A typical household in Orangeland consumes only orange juice and shorts. Last year, which was the base year, the household spent $400 on juice and $120 on shorts. In the base year, juice was $2 a bottle and shorts were $10 a pair

This year, juice is $3 a bottle, shorts are $12 a pair, and a typical household has bought 180 bottles of juice and 14 pairs of shorts. a) What is the basket used in the CPI? b) Calculate the CPI in the current year. c) Calculate the inflation rate in the current year. d) Is the inflation rate that you've calculated likely to be biased? Why or why not?

a) The CPI basket is the quantities bought in the base year. In the base year, a typical household spent $400 on juice at $2 a bottle, so the quantity of juice bought was $400/$2 = 200 bottles. The household spent $120 on shorts at $10 a pair, so the quantity of shorts bought was $120/$10 = 12. Thus the CPI basket is 200 bottles of juice and 12 pairs of shorts.
b) The cost of the CPI basket last year was $400 + $120 = $520.The cost of the CPI basket in the current year is $3 × 200 + $12 × 12 = $744. So the CPI is ($744/$520 ) × 100 = 143.1.
c) The inflation rate is the percentage change in the CPI. Because the last year was also the base year, the CPI last year was 100. So the inflation rate for the current year is [(143.1 - 100 )/100] × 100, which is 43.1 percent.
d) The calculated CPI is likely to overstate inflation because of the commodity substitution bias. The relative price of shorts has fallen from 5 to 4 bottles of juice. This fall led consumers to buy more shorts and less juice. As a result, the actual consumer basket in the current year is less expensive than the CPI basket. The CPI ignores this commodity substitution, and so overstates the inflation rate.