The inflation rate from 2010 to 2011 for a good j is defined to be Ij = (Pj/pj) ? 1, where pj was the price in 2010 and Pj was the price in 2011 (assuming for simplicity that the prices stayed fixed throughout each given year. For a consumer who consumed x1 units of good 1, x2 units of good 2 and x3 units of good 3 in 2010, the Laspeyres inflation rate from 2010 to 2011 is defined to be L = [(P1x1 + P2x2 + P3x3)/(p1x1 + p2x2 + p3x3)] ? 1. Prove that L is a weighted average of the inflation rates I1, I2 and I3. What are the weights? Find algebraic expressions for them and explain what they measure.

Hint: It may help you to give the label X to the amount p1x1 + p2x2 + p3x3, the consumer’s total spending on the three goods in 2010.