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(B) The following tabte shows the prices of three types of raw materials used by

ID: 3360188 • Letter: #

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 marks

Explanation / 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