Question

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?

Short answer

a. base year is$2018$

b. inflation rate from$2018-2019$is$10\%$

c. inflation rate from $2019-2020$is $10\%$

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

and in $2021$is $\$3000$.

Step-by-step solution

part (a) introduction 

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

part (b) explanation 

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}$

$=10\%$

part (c) explanation

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}$

$=10\%$

part (d) explanation

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$\$1800$.

part (d) explanation

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$\$3000$.