Notes: Measuring the Price Level and Inflation (Chapter 6)

CPI Construction and Calculation

  • The consumer price index (CPI) is a measure of the cost of living during a particular period.
  • Key definitions:
    • The CPI measures the cost of a standard basket of goods and services in a given year relative to the cost of the same basket in the base year.
    • The base year changes periodically.
  • Core idea: CPI is the ratio of the cost of the basket of goods in the current year to the cost in the base year, times a scaling factor.
  • Important nuance from the slides:
    • The base-year CPI is shown as 1 when expressed as a ratio, and as 100 when expressed as an index (ratio × 100).
    • BEA (Bureau of Economic Analysis) uses CPI as a percentage (ratio × 100).
  • Core formula (as a ratio):
    • extCPI(ratio)=extCostofbasketincurrentyearextCostofbasketinbaseyearext{CPI (ratio)} = \frac{ ext{Cost of basket in current year}}{ ext{Cost of basket in base year}}
    • If you multiply by 100, you get the CPI index: extCPI(index)=extCost<em>textCost</em>baseimes100ext{CPI (index)} = \frac{ ext{Cost}<em>{t}}{ ext{Cost}</em>{base}} imes 100
  • Why CPI matters:
    • It tracks changes in the cost of living over time.
    • It is used to adjust nominal values to real terms and to measure inflation.

Calculating the CPI: Worked examples from the transcript

  • Example 1 (base year 2020; items: Rent, Hamburgers, Movie tickets):
    • 2020 costs: Rent $750, Hamburgers $120, Movie tickets $70; Total cost = 1,0601,060
    • 2025 costs: Rent $945, Hamburgers $150, Movie tickets $80, Sweaters $200; Total cost = 1,3751,375
    • CPI (2025 relative to 2020 base) = 13751060imes100=130\frac{1375}{1060} imes 100 = 130
    • Interpretation: Cost of living in 2025 is 30% higher than in 2020 under this basket.
  • Example 2 (another 2020 vs 2025 basket, shows different base-year costs):
    • 2020 costs: Rent $750, Hamburgers $120, Movie tickets $70, Sweaters $120; Total = 1,0601,060
    • 2025 costs: Rent $945, Hamburgers $150, Movie tickets $80, Sweaters $200; Total = 1,3751,375
    • CPI computed as above yields a CPI of 130 for 2025 relative to the 2020 base year.
  • Higher-level note: The CPI base year is used as a reference point; the numerical values depend on the basket and base-year choice.

Cost of Living vs. Price Index

  • A price index measures the average price of a given quality of goods and services relative to the same goods/services in a base year.
  • CPI measures the change in consumer prices (cost of living for households).
  • Other indices include:
    • Core inflation: CPI excluding energy and food.
    • Producer price index (PPI).
    • Import/export price indices.

Inflation: measurement and historical examples

  • Inflation is the annual percentage change in the price level.
  • Calculation example: extInflation<em>t=extCPI</em>t−extCPI<em>t−1extCPI</em>t−1imes100%ext{Inflation}<em>{t} = \frac{ ext{CPI}</em>t - ext{CPI}<em>{t-1}}{ ext{CPI}</em>{t-1}} imes 100\%
  • Example data (selected years):
    • 2018 CPI = 251.1; 2019 CPI = 255.7; Inflation 2019 = 1.8% (given as a calculation: 255.7−251.1251.1imes100=1.8ext%\frac{255.7 - 251.1}{251.1} imes 100 = 1.8 ext{\%}).
    • 2020 Inflation = 1.3%; 2021 Inflation = 4.7%; 2022 Inflation = 8.0%.
  • Historical note: The Great Depression featured a period of falling output and falling prices (deflation when inflation is negative).
  • Table summary (selected values):
    • 2018: CPI = 251.1, Inflation = 0? (not shown)
    • 2019: CPI = 255.7, Inflation = 1.8%
    • 2020: CPI = 258.9, Inflation = 1.3%
    • 2021: CPI = 271.0, Inflation = 4.7%
    • 2022: CPI = 292.6, Inflation = 8.0%
    • Earlier Depression-era values (1929–1933) show large declines: 1929 CPI = 17.1; 1930 CPI = 16.7; Inflation in 1930 = −2.3%; 1931 = 15.2, Inflation = −9.0%; 1932 = 13.7, Inflation = −9.9%; 1933 = 13.0, Inflation = −5.1%.
  • Takeaway: Inflation rates can be positive or negative; periods of deflation reflect decreasing price levels.

Adjusting for Inflation: Real vs Nominal

  • Nominal quantity vs real quantity:
    • Nominal: measured in current dollars.
    • Real: measured in physical terms (purchasing power).
  • To compare values over time, convert to real terms by deflating nominal values with a price index.
  • General rule: Real quantity = Nominal quantity ÷ price index (as a fraction).
  • Conversion detail: If the CPI is given as a percentage, convert to a fraction by dividing by 100. Equivalently, Real = Nominal ÷ (CPI/100) = 100 × Nominal ÷ CPI.
  • Example (Family Income):
    • Nominal incomes: 2020 = $40,000; 2025 = $44,000.
    • CPI fractions: 2020 = 1.00; 2025 = 1.25.
    • Real income 2020 = $40,000 ÷ 1.00 = $40,000.
    • Real income 2025 = $44,000 ÷ 1.25 = $35,200.
  • Conclusion: Although nominal income rose from 2020 to 2025, real income fell when adjusted for inflation in this example.

