Consider the following price indexes: 90 in 2017, 100 in 2018,110 in 2019, 121 in 2020, and 150 in 2021. Answer the following questions.

a. Which year is likely the base year?

b. What is the inflation rate from 2018 to 2019?

c. What is the inflation rate from 2019 to 2020?

d. If the cost of a market basket in 2018 is 2,000$, what is the cost of the same basket of goods and services in 2017? In 2021?

The base year is$2018$as the price index is$100$.

From$2018-2019$,

The inflation rate is calculated as,

role="math" localid="1651488049003" $\frac{{\displaystyle \text{PriceIndexof}2019\text{-PriceIndexof}2018}}{PriceIndexof2018\times 100}$$=\frac{{\displaystyle 110-100}}{100\times 100}$

$=10\%$

From $2019-2020$,

The inflation rate is calculated as,

$\frac{{\displaystyle \text{PriceIndex of}2020\text{-PriceIndex of}2019}}{PriceIndexof2019\times 100}$$=\frac{{\displaystyle 121-110}}{110\times 100}$

$=10\%$

The cost of the same basket of goods and services in $2017$is,

$\text{price index of}2017\times \frac{{\displaystyle \text{cost in base year}}}{100}$

role="math" localid="1651488638497" $\Rightarrow 90\times \frac{{\displaystyle 2000}}{100}=1800$

Thus the cost of the same basket of goods and services in$2017$is$\$1800$.

The cost of the same basket of goods and services in $2020$is,

$\text{price index of}2020\times \frac{\text{cost in base year}}{100}$

$\Rightarrow 150\times \frac{2000}{100}=3000$

Thus the cost of the same basket of goods and services in $2020$is$\$3000$.