Question

Using the simple aggregate method, calculate price index number from the following data:
$\begin{array}{*{35}{l}}
   \operatorname{Commodity} & A & B & C & D & E \\
   1993 prices\left( in Rs \right) & 50 & 40 & 10 & 5 & 2 \\
   1995 prices\left( in Rs \right) & 80 & 60 & 20 & 10 & 6 \\
\end{array}$.
(a) 164.49
(b) 154.75
(c) 162.69
(d) 152.75

Answer 1

Hint: We start solving the problem by recalling the definition and formula of the price index number for the prices of commodities. Then We substitute the values in mentioned in the formula price index number = \[\dfrac{\sum\limits_{{}}^{{}}{sum of all \operatorname{commodities} in the year we saw increase in prices}}{\sum\limits_{{}}^{{}}{sum of all \operatorname{commodities} in base year}}\times 100\] and make the necessary calculations to get the required result.

Complete step by step answer:
According to the problem, we need to find the price index number of the given data.
$\begin{array}{*{35}{l}}
   \operatorname{Commodity} & A & B & C & D & E \\
   1993 prices\left( in Rs \right) & 50 & 40 & 10 & 5 & 2 \\
   1995 prices\left( in Rs \right) & 80 & 60 & 20 & 10 & 6 \\
\end{array}$.
Let us recall the definition of the price index number.
We know that the price index number is a measure to show by how much percentage the price changes from the year taken as base to the year we need to verify about. In simple words it is defined as the ratio of the sum of prices of all commodities in the year we see the new prices to the sum of prices of all commodities in the base year.
So, price index number = \[\dfrac{\sum\limits_{{}}^{{}}{sum of all \operatorname{commodities} in the year we saw increase in prices}}{\sum\limits_{{}}^{{}}{sum of all \operatorname{commodities} in base year}}\times 100\].
From the table, we can see that the prices of all commodities increased from the year 1993 to 1995.
Now, we take the base year as 1993 and the price index has to be calculated for the year 1995.
So, we get price index number = \[\dfrac{\sum\limits_{{}}^{{}}{sum of all \operatorname{commodities} in 1995}}{\sum\limits_{{}}^{{}}{sum of all \operatorname{commodities} in 1993}}\times 100\].
$\Rightarrow $ price index number = \[\dfrac{80+60+20+10+6}{50+40+10+5+2}\times 100\].
$\Rightarrow $ price index number = \[\dfrac{176}{107}\times 100\].
$\Rightarrow $ price index number = \[1.6449\times 100\].
$\Rightarrow $ price index number = \[164.49\].
So, we have found the price index number for the given data as 164.49.
∴ The correct option for the given data is (a).

Note:
We should know that the price index number is the percentage of increase or decrease in the prices overall. In Economics this is a good measure for indicating the inflation and deflation of the economy. We should know that the prices may increase or decrease in a certain year, which is not considered while calculating the price index number. We should consider the prices of commodities that were present only at the end of the financial year.