True or false: if the elderly consume the same market basket as other people, then social security would have an uncertain impact on their standard of living.

False.

When the price of a basket rises, the consumers substitute some goods in that basket by goods that are now relatively cheaper. Due to this. The actual rise in the cost of living is less than stated by the CPI. This shortcoming of the CPI is referred to as the substitution bias.

Let’s assume CPI is 2% higher than the year before, and the social security payment is indexed with CPI. In other words, social security benefits increase 2% too, however, since CPI overstates the cost of living, the actual rise in the cost of living is less than 2%. Therefore, the elderly have received a higher increase in benefits than in costs, making them better off than they were a year ago. This happens year by year, implying the standard of living of the elderly rises year by year.