3A large manufacturer purchases an identical component from

3.A large manufacturer purchases an identical component from three independent suppliers that differ in unit price and quantity supplied. The relevant data for 2009 and 2011 are given

2009           2011

A          150              5.45            6.00

B          200              5.60            5.95

C          120              5.50            6.20

Compute the price relatives for each of the component suppliers separately. Compare the price increases by the suppliers over the two-year period. Compute an unweighted aggregate price index for the component part in 2011. Compute a 2011 weighted aggregate price index for the component part. What is the interpretation of this index for the manufacturing firm?

Solution

1) Price relative for a jth supplier is a ratio of its price in current year to its base year price. Considering 2009 as base year

Pa = 6/ 5.45 = 1.1001

Pb = 5.95/ 5.6 = 1.0625

Pc = 6.2/ 5.5 = 1.127

2) On the basis of price relatives unweighted the price of a commodity is maximum increased by C then A and then
B

3) Unwieghted component price index in 2011 = [sum of (2011) / sum of (2009) ] *100

= 18.15/ 16.55 *100 = 109.668

4) Weighted Component price index = [sum of (weight * price of commodity in 2011) / sum of (weight * price of commodity in 2009) ] *100

= 2834/ 2695.5 *100 = 105.06

Index value for weighted is less then unweighted as there is a maximum price increase by C but it supplies minimum quantity so its weightage is less in weighted scenario.