Example question calculating CPI and inflation

the CPI or Consumer Price Index is used to measure the cost of a typical basket of goods the typical household in the nation of JAC Sonia buys four loaves of bread three pounds of cream cheese and eight books each week the prices of these goods in years 2015 2016 and 2017 are given in the table below and then they ask us some questions calculate the CPI in 2017 using 2016 as the base year calculate the CPI in 2015 using 2016 as the base year calculate the rate of inflation between 2015 and 2016 calculate the rate of inflation between 2016 and 2017 and then describe a reason why the inflation rate between 2016 and 2017 might overstate the changes in cost of living so pause this video and see if you can work through it before I do it with you all right now let's just do it step by step so this first two letters they want us to calculate the CPI is in 2017 and 2015 using 2016 as a base year so the way I'm going to do it I'm gonna set up a new column here which is cost of the weekly basket because and they tell us how much they buy each week cost of weekly weekly basket let's see in 2015 they buy four loaves of bread at a dollar each so it's going to be four times one plus they buy three pounds of creech cream cheese at $3 a pound plus three times three plus they buy eight books a week these people like to read and so and each book in 2015 is ten dollars so eight times ten eight times ten and this is going to be equal to 4 times 1 is 4 plus 9 is 13 plus 80 is going to be 93 dollars now that same basket that weekly basket in 2016 well we're buying 4 loaves of bread at $2 now 4 times 2 plus we're buying 3 pounds of cream cheese at $6 a pound now plus 3 times 6 plus 8 books per week at $20 per book 8 times 20 this is going to be equal to eight plus 18 which is 26 plus 160 is 186 so this is going to be 186 dollars and now we're going to do the same thing in 2017 each week you can get four loaves of bread now it's $3.00 per loaf plus we're buying three pounds of cream cheese per week three it's still at six dollars per pound plus eight books per week at $25 per book and so this is going to be equal to 12 plus 18 which is 30 plus 200 which is going to be 230 dollars and now we can calculate the CPI s so the CPI it's typical that it's going to be 100 in your base here should be 100 so I could just put that there and for the other years you could say the basket cost cost in a year divided by the cost and base year cost in base year year times 100 so obviously in 2016 that's going to be the cost in 2016 divided by the cost in 2016 times 100 you'll get 100 but for 2015 it will be the cost of the basket in 2015 which is 93 dollars divided by the cost in 2016 which is 186 dollars times 100 this one is actually pretty straightforward 93 is half of 186 so this is going to be equal to 50 and then in 2017 it's going to be the cost of the basket in 2017 divided by the cost of the basket in 2016 times 100 which is going to be equal to when we use a calculator for this one 230 divided by 186 is equal to approximately 1.2 4 if we multiply that times 100 we'll say it's approximately it is approximately 124 so calculate the CPI in 2017 using 2016 as the base year it would be 124 calculate the CPI in 2015 using 2006 seen as a base year and that is 50 calculate the rate of inflation between 2015 and 2016 so how much do prices grow if we take this basket of goods from 2015 to 2016 well you could look at your CPI went from 50 to a hundred so price is doubled and so something's W grew by a hundred percent and the rate of inflation is the growth in prices and so this is 100 percent inflation things doubled in price and you could see it here everything doubled in price right over here calculate the rate of inflation between 2016 and 2017 well if you started a hundred and you grow to a hundred and twenty four you have just grown by twenty four percent one way to think about as you multiply by 1 point 2 4 which is the same thing as growing by 24 percent so that 24 percent growth is the rate of inflation describe a reason why the inflation rate between 2016 and 2017 so that's what we answered right here in Part D might overstate changes in the cost-of-living and if you haven't answered that part yet I encourage you given all that we've done try to pause the video and try to think about that so let's look at what happened from 2016 to 2017 the price of a loaf of bread increases by 50 percent the price of a book increases by $5 on a base of 20 that's an increase of 25% but the price of cream cheese does not change plus 0% it experiences no inflation from 2016 to 2017 and so you could imagine a scenario where if some Goods their prices increase a lot while others don't the basket of goods might change people might buy less bread and less and fewer books and more cream cheese and so we could say the typical basket might get more weighted to goods that had less inflation had less inflation example in this case would be cream cheese cream cheese because they look relatively relatively cheaper to the goods that had more inflation and if that happened you would have a lower actual growth actual growth in cost of living and this last question really alludes to the fact that the CPI isn't necessarily a perfect indicator that as different goods in the basket it have a price inflation at different rates you can have a substitution effect between the various Goods now in countries they try to rebalance the basket of goods based on a perception of what is typical but once again that is not necessarily going to be perfect