Question

 Suppose that the residents of Mexico spend all their income on cauliflower, broccoli, and carrots. In 2017 they buy 110 heads of cauliflower for $220, 80 bunches of broccoli for $100, and 200 carrots for $50. In 2018, they by 50 heads of cauliflower for $200, 50 bunches of broccoli for $110, and 250 carrots for $100. Assume the base year is 2017.

1. a) What is the CPI in both years? Hints: show steps. (10 marks)
2. b) What is the inflation rate in 2018? Hints: show steps. (5 marks) 

Answer 1

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

$$Cost_{2017}=\$220+\$100+\$50=\$370.$$

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

$$Cost_{2018}=\$200+\$110+\$100=\$410.$$

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:

$$CPI_{2017}=\dfrac{Cost_{2017}}{Cost_{2017}}\times100=\dfrac{\$370}{\$370}\times100=100,$$ $$CPI_{2018}=\dfrac{Cost_{2018}}{Cost_{2017}}\times100=\dfrac{\$410}{\$370}\times100=111.$$

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

$$\%\ Inflation\ rate=\dfrac{CPI_{2018}-CPI_{2017}}{CPI_{2017}}\times100\%,$$ $$\%\ Inflation\ rate=\dfrac{111-100}{100}\times100\%=11\%.$$