Inflation, Unemployment, CPI, and Real GDP: Study Notes

Short-run relationships between inflation and unemployment

• Rate of inflation can decrease; and when unemployment is too low, prices rise due to higher demand.
• Interplay: both affect each other; inflation and unemployment are linked.
• In the short term, the link between inflation and unemployment is negative: as one goes up, the other tends to go down.
• Terminology:
  • Negative relationship: variables move in opposite directions (one up, the other down).
  • Positive relationship: variables move in the same direction (to be used later in the course).

Unemployment rate: definition and discouraged workers

• Unemployment rate definition (in simplest terms): the percentage of people who are actively looking for a job and are available for work.
• In class terms: people who have been actively looking for a job within the last four weeks.
• Discouraged workers: people who have stopped looking for a job in the last four weeks and are not contacted; they are not counted as unemployed.

Key concepts: inflation, CPI, and related indices

• Inflation = sustained increase in the general price level.
• Market basket approach: we cannot track all goods and services, so we track a representative basket of goods and services.
• Common price index: CPI (Consumer Price Index); PPI (Producer Price Index) is also used but CPI is more common.
• CPI definition (in words): the price of a fixed basket of goods and services purchased by typical households, measured over time.
• CPI vs. wage measures:
  • Real wages capture purchasing power and living standards; nominal wages are measured in current dollars and may not reflect changes in prices.
• Why economists focus on real wages: to assess changes in living standards rather than what nominal dollars buy at current prices.

Measuring inflation with the CPI: formulas and base year concepts

• CPI for year t:
  $CPI_t = \frac{Cost\ of\ basket\ in\ year\ t}{Cost\ of\ basket\ in\ base\ year} \times 100$
• Base year property:
  • The base year CPI is set to 100 by construction, i.e., $CPI_{base} = 100$.
• Inflation rate (annual) relative to the previous year:
  $\pi<em>t = \frac{CPI</em>t - CPI<em>{t-1}}{CPI</em>{t-1}} \times 100$
• Note about wording in class material: the general idea is to compare current basket cost to base-year basket cost and scale to 100; then compute year-over-year changes for inflation.
• Practical note: you can compute CPI for multiple years by calculating the basket cost in each year and applying the CPI formula; base year remains fixed.

Example: CPI calculation with a fixed basket (base year = 2020)

• Basket contents (example): 1 loaf of bread, 1 movie ticket, 1 gallon of gasoline, 1 scented candle.
• Basket costs by year (example):
  • Base year cost = 26 → CPI_{2020} = \frac{26}{26} \times 100 = 100.
  • Year 2 basket cost = 29 → CPI_{2021} = \frac{29}{26} \times 100 = 111.54.
  • Year 3 basket cost = 30 → CPI_{2022} = \frac{30}{26} \times 100 = 115.38.
  • Year 4 basket cost = 30.50 → CPI_{2023} = \frac{30.50}{26} \times 100 = 117.31.
• Annual inflation (using year-to-year changes):
  • Year 2021 inflation: $\pi_{2021} = \frac{111.54 - 100}{100} \times 100 = 11.54\%.$
  • Year 2022 inflation: $\pi_{2022} = \frac{115.38 - 111.54}{111.54} \times 100 \approx 3.46\%.$
  • Year 2023 inflation: $\pi_{2023} = \frac{117.31 - 115.38}{115.38} \times 100 \approx 1.68\%.$
• Summary: CPI provides a way to translate a fixed basket of goods into a price index over time and then derive inflation rates.

Real vs nominal wages

• Nominal wages: wages measured in current dollars (nominal terms).
• Real wages: wages adjusted for inflation to reflect purchasing power.
• Why real wages matter: real wages reveal changes in living standards and purchasing power, not just dollar amounts.
• Formula:
  $RealWage<em>t = \frac{NominalWage</em>t}{\frac{CPI<em>t}{100}} = NominalWage</em>t \times \frac{100}{CPI_t}$

Unemployment: types and causes

• Three types of unemployment:
  • Frictional unemployment: short-term unemployment as workers search for new jobs or transition between jobs.
  • Structural unemployment: long-term unemployment due to mismatches between skills and jobs or due to technological/sectoral changes.
  • Cyclical unemployment: unemployment linked to the business cycle; rises during recessions and falls during expansions.
• Note on crises: cyclical unemployment tends to rise during recessions (economic downturns) and fall during recoveries; structural and frictional unemployment persist independently of the business cycle.
• Pandemic example (from class discussion): during the pandemic, unemployment was largely frictional in nature because many positions were temporarily paused rather than permanently lost.

