Question

According to the Bureau of Labor Statistics, the Consumer Price Index (CPI) increased by 27.0% between 2004 and 2014. In 2004, a gallon of unleaded gasoline cost $1.58. In 2014, it cost $3.26.

(a) What was the annual inflation rate between 2004 and 2014?

(b) What is the change in the real price of a gallon of gasoline between 2004 and 2014?

Answer 1

(a) % Change in CPI Value = 27 % and Time Period of Change = 2014 - 2004 = 10 years

Annual Inflation Rate in % = [1+(27/100)]^(1/10) - 1 = 0.0242 or 2.42 %

(b) 2004 Gasoline Price = $ 1.58 and 2014 Gasoline Price = $ 3.26

% Change in Gasoline Price = [3.26 - 1.58] / 1.58 = 1.0633 or 106.33 %

Annual % Change in Nominal Price = [1+1.0633]^(1/10) - 1 = 0.07512 or 7.512 %

Annual % Change in Real Price = [1.07512 / 1.0242] - 1 = 0.04972 or 4.972 %

Total % Change in Real Price between 2004 to 2014 = [1.04972]^(10) -1 = 0.6245 or 62.45 %