Index Number related question...

Jun 2013
4
0
Malaysia
The sale values (output quantity multiplied by price) for four types of product of a company at current price and 1998 price arc as follows:



(RM million)
Sale value at current price​
Sale value at 1998 price​
Type of product​
1998​
2009​
2010​
2009​
2010​
A​
50​
120​
175​
100​
125​
B​
10​
30​
24​
25​
20​
C​
40​
40​
50​
20​
20​
D​
20​
50​
90​
40​
60​
Total​
120​
240​
339​
185​
225​

Calculate:

(a) the Laspeyres quantity index for the year 2010 by using 1998 as the base year, [2 marks]

(b) the Laspeyres quantity index for the year 2010 by using 2009 as the base year, [3 marks]

(c) the percentage change in the output quantity of the company from 2009 to 2010. [1 marks]

Just in case you want to know, this is one of the question of STPM Maths S 2011.

(a) 225/120 * 100 = 187.5

(b) No clue at all...

(c) Since (c) is related to (b)...
 

chiro

MHF Helper
Sep 2012
6,608
1,263
Australia
Hey ystiang.

What is the definition for the Laspeyres quantity index?
 
Jun 2013
4
0
Malaysia
Hey ystiang.

What is the definition for the Laspeyres quantity index?
Laspeyres quantity index: Lq = (q_n p_0)/(q_0 p_0 )×100

where,
q_n : quantity in current period
q_0 : quantity in base period
p_0 : price in base period

But the question twisted like... ._.
 

chiro

MHF Helper
Sep 2012
6,608
1,263
Australia
You have two p_0 terms: is one of them meant to be different or should they be cancelled out?
 
Jun 2013
4
0
Malaysia
You have two p_0 terms: is one of them meant to be different or should they be cancelled out?
Oops, sorry I forgot the sum... Should be Lq = ∑(q_n p_0)/∑(q_0 p_0 )×100
 

chiro

MHF Helper
Sep 2012
6,608
1,263
Australia
So given your formula, you have the p_x*q_x as 120 30 40 50. Remember that the total sales is the cost_per_item * number of items.
 
Jun 2013
4
0
Malaysia
No, it's sum of, (q_n p_0)/(q_0 p_0 )×100,
you can't simplify p_0...

Usually Index Numbers' question directly give the price and quantity of current and base period...
We just need to remember the formula and apply them, BUT this question twisted seriously...
 

chiro

MHF Helper
Sep 2012
6,608
1,263
Australia
Isn't q_0 * p_0 just the sales volume for base-line?