The consumer price index is computed by looking at a fixed basket of goods and t

Question

The consumer price index is computed by looking at a fixed basket of goods and tracking price changes used to track welfare in the economy. Consider a world with only two goods. At initial prices at time t = 0 the consumer buys bundle q10,q20. We now want to understand how prices affect welfare by looking at how prices change over time. In a two good world the CPI computation would look like this:

CPI = p11q10 + p21q20 / p10q10 + p20q20

where (q10,q20) is the reference bundle, which is the original bundle, and pti is the price of good i at time t. Essentially, the CPI is the total expenditure on the reference bundle in one period over the previous period. Explain by using a diagram why this computation over-estimates the true level of inflation in the economy. Indicate in your diagram points that relate to the computation of the price index.

Explanation / Answer

This method of calculating CPI over-estimates inflation because as P1 increases q1 decreases to the total expenditure on good 1 doesn't increase by as much as the CPI would suggest (i.e. if P10<P11, then P11q11<P11q10).

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