Question

A large manufacturer buys an identical component from three different independent suppliers, each with a different unit price and quantity supplied. The pertinent data for 2012 and 2014 are provided here.

Unit Price ($) Unit Price ($)
Supplier Quantity (2012) 2012 2014
A 150 5.45 6.00
B 200 5.60 5.95
C 120 5.50 6.20

a. Separately compute the price relations for each component supplier. Compare the price increases by suppliers over the last two years. b. In 2014, compute an unweighted aggregate price index for the component part. c. Create a weighted aggregate price index for the component part in 2014. What is the manufacturing firm's interpretation of this index?

Solution

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Answered 1 year ago
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a. Let Pi0P_{i0} and PitP_{it} be the prices of item i=A,B,Ci=A,B,C in the earlier year and in the later year, respectively. The relative prices of items with earlier year as the base period, are:

ri=PitPi0100r_i=\dfrac{P_{it}}{P_{i0}}\cdot 100

As indicated by formula, it is the later year price in percentages of the earlier base year price. Substituting the knowns find:

rA=65.45=110,rB=106, rC=113r_A=\dfrac{6}{5.45}=110,\quad r_B=106,\ r_C=113

The third firm raised its price the most, but all increases are about the same.

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