Index Number Long Questions (Question 2)


Question 2:
Diagram below is a bar chart indicating the weekly cost of the items A, B, C, D and E  for the year 2000. Table below shows the prices and the price indices for the items.


Items

Price in 2000

Price in 2006
Price Index in 2006 based on 2000
A
x
RM 1.75
140
B
RM 2.00
RM 2.50
125
C
RM 4.00
RM4.80
y
D
RM 6.00
z
125
E
RM 2.50
2.75
110

(a) Find the value of
    (i) x
    (ii) y
    (iii) z                                                                                                   

(b) Calculate the composite index for items in the year 2006 based on the year 2000.
                                                                                                                            
(c) The total monthly cost of the items in the year 2000 is RM456. Calculate the
      corresponding total monthly cost for the year 2006.
                                                                                                                            
(d) The cost of the items increases by 15 % from the year 2006 to the year 2009.
      Find the composite index for the year 2009 based on the year 2000.

Solution:
(a)(i)
I= P 1 P 0 ×100 I= P 2006 P 2000 ×100 140= 1.75 x ×100 x=RM1.25
(a)(ii)
I= P 2006 P 2000 ×100 y= 4.80 4.00 ×100 y=120
(a)(iii)
I= P 2006 P 2000 ×100 125= z 6.00 ×100 z=RM7.50
(b)
Items
Price Index in 2006 based on 2000
Weightage
(from the diagram above)
A
140
15
B
125
30
C
120
24
D
125
33
E
110
12

Composite index for items in the year 2006 based on the year 2000,  I ¯ I ¯ = IW W I ¯ = ( 140 )( 15 )+( 125 )( 30 )+( 120 )( 24 )+( 125 )( 33 )+( 110 )( 12 ) 15+30+24+33+12 I ¯ = 14175 114 I ¯ =124.34
(c)
I= P 1 P 0 ×100 Lets total monthly cost for the year 2006 is  P 2006 I= P 2006 P 2000 ×100 124.34= P 2006 RM456 ×100 P 2006 =RM567
(d)
Lets composite index for the year 2009 based on year 2000 is  I ¯ 2009 I ¯ 2009 =124.34× 115 100 I ¯ 2009 =143