Source: Intermediate Microeconomics, Problem Set 2, Texas A&M University
Tags: CPI, consumer price index, real income, nominal income, inflation adjustment, purchasing power, CPI-U, base year, constant dollars, BLS, ECON 323
Nominal income figures across different years are not directly comparable because price levels change over time. The Consumer Price Index (CPI) lets you convert nominal income into real income (constant dollars), revealing whether people's purchasing power has truly grown or merely kept pace with inflation.
Nominal income
Income measured in current-year dollars, without any adjustment for inflation. The raw dollar figure you see on a pay stub or census report.
Real income
Income adjusted for changes in the price level, expressed in the dollars of a chosen base year. It measures actual purchasing power: how much stuff the money can buy.
Consumer Price Index (CPI)
A measure of the average change over time in the prices paid by urban consumers for a basket of goods and services. Published monthly by the Bureau of Labor Statistics (BLS). The CPI-U (All Urban Consumers) is the most commonly cited version.
Base year
The reference year whose price level is used as the denominator when converting nominal values to real values. The choice of base year affects the scale of real values but not the comparison between them.
Constant dollars (real dollars)
Dollar amounts that have been adjusted for inflation using a price index, so that values from different years reflect the same purchasing power.
To convert a nominal value from Year X into real terms expressed in Year B (base year) dollars:
Real income (in Year B dollars) = Nominal income in Year X × (CPI in Year B / CPI in Year X)
This scales the nominal figure up or down to reflect the price level of the base year.
The problem provides:
Average income per household member in 1980: $7,720 (nominal)
Average income per household member in 2000: $22,132 (nominal)
Historically (from BLS data), the annual average CPI-U values were approximately:
CPI for 1980: 82.4
CPI for 2000: 172.2
(These are representative values; the exact figures depend on the BLS table version.)
To express 1980 income in 2000 dollars:
Real income (1980, in 2000 $) = $7,720 × (172.2 / 82.4) ≈ $7,720 × 2.09 ≈ $16,134
The 2000 income is already in 2000 dollars, so it stays at $22,132.
Nominal income nearly tripled from $7,720 to $22,132. But once you adjust for inflation, real income grew from about $16,134 to $22,132, a more modest increase of roughly 37%.
The large gap between nominal and real growth reflects the substantial inflation of the late 1970s and 1980s. Without the CPI adjustment, you would overstate how much better off households became.
The CPI is a Laspeyres-type price index, meaning it uses a fixed basket of goods from a base period. This introduces a well-known upward bias: the CPI overstates inflation because it does not account for consumers substituting away from goods that have become relatively more expensive (the substitution bias).
This connects directly to consumer theory: when relative prices change, rational consumers substitute toward cheaper goods, a behaviour the fixed-basket CPI ignores. Consequently, real income growth calculated using CPI may be slightly understated.
Real income conversion:
Real income (base-year $) = Nominal income × (CPI_base / CPI_current)
Inflation rate between two years:
Inflation rate = (CPI_later − CPI_earlier) / CPI_earlier × 100%
Price level ratio (scaling factor):
Scaling factor = CPI_target year / CPI_source year
⚠️ The formula has the base year CPI in the numerator and the source year CPI in the denominator. Flipping them gives the reciprocal and an incorrect answer.
⚠️ "In terms of 2000 dollars" means 2000 is the base year. The 2000 income needs no conversion; the 1980 income does.
⚠️ The CPI-U "All Items" index is the standard one unless specified otherwise. If a problem says "use the CPI," this is what they mean.
⚠️ The CPI's substitution bias is a common exam topic in its own right. Know that it overstates inflation, which means it understates real income growth.
Q: Nominal income in Year A is $15,000 and the CPI in Year A is 120. The CPI in the base year (Year B) is 180. What is real income in Year B dollars?
A: Real income = $15,000 × (180 / 120) = $15,000 × 1.5 = $22,500.
Q: If nominal income doubles from 1980 to 2000 but the CPI also doubles, what happened to real income?
A: Real income stayed the same. The entire increase in nominal income was absorbed by inflation.
Q: Why does the CPI tend to overstate inflation?
A: The CPI uses a fixed basket of goods and does not account for consumers substituting toward relatively cheaper goods when prices change. This substitution bias means the index overstates the cost of maintaining a given standard of living.
Q: You are given CPI(1980) = 82.4 and CPI(2000) = 172.2. By what factor did the general price level rise between 1980 and 2000?
A: The price level roughly doubled: 172.2 / 82.4 ≈ 2.09. Prices in 2000 were about 2.09 times higher than in 1980.
CPI, consumer price index, CPI-U, real income, nominal income, inflation adjustment, purchasing power, constant dollars, base year dollars, Laspeyres index, substitution bias, Bureau of Labor Statistics, BLS, price level, cost of living, deflating income