Question

Suppose you work at the Bureau of Labor Statistics and you are devising a fixed weight price index for inflation measurement. You are given the following array of purchases and prices to create your index.

Quantity 2014 2015 2016

Good A 10 2.00 2.50 2.50

Good B 4 5.00 5.00 4.00

Good C 5 6.00 7.00 9.00

a) Calculate the cost of the basket of goods in 2014, 2015, 2016.

b) Let’s choose 2015 as the base year. If we set the base year index level to 100, what are the index levels for 2014 and 2016?

c) What is the inflation rate in 2015 and 2016?

Answer 1

a) Cost of the basket of goods in 2014 = ($2.00 * 10) + ($5.00 * 4) + ($6.00 * 5) = 20 + 20 + 30 = $70

Cost of the basket of goods in 2015 = ($2.50 * 10) + ($5.00 * 4) + ($7.00 * 5) = 25 + 20 + 35 = $80

Cost of the basket of goods in 2016 = ($2.50 * 10) + ($4.00 * 4) + ($9.00 * 5) = 25 + 16 + 45 = $86

b) Index level for 2014 = (Cost of the basket of goods in 2014 / Cost of the basket of goods in 2015) * 100

                                    = (70 / 80) * 100 = 87.5

Index level for 2016 = (Cost of the basket of goods in 2016 / Cost of the basket of goods in 2015) * 100

                                    = (86 / 80) * 100 = 107.5

c) Inflation rate in 2015 = [(100 - 87.5) / 87.5] * 100 = 14.29%

Inflation rate in 2016 = [(107.5 - 100) / 100] * 100 = 7.5%