Question

Assume that the CPI base year is 1990 and also assume that the CPI market basket has .04 houses, .1 cars, and 1,500 gallons of gasoline. Please use 1 decimal place in your answers.

Year

House Price

Car Price

Nominal Gasoline Price per Gallon

1990

$150,000

$10,000

$2.00

2000

$210,000

$18,000

$2.10

2010

$225,000

$25,000

$2.30

2019

$250,000

$30,000

$2.50

2020

$252,000

$30,500

$2.70

What is the value of the CPI in 1990 and in 2020? What is the value of the core CPI in 2020?

Answer 1

CPI = cost of market basket in given year / cost of market basket in base year ) * 100

CPI in 1990 = 100

CPI in 2020 = Cost of market basket in 2020 / cost of market basket in 1990 ) * 100

cost of market basket in 2020 = [(.04*252000) + (.1*30500) + ( 1500 *2.7) ] = 100800 +3050 +4050 = 1,07,900

cost of market basket in 1990 =[ ( 0.4 *150000 ) + ( .1*10000) + ( 1500+2) ] = 60000 + 1000 + 3000 = 64000

CPI in 2020 = { 107900 / 64000) * 100 = 168.59

in core inflation we exclude those commodities price which are high volatile like foods and energy , etc.

thereforewe exclude gasoline price .

Core CPI in 2020 = 103850 / 61000 ) *100 = 170.24