LK-CKLDL
Lembaran Kerja- Contoh Kerja Langkah Demi Langkah
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1.
Fahami contoh soalan dan langkah penyelesaiannya
2.
Cuba selesaikan soalan lain menggunakan kaedah yang sama.
(CHAPTER 11: INDEX NUMBER)
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LIST OF MATHEMATICAL FORMULAE
Simple relative price index
I
Laspeyres price index
p1
 100
p
I
Average relative price index
I
1  p1 
   100
k  p 


p1
p
k  number of components
 100
I
Where
p  price at base year
p1  price at current year
q  quantity at base year
Weighted average relative price index
p1
w p
I
w

 100
Weighted aggregate price index
I
 wp
 wp
1

 100
 100
q p
q p
 100

1


Paasche price index
Simple aggregate price index
I
q p
q p
q1  quantity at current year
1
1
1

PSPM 2003/2004
(1)
A mobile phone company recorded the following simple relative
price indices for two models A and B from July to December 2003
as shown in the following table.
Month
Model
July
Aug
Sept
Oct
Nov
Dec
A
117
103
95
86
75
125
B
124
115
106
98
92
105
Base month : June
(a) Explain the value of simple relative price index of model A for
September and December.
(b) If the price of model B in June was RM850.00, what was the
price in December?
PSPM 2004/2005
(2)
The table below shows the mean price per unit and the number of
printers sold by MAJU company for the years 2003 and 2004.
Mean Price (RM/unit)
Sales (‘000)
Model
2003
2004
2003
2004
A
395
413
20
35
B
615
597
45
65
C
348
389
40
70
Calculate
(a) the Laspeyres price index.
(b) the Paasche quantity index.
PSPM 2005/2006
(3)
The following table shows the price for three type of food in year
2003 and year 2004.
Price Per Kilogram (RM)
Type of food
2003
2004
Fish
4.00
5.00
Meat
6.00
6.80
Prawn
3.60
3.00
Using 2003 as the base year, calculate and explain the
(a) simple relative price index for year 2004.
(b) simple aggregate price index for year 2004.
PSPM 2006/2007
(4) The table below shows the average price and sales quantity for
three types of fruit at a supermarket in Kuala Lumpur for the years
2004 and 2005.
2004
2005
Types of
Average
Quantity
Average
Quantity
Fruits
Price
(100 kg)
Price
(100 kg)
(RM/kg)
(RM/kg)
Mango
2.50
450
3.20
750
Orange
3.00
300
4.10
360
Apple
2.30
500
3.00
800
Calculate the value of the
(a) simple aggregate price index for the year 2005 and interpret the
value.
(b) Paasche price index for the year 2005.
(c) Laspeyres quantity index for the year 2005.
PSPM 2007/2008
(5) The table below shows the average price (RM per Kg) and price
indices for three items in years 2006 and 2007.
Item
2006
2007
Price Index
A
x
4.55
130
B
5.00
6.00
120
C
7.00
8.40
y
2006 : 100
(a) Find the values of x and y.
(b) Find the average relatives price index and explain the answer
obtained.
(c) Given the quantity (in metrics tonnes) for the three items are 30,
50 and 80 respectively.
i.
Obtained the weighted price index.
ii.
State the name of the above weighted price index.
PSPM 2008/2009
(6) The price and quantity of kitchen utensils used in a restaurant
for the years 2007 and 2008 are shown in the following table.
2007
2008
Kitchen
Price
Quantity
Price
Quantity
Utensils
(RM per
(unit)
(RM per
(unit)
unit)
unit)
A
17.90
20
18.80
28
B
10.00
55
11.90
60
C
12.10
45
13.50
52
D
8.00
38
9.60
45
By using 2007 as the base year, find
(a) the average relative quantity index and explain the answer
obtained.
(b) the Laspeyres price index.
(c) the Paasche quantity index
PSPM 2009/2010
(7) The table below shows the price per unit (RM) and the number
of units sold for each brand of handphones in a shop for the year
2007 and 2008.
2007
Brand
2008
Price per unit
No. of units
Price per
No. of
(RM)
sold
unit
units sold
(RM)
A
700.00
q
680.00
40
B
480.00
60
450.00
30
C
680.00
50
650.00
60
D
600.00
27
580.00
60
By using 2007 as the base year, find q , if given the simple
aggregate quantity index is 113.772.
Hence, calculate and interpret the
(a) Laspeyres quantity index.
(b) Paasche quantity index.
State the difference between the Laspeyres and Paasche index.
PSPM 2010/2011
(8) The selling price and quantity for several grocery items are
given below.
2009
Item
2010
Price
Quantity
Price
Quantity
(RM/kg)
(kg)
(RM/kg)
(kg)
A
0.25
210
0.40
210
B
0.85
180
1.15
210
C
10.00
40
8.00
60
D
0.35
35
0.60
40
2009 : 100
Calculate
(a) the simple aggregate price index. Explain the value obtained.
(b) the Laspeyres quantity index.
(c) the Paasche price index.
PSPM 2011/2012
(9) The following table indicates the price and quantity for three
brands of personal computer sold for the year 2010 and 2011 by
company A.
2010
2011
Brand
Price (RM)
Quantity
Price (RM)
Quantity
X
2500
100
2200
130
Y
2100
145
q
150
Z
1800
185
1600
195
(a) By using 2010 as the base year, find q , if given the simple
aggregate price index is 89.0625.
(b) Hence, calculate
i.
the Laspeyres price index.
ii.
the Paasche price index.
Interpret your answer for the Paasche price index calculated in part
(b)(ii).
PSPM 2012/2013
(10) The below shows the price per unit and quantity sold for three
electrical appliances at shop in year 2010 and 2012.
2010
2012
Electrical
Price
Appliances
(RM)
A
77
50
89
55
B
185
26
184
20
C
88
102
101
130
Quantity
Price
Quantity
(RM)
By using 2010 as the base year, calculate
(a) the simple aggregate quantity index.
(b) the Laspeyres price index and Paasche price index. Explain why
there a difference between the two values obtained.