If the Consumer Price Index (CPI) falls from 100 to 98 between two consecutive years, this implies that prices fell by 2% between those two years.

Question

BlackTom AI · Accepted Answer

We begin by restating the problem and options to ensure clarity: The statement is: If the Consumer Price Index (CPI) falls from 100 to 98 between two consecutive years, this implies that prices fell by 2% between those two years. Answer options: True; False.

Option 1: True. To evaluate, compute the percentage change in the CPI from 100 to 98. The change is 98 − 100 = −2. Dividing by the original level (100) gives −2/100 = −0.02, which is −2%. This matches the claim that prices fell by 2% over the period, so the statement aligns with the standard CPI percentage change calculation. In other words, a drop from 100 to 98 represents a 2% decrease.

Option 2: False. This would be the position that a CPI decline from 100 to 98 does not correspond to a 2% price decrease, perhaps suggesting a miscalculation or a misunderstanding of how percentage changes are measured. However, the straightforward calculation shows a 2% decline, so this option would be incorrect because it disputes the correct percent change derived from the base CPI value.

Further nuance: The CPI is typically reported relative to an index where 100 is a reference period. When the index falls from 100 to 98, the relative change is (98/100) − 1 = 0.98 − 1 = −0.02, which is a −2% change. This reinforces that the statement describes the correct magnitude and direction of change in prices between the two years.

In summary, evaluating the arithmetic confirms the 2% decrease interpretation is correct for the given CPI movement, while the alternative claim would be inconsistent with the standard percent-change calculation.

If the Consumer Price Index (CPI) falls from 100 to 98 between two consecutive years, this implies that prices fell by 2% between those two years.True/False

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