Part 2: Calculations using CPI (step-by-step approach)

• Steps:
  1) Determine basket cost in base year.
  2) For each year t, determine basket cost with current prices.
  3) Compute $CPI<em>t = \frac{Cost\ of\ basket\ in\ year\ t}{Cost\ of\ basket\ in\ base\ year} \times 100.$ 4) Compute annual inflation: $\pi</em>t = \frac{CPI<em>t - CPI</em>{t-1}}{CPI<em>{t-1}} \times 100$ for t ≥ 2; $\pi</em>1$ is NA (no previous year).
• Example values (from the discussion):
  • Base year: cost = 26 → $CPI_{base} = 100.$ (So Year 1 CPI = 100 by construction.)
  • Year 2: cost = 29 → $CPI_{Year2} = 111.54.$ (29/26 × 100)
  • Year 3: cost = 30 → $CPI_{Year3} = 115.38.$ (30/26 × 100)
  • Year 4: cost = 30.50 → $CPI_{Year4} = 117.31.$ (30.50/26 × 100)
• Resulting inflation rates (from year-to-year):
  • Year 2: $\pi_{Year2} = 11.54\%.$
  • Year 3: $\pi_{Year3} \approx 3.46\%.$
  • Year 4: $\pi_{Year4} \approx 1.68\%.$

Real GDP: inflation-adjusted measure

• Concept: Real GDP removes the effects of inflation to compare true output across years.
• Method (using CPI):
  $RealGDP<em>t = \frac{NominalGDP</em>t}{\frac{CPI<em>t}{100}} = NominalGDP</em>t \times \frac{100}{CPI_t}$
• Example (using numbers from the discussion):
  • Base year: NominalGDP{Year1} = 5; CPI{Year1} = 100 → RealGDP_{Year1} = 5.00.
  • Year 2: NominalGDP{Year2} = 6.1; CPI{Year2} = 111.54 → RealGDP_{Year2} ≈ 6.1 × 100 / 111.54 ≈ 5.47.
  • Year 3: NominalGDP{Year3} = 6.5; CPI{Year3} = 115.38 → RealGDP_{Year3} ≈ 6.5 × 100 / 115.38 ≈ 5.63.
  • Year 4: NominalGDP{Year4} = 6.5; CPI{Year4} = 117.31 → RealGDP_{Year4} ≈ 6.5 × 100 / 117.31 ≈ 5.54.
• Important use: Real GDP is central to tracking business cycles and recessions, since it reflects true production after removing price changes.
• Connection to wages: the same inflation-adjustment method applies to wages and other economic variables when you want to compare across time in real terms.

Practical implications and connections

• Real-world relevance: CPI and real vs nominal concepts are used to assess living standards, growth, and policy impacts.
• Historical context: references to business cycles such as recessions, the Great Recession, and discussions of how unemployment reacts to economic events (e.g., crises, pandemics).
• Methodological note: the approach shown (CPI-based deflators) can be used to adjust any nominal variable to real terms for comparison over time.

Quick reference: key formulas to remember

• CPI (year t):
  $CPI_t = \frac{Cost\ of\ basket\ in\ year\ t}{Cost\ of\ basket\ in\ base\ year} \times 100$
• Inflation rate (year t relative to t-1):
  $\pi<em>t = \frac{CPI</em>t - CPI<em>{t-1}}{CPI</em>{t-1}} \times 100$
• Real GDP from nominal GDP (using CPI):
  $RealGDP<em>t = NominalGDP</em>t \times \frac{100}{CPI_t}$
• Real wages from nominal wages (using CPI):
  $RealWage<em>t = NominalWage</em>t \times \frac{100}{CPI_t}$
• Unemployment rate (standard definition):
  $UR = \frac{U}{LF} \times 100$
• Unemployment types (descriptions in words): frictional, structural, cyclical

Notes on terminology used in class

• Negative vs positive relationships:
  • Negative: when one variable rises and the other falls (e.g., short-run unemployment vs inflation).
  • Positive: when both variables move in the same direction (used later in the course).
• Discouraged workers are not counted among the unemployed because they are not actively seeking work.
• The base-year CPI is set to 100, and all subsequent CPIs are expressed relative to that base.

Summary takeaway

• CPI provides a controlled way to measure how the cost of living changes over time.
• Inflation rates are derived from year-to-year changes in the CPI.
• Real GDP and real wages are obtained by adjusting nominal values with the CPI, allowing comparisons that reflect true purchasing power and production levels across years.
• Understanding unemployment requires distinguishing frictional, structural, and cyclical causes, with cyclical unemployment being tied to the business cycle.