Q.6 (B) (i) Given that \(\Sigma p_0q_0=120,\ \Sigma p_0q_1=160,\ \Sigma p_1q_1=140\) and \(\Sigma p_1q_0=200\). Find Laspeyre's, Paasche's, Dorbish-Bowley's and Marshall-Edgeworth's Price Index Numbers.
Best answer
Answer: \(L=166.67,\ P=87.5,\ D\text{-}B=127.08,\ M\text{-}E=121.43\)
Laspeyre's: \(P_{01}(L)=\frac{\Sigma p_1q_0}{\Sigma p_0q_0}\times 100=\frac{200}{120}\times 100=166.67\).
Paasche's: \(P_{01}(P)=\frac{\Sigma p_1q_1}{\Sigma p_0q_1}\times 100=\frac{140}{160}\times 100=87.5\).
Dorbish-Bowley's: \(P_{01}(D\text{-}B)=\frac{P_{01}(L)+P_{01}(P)}{2}=\frac{166.67+87.5}{2}=127.08\).
Marshall-Edgeworth's: \(P_{01}(M\text{-}E)=\frac{\Sigma p_1q_0+\Sigma p_1q_1}{\Sigma p_0q_0+\Sigma p_0q_1}\times 100=\frac{200+140}{120+160}\times 100=\frac{340}{280}\times 100=121.43\).
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