Question

Inflation rate (percent per year) Pete is a student who spends 10 percent of his expenditure on books and supplies, 30 percent on tuition, 30 percent on rent, 10 percent on food and drink, 10 percent on transportation, and the rest on clothing. The price index for each item was 100 in 2006. The table shows the price indexes in 2016. Item Price index in 2016 Books and supplies 172.6 Tuition 169.0 Rent 159.0 Food and drink 129.8 Transportation 115.4 Clothing 92.9 Pete's CPI in 2016 is . >>> Answer to 1 decimal place. [Hint: The contribution of each item to the CPI is its price weighted by its share of total expenditure] 2006 2008 2010 2012 Year 2014 2016

Answer 1

Given,

Item	% of expenditure	Price Index in 2016
Books and supplies	10	172.6
Tuition	30	169.0
Rent	30	159.0
Food and Drink	10	129.8
Transportation	10	115.4
Clothing	10	92.9

Pete's CPI is calculated by the sum of the product of Price indices of the items with their respective share of expenditure

Pete's CPI = 10% x 172.6 + 30% x 169.0 + 30% x 159.0 + 10% x 129.8 + 10% x 115.4 + 10% x 92.9 = 0.10 x 172.6 + 0.30 x 169.0 + 0.30 x 159.0 + 0.10 x 129.8 + 0.10 x 115.4 + 0.10 x 92.9 = 17.26 + 50.70 + 47.70 + 12.98 + 11.54 + 9.29 = 149.47

Ans: Pete's CPI in 2016 = 149.47