Question

In year 2017, suppose that people consume only three types of vegetables, X, Y and Z. They  purchase 100 units of X for $200, 50 units of Y for $75, and 500 units of Z for $100. In year  2018, they buy 75 units of X for $225, 80 units of Y for $120, and 500 units of Z for $100.  Based on the above information, calculate the price of each vegetable in each year. Using  2017 as the base year, calculate the Consumer Price Index (CPI) for each year. Compute the  inflation rate in 2018?

Answer 1

(a) Let's calculate the prices of each vegetable (X, Y and Z) in 2017 year:

$$P_{X,2017}=\dfrac{\$200}{100\ units}=\$2,$$ $$P_{Y,2017}=\dfrac{\$75}{50\ units}=\$1.5,$$ $$P_{Z,2017}=\dfrac{\$100}{500\ units}=\$0.2.$$

Let's calculate the prices of each vegetable (X, Y and Z) in 2018 year:

$$P_{X,2018}=\dfrac{\$225}{75\ units}=\$3,$$ $$P_{Y,2018}=\dfrac{\$120}{80\ units}=\$1.5,$$ $$P_{Z,2018}=\dfrac{\$100}{500\ units}=\$0.2.$$

(b) Let's find the cost of the market basket in the base year (2017):

$$Cost_{2017}=\$200+\$75+\$100=\$375.$$

Then, let's find the cost of the market basket in year 2018:

$$Cost_{2018}=\$225+\$120+\$100=\$445.$$

The Consumer Price Index can be calculated as follows:

$$CPI=\dfrac{Cost\ of\ market\ basket\ in\ a\ given\ year}{Cost\ of\ market\ basket\ at\ base\ year}\times100.$$

Let's calculate CPI in both years:

$$CPI_{2017}=\dfrac{Cost_{2017}}{Cost_{2017}}\times100=\dfrac{\$375}{\$375}\times100=100,$$ $$CPI_{2018}=\dfrac{Cost_{2018}}{Cost_{2017}}\times100=\dfrac{\$445}{\$375}\times100=118.6.$$

b) The % inflation rate in 2018 compared to 2017 can be calculated as follows:

$$\%\ Inflation\ rate=\dfrac{CPI_{2018}-CPI_{2017}}{CPI_{2017}}\times100\%,$$ $$\%\ Inflation\ rate=\dfrac{118.6-100}{100}\times100\%=18.6\%.$$