Real Wages and Historical Salaries

  • The real wage is the wage paid to workers measured in purchasing power.
  • Real wage for a period = Nominal wage ÷ CPI for that period (CPI as a fraction).
  • Baseball salaries example (1930 vs 2022):
    • Babe Ruth (1930): nominal $80,000; Real salary $479,042; CPI as a fraction ≈ 0.167.
    • Max Scherzer (2022): nominal $43,300,000; Real salary ≈ $14,778,157; CPI as a fraction ≈ 2.93.
  • Another example: U.S. production workers’ wages with CPI base 1982–84: 1970 CPI ≈ 38.8; 2022 CPI ≈ 292.6; Real wages stayed roughly the same despite nominal wages rising about 8x from 1970 to 2022.
    • 1970 Average wage = $3.40; 2022 Average wage = $27.55.
    • Real wage calculations: extRealwage<em>1970=3.400.388 (ext≈8.76)ext{Real wage}<em>{1970} = \frac{3.40}{0.388} \,( ext{≈ }8.76); extRealwage</em>2022=27.552.93 (ext≈9.40)ext{Real wage}</em>{2022} = \frac{27.55}{2.93} \,( ext{≈ }9.40)
  • Visuals show production workers’ wages over time (nominal vs real), illustrating that real wages may not grow proportionally to nominal wages due to inflation.

Indexing and Its Uses

  • Indexing definition: increases a nominal quantity by the percentage increase in a specified price index to protect purchasing power.
  • Practical uses:
    • Social Security payments are indexed to inflation; no congressional action required.
    • Some labor contracts include indexing to inflation.
  • Example: If prices rise 3% in a year and benefits are indexed, benefits rise by 3% automatically.

Indexed Wages and Real Income Growth (Labor Contracts)

  • Indexed labor contract example: Real wage growth 2% per year for next 2 years with CPI path: 100 in year 1, 105 in year 2, 110 in year 3.
  • Relationship: Nominal wage = Real wage × Price level (CPI as a fraction).
    • Year 1: Real wage $12.00; CPI 1.00; Nominal wage $12.00.
    • Year 2: Real wage $12.24; CPI 1.05; Nominal wage $12.85.
    • Year 3: Real wage $12.48; CPI 1.10; Nominal wage $13.73.
  • Practical implication: With indexing, nominal wages rise with inflation, preserving real purchasing power.

Minimum Wage and Indexing

  • The national minimum wage is set in nominal terms and has risen over time.
  • Indexing the minimum wage to inflation would simplify adjustments and reduce political controversy.
  • Real minimum wage has declined by about 30% since 1970, despite nominal increases in minimum wage.

CPI and Inflation: Policy and Measurement Implications

  • CPI and other indices influence policy decisions and wage increases.
  • Inflation might be overstated or understated, affecting government spending and measured living standards.
  • Example: If CPI indicates 3% inflation but actual cost of living rose by 2%, real income would rise by 1% more than the CPI suggests.
  • The Bureau of Labor Statistics makes ongoing efforts to improve CPI calculations.

CPI Quality Adjustment Bias

  • One major CPI bias: not fully capturing quality changes in products.
  • Example: A PC with 20% more memory costs 20% more, but this extra value is not a perfect substitution for the older model.
  • Difficulties in quality adjustment:
    • Large numbers of goods and subjective differences in value.
    • New goods introduce base-year issues with no direct price history for the new features.
  • Consequence: Without proper quality adjustments, inflation may be overstated for some goods.

CPI Substitution Bias and the Fixed Basket Issue

  • The CPI uses a fixed basket of goods; when prices change, consumers substitute cheaper alternatives, but CPI often doesn't fully account for substitution.
  • Example (illustrative): 2015 base basket: Coffee (50 cups at $1.00), Tea (50 cups at $1.00), Scones (100 at $1.00) → Total $200.
  • In 2020, prices rise and substitutions occur (e.g., more tea, less coffee), changing the effective basket.
  • Hypothetical 2020 basket with fixed items: Coffee $2.00 (50 cups) → $100, Tea $1.00 (50 cups) → $50, Scones $1.50 (100) → $150; Total $300 → CPI = 300/200 × 100 = 150.
  • Truth about substitution: If consumers substitute tea for coffee and keep the same overall consumption, true CPI would be lower:
    • True CPI = 250/200 × 100 = 125, which is 25% lower than the fixed-basket CPI of 150.
  • Takeaway: Substitution bias causes the fixed-basket CPI to overstate true inflation when relative prices change and substitutions occur.

