Question

1. Assume that a consumer price index for all items in the U.S. is based on a specific basket of goods in the initial (base year), and that the mix of goods does not change from year to year (i.e. same amounts and brands of food items, electronic goods, housing sizes, etc), though the quality of some of the goods in the basket increases over time. Explain why the price changes measured by the index will overstate the actual increase in the cost of living.

Answer 1

CPI =( $\sum$ Pxi Xi in current year ) / ( $\sum$ Pxi Xi in base year )

Important thing to note is the quantities of each good Xi are the same for every year, only the prices change.

Hence if the quality of a certain good increases, then we require less amount of money to buy the same good of the original lower quality.

Hence the actual cost of living is lesser. (Because we can still survive with lower quality goods)

But since we can buy only better quality of goods, our cost of living has virtually increased more than expected. Hence we can say that the index overstates the actual increase in the cost of living as it doesn't take into account the quality of goods, just the quantity of goods.