The consumer price index is a useful index of inflation, and may be used to adjust the limits of each tax bracket for the upcoming year. Nevertheless the CPI has its critics. A lot of things are used in the determination of the value of the index at a given time – take a look at the latest (May 2016) values for a few of the categories listed under the Consumer Price Index Summary http://www.bls.gov/news.release/cpi.t01.htm – and you’ll see it is easy to argue against the balance of the categories used. Note that 100 is the base CPI value from December 1982. The May 2016 CPI is that listed under unadjusted ‘All Items’; values higher than this number have increased more than average since December 1982; those less than this have increased less than average.Consider the effects of inflation on retirees. (We painted a pessimistic picture in Section 4B – one example showed that $40,000 per year in 40 years time equates to just $12,262 in today’s dollars.) It should be clear that some categories used in the CPI calculation are less of an issue for retired folks:a) List 3 categories whose index is lower (better) than the overall CPI and 3 categories that are higher (worse) than the overall CPI. Be sure to state the overall CPI and the values of the categories you choose.b) Writing in Mathematics. Write a short paragraph to discuss whether the retirement gloom shown in 4B was pessimistic or a reality. Are any of the individual categories that are ‘much worse’ than the overall likely to be a major expense for retirees?