The Costs of Inflation: How it Affects the Economy

  • The price level vs relative prices:
    • Price level: overall average of prices across the economy, captured by indices like the CPI.
    • Relative price: price of a single good relative to others; can change even if the overall price level is stable.
  • Inflation tends to affect the communication of price signals (noisy prices):
    • Inflation creates static in price information, making it harder to discern whether a change in a single good’s price reflects a relative change or general inflation.
    • Decision-making costs rise because market participants must gather more information to interpret price signals.

Relative Prices: Inflation vs Individual Changes

  • Relative prices can move a lot even when overall inflation is moderate or stable.
  • Examples of relative price changes:
    • Higher relative prices for oil, gas, and travel services (e.g., beach hotels, cruises, gas).
    • Lower relative prices for fresh fruits and vegetables, heating oil.
  • The difference between overall inflation and relative price changes matters for consumers and allocation of resources.

Inflation and Prices: A Quick Summary Diagram (Conceptual)

  • Inflation: overall price level rises over time.
  • Price index: tracks the average price level; CPI is a commonly used index for consumers.
  • Relative prices: price of one good relative to another; can rise or fall independently of overall inflation.
  • Noisy prices: inflation obscures signal in price changes, increasing information costs.
  • Indexing: a mechanism to compensate for expected inflation, reducing distortions when wages, transfers, or payments are tied to prices.

Hyperinflation and Extreme Scenarios

  • Hyperinflation definition: an extremely high and typically accelerating inflation rate.
  • Historical example: In 1923 Germany, workers were paid twice daily to keep up with price increases.
  • Consequences: magnifies the costs of inflation and encourages keeping less cash (to avoid loss of purchasing power).

Inflation, Interest Rates, and the Fisher Effect

  • Relationship overview:
    • Real interest rate r is the increase in the purchasing power of an asset: r = i -
      ho where ii is the nominal interest rate and
      ho is the inflation rate.
    • The nominal rate i is the stated annual percentage increase in the dollar value of an asset.
  • Unanticipated inflation effects:
    • For a given nominal rate, higher inflation lowers the real rate, benefiting borrowers and hurting lenders.
    • If inflation is higher than expected, lenders lose; if inflation is lower than expected, borrowers lose.
  • Inflation-protected securities: pay a real rate plus the inflation rate, providing a hedge against unexpected inflation.
  • Fisher effect: the tendency for nominal interest rates to move with expected inflation (high inflation → higher nominal rates; low inflation → lower nominal rates).

Historical Context: Nominal vs Real Interest Rates (Selected Data Points)

  • General ranges (illustrative):
    • Nominal interest rate range across years: roughly 0.05% to 11.5%.
    • Inflation rate range across years: roughly 0.12% to 13.5%.
  • Relationship:
    • Real interest rate = nominal rate − inflation rate.
    • In some periods, nominal rates have been high while inflation was high, affecting real returns differently than expected.
  • Notable observation: U.S. real interest rates varied significantly from the 1970s through 2020s, with the highest real rate around the mid-1980s (~3.9%) and the lowest around mid-1970s (approximately −3.3%).

Practical Implications: Why Low, Stable Inflation Matters

  • Stable inflation facilitates long-term planning (retirement, investments, big capital decisions).
  • It reduces the costs of price signaling and uncertainty in economic decisions.
  • It minimizes unexpected redistribution of wealth created by surprise inflation (e.g., borrowers vs lenders, workers vs employers).
  • It reduces shoe-leather costs and tax distortions associated with inflation and cash management.

Quick Mathematical Recap (Key Formulas)

  • CPI index (ratio form): extCPI=extCostofbasketincurrentyearextCostofbasketinbaseyearimes100%ext{CPI} = \frac{ ext{Cost of basket in current year}}{ ext{Cost of basket in base year}} imes 100\%
  • Inflation rate: extInflation<em>t=extCPI</em>t−extCPI<em>t−1extCPI</em>t−1imes100%ext{Inflation}<em>{t} = \frac{ ext{CPI}</em>{t} - ext{CPI}<em>{t-1}}{ ext{CPI}</em>{t-1}} imes 100\%
  • Real income or real value (with CPI as a percent):
    • If CPIt is a percentage, extRealquantity=extNominalquantityextCPI</em>t/100=100imesextNominalquantityextCPItext{Real quantity} = \frac{ ext{Nominal quantity}}{ ext{CPI}</em>t/100} = \frac{100 imes ext{Nominal quantity}}{ ext{CPI}_t}
    • If CPI is given as a fraction (e.g., 1.25), then extRealquantity=extNominalquantityextCPIasafractionext{Real quantity} = \frac{ ext{Nominal quantity}}{ ext{CPI as a fraction}}
  • Real interest rate (Fisher relation): r = i -
    ho
  • Indexed wage path example: Nominal wage = Real wage × CPI (as a fraction)

Notes on Data Interpretation from the Transcript

  • CPI and dollar values are used in multiple ways (index form vs. percentage form); keep track of the base-year convention.
  • Examples illustrate the importance of considering substitutions and quality changes when interpreting CPI numbers.
  • The material emphasizes that inflation has both cognitive/measurement implications (how we measure price changes) and real economic consequences (how it redistributes wealth, affects planning, and changes incentives).