Question

Construct price index number of the following data by using:
(i) Laspeyre's Method, (ii) Paasche's Method, and (iii) Fisher's Method.

Items	Base Year		Current Year
	Quantity	Price	Quantity	Price
A B C D	3 7 4 6	5 4 7 6	2 5 3 5	8 6 10 7

Answer 1

	q0	p0	p0q0	p1	q1	p1q1	p1q0	p0q1
A B C D	3 7 4 6	5 4 7 6	15 28 28 36	8 6 10 7	2 5 3 5	16 30 30 35	24 42 40 42	10 20 21 30
			$\Sigma p_0{q}_0=107$			$\Sigma p_1{q}_1=111$	$\Sigma p_1{q}_0=148$	$\Sigma p_0{q}_1=81$

(i) Laspeyre's Price index:
$$\begin{gathered} P_{01}=\frac{\Sigma P_1{q}_0}{\Sigma P_0{q}_0}\times 100 \\ or,P_{01}=\frac{148}{107}\times 100=138.31 \end{gathered}$$

(ii) Paasche's Price index:
$$\begin{gathered} P_{01}=\frac{\Sigma P_1{q}_1}{\Sigma P_0{q}_1} \\ or,P_{01}=\frac{111}{81}\times 100=137.04 \end{gathered}$$

(iii) Fisher's Price index:
$$\begin{gathered} P_{01}=\sqrt{\frac{\Sigma P_1{q}_0}{\Sigma P_0{q}_0}\times \frac{\Sigma P_1{q}_1}{\Sigma P_0{q}_1}}\times 100 \\ or,P_{01}=\sqrt{\frac{148}{107}\times \frac{111}{81}}\times 100=137.67 \end{gathered}$$