Question

Calculate (a) Laspeyre’s and (b) Paasche's Price Index Numbers for the following data:

Commodity	Base year		Current year
	Price	Quantity	Price	Quantity
P	12	20	18	24
Q	14	12	21	16
R	8	10	12	18
S	16	15	20	25

Answer 1

Compute the required products:

Commodity	Base year		Current year		p0q0	p1q0	p0q1	p1q1
	Price (p0)	Quantity (q0)	Price (p1)	Quantity (q1)
P	12	20	18	24	12 × 20 = 240	18 × 20 = 360	12 × 24 = 288	18 × 24 = 432
Q	14	12	21	16	14 × 12 = 168	21 × 12 = 252	14 × 16 = 224	21 × 16 = 336
R	8	10	12	18	8 × 10 = 80	12 × 10 = 120	8 × 18 = 144	12 × 18 = 216
S	16	15	20	25	16 × 15 = 240	20 × 15 = 300	16 × 25 = 400	20 × 25 = 500
`bb∑`					728	1032	1056	1484

(a) Laspeyres’s Price Index Number:

L = `(∑p_1 q_0)/(∑p_0 q_0) × 100`

L = `1032/728 xx 100`

= 141.76

Laspeyres’s Price Index = 141.76

(b) Compute the required products:

Paasche’s Price Index Number:

P = `(∑p_1 q_1)/(∑p_0 q_1) × 100`

`P = 1484/1056 xx 100 = 140.53`

Paasche’s Price Index = 140.53