Definitions [3]
The base period of an index number is the period against which comparisons are made.
Cost of Living Index Number, also known as Consumer Price Index Number, is an index number of the cost of buying goods and services in day-to-day life for a specific consumer class.
- An Index Number is a statistical measure of changes in a variable or a group of variables with respect to time, geographical location, or some other characteristic, such as production, income, etc.
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An Index Number is used for measuring changes in a quantity that can not be measured directly.
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An Index Number is a single ratio, usually expressed as a percentage, that measures aggregate (or average) change in several variables between two different times, places, or situations.
Formulae [7]
\[P_{01}=\frac{\sum p_1w}{\sum p_0w}\times100\]
Laspeyre’s Price Index Number:
\[P_{01}(L)=\frac{\sum p_1q_0}{\sum p_0q_0}\times100\]
Paasche’s Price Index Number:
\[P_{01}(P)=\frac{\sum p_1q_1}{\sum p_0q_1}\times100\]
Dorbish-Bowley’s Price Index Number:
\[P_{01}(D-B)=\frac{P_{01}(L)+P_{01}(P)}{2}\]
Fisher’s Ideal Price Index Number:
\[P_{01}(F)=\sqrt{P_{01}(L)\times P_{01}(P)}\]
Marshall-Edgeworth’s Price Index Number:
\[P_{01}(M-E)=\frac{\sum p_1(q_0+q_1)}{\sum p_0(q_0+q_1)}\times100\]
Walsh’s Price Index Number:
\[P_{01}(W)=\frac{\sum p_1\sqrt{q_0q_1}}{\sum p_0\sqrt{q_0q_1}}\times100\]
\[CLI=\frac{\sum p_1q_0}{\sum p_0q_0}\times100\]
Same as Laspeyre’s Price Index
Price Index:
\[P_{01}=\frac{\sum p_1}{\sum p_0}\times100\]
Quantity Index:
\[Q_{01}=\frac{\sum q_1}{\sum q_0}\times100\]
Value Index:
\[V_{01}=\frac{\sum p_1q_1}{\sum p_0q_0}\times100\]
\[CLI=\frac{\sum IW}{\sum W}\]
Where,
\[I=\frac{p_1}{p_0}\times100\]
W = p0q0
\[\text{Purchasing Power}=\frac{1}{CLI}\]
\[\mathrm{Real~Wages}=\frac{\text{Money Wages}}{CLI}\times100\]
Key Points
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Price Index Number – Measures change in prices (Inflation indicator)
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Quantity Index Number – Measures change in output/quantity
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Value Index Number – Measures change in total value (Price × Quantity)
| Symbol | Meaning |
|---|---|
| p0 | Price in base year |
| p1 | Price in current year |
| q0 | Quantity in base year |
| q1 | Quantity in current year |
| w | Weight |
| I | Price Relative |
| Base Year | Year taken as 100 |
| Current Year | Year under comparison |
Important Questions [16]
- If ∑p0q0 = 140, ∑p0q1 = 200, ∑p1q0 = 350, ∑p1q1 = 460, find Laspeyre’s, Paasche’s, Dorbish-Bowley’s and Marshall-Edgeworth’s Price Index Numbers.
- Given that ∑p0q0 = 220, ∑p0q1 = 380, ∑p1q1 = 350 and Marshall-Edgeworth’s Price Index Number is 150, find Laspeyre’s Price Index Number.
- State whether the following statement is true or false: Dorbish-Bowley's Price Index Number is the square root of the product of Laspeyre's and Paasche's Index Numbers.
- If P01 (L) = 121, P01 (P) = 100, then P01 (F) = ______.
- Laspeyre’s Price Index Number uses current year’s quantities as weights.
- Calculate Marshall – Edgeworth’s price index number for the following data: Commodity Base year Current year Price Quantity Price Quantity P 12 20 18 24 Q 14 12 21 16 R 8 10 12 18 S 16 15 20 25
- Choose the correct alternative : The price Index Number by Weighted Aggregate Method is given by ______.
- Paasche’s Price Index Number is given by ______.
- Dorbish-Bowley’s Price Index Number is given by ______.
- Walsh’s Price Index Number is given by _______.
- ∑p0(q0+q1)∑p1(q0+q1)×100 is Marshall-Edgeworth’s price index number.
- Solve the following problem: If find x is Walsh’s Price Index Number is 150 for the following data
- The cost of living index number using Weighted Relative Method is given by ______.
- Calculate the cost of living index number for the following data by aggregative expenditure method: Group Base year Current year Price Quantity Price Food 120 15 170 Clothing 150
- Find x if the cost of living index is 150. Group Food Clothing Fuel and Lighting House Rent Miscellaneous I 180 120 300 100 160 W 4 5 6 x 3
- Base year weights (W) and current year price relatives (I) are given in Problem. Calculate the cost of living index in: Find y if the cost of living index is 200.
