# Index Number related question...

#### ystiang

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
Hey ystiang.

What is the definition for the Laspeyres quantity index?

#### ystiang

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
You have two p_0 terms: is one of them meant to be different or should they be cancelled out?

#### ystiang

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
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.

#### ystiang

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
Isn't q_0 * p_0 just the sales volume for base-line?