Question

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Answer 1

ANSWER :

• (i) Price Index of the given data by using Laspeyre's Method is 89.15
• (ii) Price Index of the given data by using Paasche's Method is 92.62

• (iii) Price Index of the given by using Fisher's Method is 90.87

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SOLUTION :

❒ To Calculate :-

• (i) Price Index by using Laspeyre's Method

• (ii) Price Index by using Paasche's Method

• (iii) Price Index by using Fisher's Method

❒ Required Formulas :-

• ✎ Laspeyre's Method for calculating Price Index :

$\dag \: \: \underline{ \boxed{\sf{p_{01} = \dfrac{ \sum \: p_1q_0}{ \sum \: p_0q_0} \times 100}}}$

• ✎ Paasche's Method calculating Price Index :

$\dag \: \: \underline{\boxed{\sf{p_{01} = \dfrac{ \sum \: p_1q_1}{ \sum \: p_0q_1} \times 100}}}$

• ✎ Fisher's Method calculating Price Index :

$\dag \: \: \underline{ \boxed{ \sf{p_{01} = \sqrt{\dfrac{ \sum \: p_1q_0}{ \sum \: p_0q_0} \times \dfrac{ \sum \: p_1q_1}{ \sum \: p_0q_1}} \times 100}}}$

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❒ Calculation :-

From the data table (in the attachment), we get,

• Σp₀q₀ = 507

• Σp₁q₁ = 578

• Σp₁q₀ = 452

• Σp₀q₁ = 624

(i) Calculation of Price Index by using Laspeyre's Method :-

• $\tt{ \bigstar \: \: p_{01} = \dfrac{ \sum \: p_1q_0}{ \sum \: p_0q_0} \times 100}$

$\tt{\longrightarrow \: p_{01} = \dfrac{452}{507} \times 100}$

$\tt{\therefore \: \underline{p_{01} = 89.15}}$

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(ii) Calculation of Price Index by using Paasche's Method :-

• $\tt{ \bigstar \: \: p_{01} = \dfrac{ \sum \: p_1q_1}{ \sum \: p_0q_1} \times 100}$

$\tt{\longrightarrow \: p_{01} = \dfrac{578}{624} \times 100}$

$\tt{\therefore \: \underline{p_{01} = 92.62}}$

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(iii) Calculation of Price Index by using Fisher's Method :-

• $\tt{ \bigstar \: \: p_{01} = \sqrt{\dfrac{ \sum \: p_1q_0}{ \sum \: p_0q_0} \times \dfrac{ \sum \: p_1q_1}{ \sum \: p_0q_1}} \times 100 }$

$\tt{\longrightarrow \: p_{01} = \sqrt{ \dfrac{452}{507} \times \dfrac{578}{624} } \times 100 }$

$\tt{\therefore \: \underline{p_{01} = 90.87}}$