The consumer price index, or CPI, measures the cost of living for a typical urban household by multiplying the price for each category of expenditure (housing, food, and so on) times a measure of the importance of that expenditure in the average consumer’s market basket and summing over all categories. However, using data from the consumer price index, we can see that changes in the cost of living for different types of consumers can vary a great deal. Let’s compare the cost of living for a hypothetical retired person and a hypothetical college student. Let’s assume that the market basket of a retired person is allocated in the following way: 10% on housing, 15% on food, 5% on transportation, 60% on medical care, 0% on education, and 10% on recreation. The college student’s market basket is allocated as follows: 5%

on housing, 15% on food, 20% on transportation, 0% on medical care, 40% on education, and 20% on recreation.

The accompanying table shows the September 2012 CPI for each of the relevant categories.

CPI September 2012 Housing 223.9 Food 234.2 Transportation 221.7 Medical care 418.0 Education 134.6 Recreation 115.0 Calculate the overall CPI for the retired person and for the college student by multiplying the CPI for each of the categories by the relative importance of that category to the individual and then summing each of the categories.

The CPI for all items in September 2012 was 231.4. How do your calculations for a CPI for the retired person and the college student compare to the overall CPI?