(B) The following tabte shows the prices of three types of raw materials used by
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Question
(B) The following tabte shows the prices of three types of raw materials used by manufacturing plants and the quantities used in the two years 2004 and 2005: (15 marks) Year 2004 2005 Quantity Quantity used (000s) 30 80 Price Price used (000s) 40 80 Group Coal (tonnes) oil (barrels) Iron ore tonnes) 20 30 75 80 40 96 36 98 Construct a simple aggregate index of raw material prices for 2005, using 2004 as the base year. (A) (4 marks) (B) Construct a Laspeyres index of raw material prices for 2005, using 2004 as the base year. 4 marks) Construct a Paasche index of raw material prices for 2005, using 2004 as the base year. (C) 4 marks) (D) Explain why the three index numbers you have calculated all give different results. 3 marksExplanation / Answer
Simple aggregate index : pn / p0
Where pn is the price in the current year
And p0 is the price in the base year
Simple aggregate index = 146/135 = 1.08148
Laspeyres index: pn * q0 / po * q0
Where q0 is the quantity in the base price
2004
2005
price
quantity
price
quantity
pn * q0
po * q0
20
40
30
30
1200
800
75
80
80
80
6400
6000
40
96
36
98
3456
3840
Laspeyres index = 11056/10640 = 1.03909
Paasche index: pn * qn / po * qn
Where qn is the quantity in the current year
2004
2005
price
quantity
price
quantity
pn * qn
po * qn
20
40
30
30
900
600
75
80
80
80
6400
6000
40
96
36
98
3528
3920
Paasche index = 1.029277
The indices:
Simple aggregate index = 108.148%
Laspeyres index= 103.909%
Paasche index = 102.9277%
All the three methods are equally useful. Simple aggregate is easy to calculate and it involves only the price of the commodity. It is most useful when only the prices are known. The main difference between Laspeyres’ index and Paasche’s index is that, Laspeyres’ uses base year quantities of commodities as their relative weights, while Paasche’s uses current year quantities of commodities as their relative weights for preparing a price index.
2004
2005
price
quantity
price
quantity
pn * q0
po * q0
20
40
30
30
1200
800
75
80
80
80
6400
6000
40
96
36
98
3456
3840
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