Question

The following graph shows the inflation rate in the US between 1965 and 2015

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Inflation 16% rate 14 (percent) 12 10 8 6 4 typ harth 2 0 1965 1975 1985 1995 2005 2015 -4

0. 1. From 1965 to 1995, does CPI in the US always increase over time? Explain.
   2. Suppose 2009 is the base year, and the inflation rate between 2009 and 2010 is -2%.
1. What is the CPI in 2009?
2. Calculate the CPI in 2010.
3. Between 2009 and 2010, the nominal interest rate is 3%, calculate the real interest rate.

Answer 1

Solution:

Interest rate = (CPIt+1 - CPIt)*100/CPIt

where CPIt+1 is consumer price index in year t + 1, and CPIt is consumer price index in year t.

Further CPIt = (cost of market basket in year t/cost of market basket in base year)*100

So, as CPI can never be negative, if the interest rate is positive, it means CPI in next year is greater than that in previous year. Similarly, if interest rate is negative, it means that CPI in next year is less than CPI in previous year.

a) From 1965 to 1995, we can easily see in the graph that interest rate is always positive, so yes, CPI in the US seems to have increased over time in this period (reason mentioned above mathematically).

b) Base year as 2009, inflation rate between 2009 and 2010 = -2% or -0.02

ii) CPI in 2009 = (Cost of market basket in 2009/cost of market basket in base year, which is 2009)*100

CPI in 2009 = 1*100 = 100

Note that CPI in base year, thus, is always 100.

iii) inflation rate = (CPI in 2010 - CPI in 2009)*100/CPI in 2009

-0.02 = (CPI in 2010 - 100)*100/100

CPI in 2010 = -0.02 + 100 = 99.98

iv) Real interest rate = (1 + nominal interest rate)/(1 + inflation rate) - 1

Real interest rate = (1 + 3%)/(1 + (-2%)) - 1

Real interest rate = (1 + 0.03)/(1 - 0.02) - 1

Real interest rate = 1.051 - 1 = 0.051 or 5.1%

(Approximation says real interest rate is approximately equal to nominal interest rate - inflation rate; so, real interest rate = 3% - (-2%) = 5% approximately, which is true).