hello, in this video, we're gonna look at
how to calculate the consumer price index and the inflation rate. so we'll
start here with the definition of the consumer price index, which is
technically the CPI-U. it's a measure of the overall cost of goods purchased
by people living in metropolitan urban areas. the CPI is used to calculate
inflation, which is just an increase in the average level of prices in the
economy. let me present the formula for the annual inflation rate. we'll be doing
this at the end of this presentation. the annual the annual inflation rate is
the percentage change in the CPI from its preceding year. using this formula
right here... it would be the CPI, say, in 2017
minus the CPI in 2016 all divided by the CPI in 2016 and all
multiplied by a hundred... would give us the inflation rate for 2017.. all right
let's begin here we have a simple economy. this economy has three
goods that consumers buy: soccer balls shoes and concert tickets. we have data
for three years. in the base year, 2016, we have the price of each item and the
quantity that consumers purchased in 2017. we have the prices and in 2018 we
have the prices for those three items. we do not need quantity data for any other
year but the base year, so I do not need quantity data for 2017 or quantity data
for 2018. so an important point to keep in mind we only need quantity data from
the base year so the first step in calculating the consumer price index is
to calculate the total cost of purchasing the base year fix basket
which I highlighted in red we're going to call that the fixed basket we're
gonna assume that consumers keep buying that same quantity year in and year out
so for 2016 what is the cost of that basket that
fixed basket so in 2016 it's just a price times the quantity and we're gonna
just sum those up and we get five thousand dollars ten times 150 times
forty and a hundred times twenty what is the cost of this fixed basket in 2017
using 2017 prices it's 15 times 152 times 40 and $104 times 20 so the
quantities never change okay the prices will change but the
quantities from the base year the fixed basket will not change and finally in
2018 we're gonna evaluate that fixed basket at 2018 prices eighteen times one
hundred fifty six times forty one hundred and ten times twenty here's the
calculation down here adding that up the cost of that fixed basket in 2018 is a
little over six thousand dollars so just rewriting our findings from the last
screen noting that the base year is 2016 we're gonna construct the CPI index
here's the formula the all-important formula so in general the CPI in year ax
is going to be the cost of that fixed basket near X divided by the base year
cost of the fixed basket so here's our calculation in 2016 in 2016 the cost of
the fixed basket is five thousand what is the base year cost well the base year
cost since the base year is 2016 it is also five thousand so the CPI in the
base year is going to be a hundred and it'll always be a hundred in the base
year the CPI in 2017 is going to be the cost of the fixed basket in 2017 which
is five thousand six hundred and six dollars up here the base year cost
doesn't change it's $5,000 so the CPI in 2017 equals one hundred and thirteen
point two the CPI in 2018 the cost of the fix basket in 2018 6240 that goes in
the numerator dividing once again by the base year cost of the fixed basket which
is five thousand we get a CPI of a hundred and twenty four point eight rewriting those CP is for each year and
now it's time to calculate the inflation rate the annual inflation rate in 2017
and the annual inflation rate in 2018 here again I'll rewrite the inflation
rate formula so we're gonna use that to guide us in calculating the inflation
rate so in 2017 the inflation rate is the CPI in 2017 minus the CPI in the
preceding year in 2016 all divided by the CPI in 2016 this gives us a
inflation rate of thirteen point two percent on average prices rose thirteen
point two percent in 2017 and in 2018 we're gonna take the CPI in 2018 minus
the CPI from 2017 divided by the CPI in 2017 we get an annual inflation rate
here of ten point two five percent in 2018 alright that's it. I hope you found
this video helpful.