Question

Given the following data and taking 2004 as the base year, construct index of prices using:

(i) Laspeyre's Method, (ii) Paasche's Method, and (iii) Fisher's Method.

Year	Commodities
	A		B		C		D
	Price	Quantity	Price	Quantity	Price	Quantity	Price	Quantity
2004 2018	24 30	8 10	9 10	3 4	16 20	5 8	10 9	3 4

Answer 1

	P0	q0	P0q0	P1	q1	P1q1	P1q0	P0q1
A B C D	24 9 16 10	8 3 5 3	192 27 80 30	30 10 20 9	10 4 8 4	300 40 160 36	240 30 100 27	240 36 128 40
			∑P0q0 = 329			∑P1q1 = 536	∑P1q0 =397	∑P0q1​ = 444

Laspeyre's Price index
$$\begin{gathered} P_{01}=\frac{\Sigma P_1{q}_0}{\Sigma P_0{q}_0}\times 100 \\ or,P_{01}=\frac{397}{329}\times 100=120.66 \end{gathered}$$

Paasche's Price index
$$\begin{gathered} P_{01}=\frac{\Sigma P_1{q}_1}{\Sigma P_0{q}_1}\times 100 \\ or,P_{01}=\frac{536}{444}\times 100=120.72 \end{gathered}$$

Fisher's Price index
$$\begin{gathered} P_{01}=\sqrt{\frac{\Sigma P_1{q}_0}{\Sigma P_0{q}_0}\times \frac{\Sigma P_1{q}_1}{\Sigma P_0{q}_0}}\times 100 \\ or,P_{01}=\sqrt{\frac{397}{329}\times \frac{536}{329}}\times 100=120.65 \end{gathered}$$