	1400	200	500	200	250

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ANSWER Take 1995 as base. Cost-of-living index = ΣWR / ΣW, where R = (P₂₀₀₄/P₁₉₉₅) × 100 and W is the % weight.

Item	Weight W (%)	P (1995)	P (2004)	R = (P₂₀₀₄/P₁₉₉₅)×100	WR
Food	35	1400	1500	107.14	3750.00
Fuel	10	200	250	125.00	1250.00
Clothing	20	500	750	150.00	3000.00
Rent	15	200	300	150.00	2250.00
Misc.	20	250	400	160.00	3200.00
Total	100				13450.00

Cost-of-living index (2004) = ΣWR / ΣW = 13450 / 100 = 134.5. Interpretation: the cost of living of middle-class families in this city rose by about 34.5 per cent in 2004 compared with 1995.

Q20Written answer

Record the daily expenditure, quantities bought and prices paid per unit of the daily purchases of your family for two weeks. How has the price change affected your family?

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ANSWER This is a project, so use your family’s real data. Method: each day, note every item bought, its quantity and the price per unit, and the amount spent. Tabulate the data day-wise, then for the two-week period compute, for each item, the price relative R = (current price / first-day price) × 100 and a weighted daily price index using expenditure shares as weights. How to comment on the effect: if the price index for the second week is higher than the first, prices have risen and your family had to spend more for the same quantities (or buy less); if it is lower, prices fell and the family saved or could buy more. Note which items (e.g. vegetables, fuel) changed most and how the family adjusted — substituting cheaper items, reducing quantity, or spending extra. (Answer using your own recorded figures.)

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