Paasche’s Index Number

Management > Managerial Statistics > Index Number By Paasche’s Method

Price Index Number by Paasche’s Method:

Paasche’s method is based on fixed weights of the current year. For price index current year’s quantities are used as weights.

Steps involved:

1. Denote prices of the commodity in the current year as P1 and its quantity consumed in that year by Q1.
2. Denote prices of the commodity in the base year as P₀.
3. Find the quantities P₀Q₁ and P₁Q₁ for each commodity.
4. Find the sum of each column of P₀Q₁ and P₁Q₁ and denote the sums by ∑ P₀Q₁ and ∑ P₁Q₁ respectively.
5. Use the following formula to find the Price index number

PP₀₁ = (∑ P₁ x Q₁) / ( ∑ P₀ x Q₁ ) × 100

Example – 01:

Compute Price index by Paasche’s Method from the following data .

Commodity	Base Year		Current Year
	Price	Quantity	Price	Quantity
A	3	25	5	28
B	1	50	3	60
C	2	30	1	30
D	5	15	6	12

Solution:

Commodity	Base Year		Current Year
	Price (P0)	Quantity (Q0)	Price (P1)	Quantity(Q1)	P0Q1	P1Q1
A	3	25	5	28	84	140
B	1	50	3	60	60	180
C	2	30	1	30	60	30
D	5	15	6	12	60	72
Total					∑P0Q1=264	∑P1Q1=422

PP₀₁ = (∑ P₁ x Q₁) / (∑ P₀ x Q₁) × 100

PP₀₁ = (422 / 264) × 100

PP₀₁ = 159.85

Thus Paasche’s price index number is 159.85

Quantity Index by Paasche’s Method

Paasche’s method is based on fixed weights of the current year. For quantity index, current year’s prices are used as weights.

Steps involved:

1. Denote prices of the commodity in the current year as P1 and its quantity consumed in that year by Q1.
2. Denote prices of the commodity in the base year as P0 and its quantity consumed in that year by Q0.
3. Find the quantities Q₀P₁ and Q₁P₁ for each commodity.
4. Find the sum of each column of Q₀P₁ and Q₁P₁ and denote the sums by ∑ Q₀P₁ and ∑ Q₁P₁ respectively.
5. Use the following formula to find the Quantity index number

PQ₀₁ = (∑ Q₁ x P₁) / ( ∑ Q₀ x P₁) × 100

Example – 02:

Compute Quantity index by Laspeyre’s Method from the following data by Laspeyre’s method .

Commodity	Base Year		Current Year
	Price	Quantity	Price	Quantity
A	3	25	5	28
B	1	50	3	60
C	2	30	1	30
D	5	15	6	12

Solution:

Commodity	Base Year		Current Year
	Price (P0)	Quantity (Q0)	Price (P1)	Quantity(Q1)	Q0P1	Q1P1
A	3	25	5	28	125	140
B	1	50	3	60	150	180
C	2	30	1	30	30	30
D	5	15	6	12	90	72
Total					∑Q0P1=395	∑Q1P1=422

PQ₀₁ = (∑ Q₁ x P₁) / ( ∑ Q₀ x P₁) × 100

PQ₀₁ = (422 / 395) × 100

PQ₀₁ = 106.84

Thus Paasche’s quantity index number is 106.84

Example – 03:

Compute Price index and Quantity index by Paasche’s Method from the following data.

Commodity	Base Year 1997		Current Year 2005
	Price	Quantity	Price	Quantity
A	16	110	25	132
B	5	220	5	264
C	10	132	15	165
D	25	66	30	55

Solution:

Commodity	Base Year		Current Year
	(P0)	(Q0)	(P1)	(Q1)	Q1P1	Q0P1	Q1P0
A	16	110	25	132	3300	2750	2112
B	5	220	5	264	1320	1100	1320
C	10	132	15	165	2475	1980	1650
D	25	66	30	55	1650	1980	1375
Total					8745	7810	6457

Price Index:

PP₀₁ = (∑ P₁ x Q₁) / (∑ P₀ x Q₁) × 100

PP₀₁ = (8745 / 6457) × 100

PP₀₁ = 135.43

Thus Paasche’s price index number is 135.43

Quantity Index:

PQ₀₁ = (∑ Q₁ x P₁) / ( ∑ Q₀ x P₁) × 100

PQ₀₁ = (8745 / 7810) × 100

PQ₀₁ = 111.97

Thus Paasche’s quantity index number is 111.97

Merits of Paasche’s Method :

• Uses current quantities (weights) and so takes changes in consumption patterns into account.  
• Does not overstate price increases.

Demerits of Paasche’s Method :

• Not a pure index as price and quantities change.
• Long and expensive to update weights.
• The indexes for each year cannot be compared directly since the quantities change
• Paasche index tends to underestimate the rise in prices or has a downward bias.
• Paasche index is not frequently used in practice when the number of commodities is large. This is because, for Paasche index, revised weights or quantities must be computed for each year examined. Such information is either unavailable or hard to gather. It makes the data gathering expensive.

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Management > Managerial Statistics > Index Number By Paasche’s Method