Measuring the Cost of Living – Construction of the CPI & Introduction to Inflation

Learning Objectives

• Understand five key goals for the chapter:
  • Learn how the Consumer Price Index (CPI) is constructed.
  • Recognize why the CPI is an imperfect measure of the cost of living.
  • Compare CPI with the GDP deflator as alternative measures of the overall price level.
  • Use a price index to translate dollar figures from different time periods into comparable purchasing-power terms.
  • Distinguish between real and nominal interest rates.

Motivating Example: Gasoline Prices 1957 vs. 2018

• Historical price comparison
  • 1957: $\$0.43$ per gallon ≈ $9.5$ cents per litre.
  • 2018: approximately $\$1.30$ per litre.
• Possible explanations initially considered
  • OPEC’s monopoly power and crude-oil price manipulation.
  • Increased mark-ups by large oil companies.
  • Rising demand colliding with a shrinking supply of a non-renewable resource.
• Core analytical question
  • Are higher nominal prices signalling greater scarcity/value of gasoline, or do they merely reflect a general decline in the purchasing power of money?
  • Need to know whether gasoline has truly become less affordable relative to incomes.

Why a Price Index Is Needed

• Nominal prices and nominal incomes rise over time; direct comparison of dollar amounts across years is misleading.
• Economists therefore convert current-dollar amounts into “real” purchasing-power equivalents using a price index.
• The CPI is the principal tool for monitoring changes in the cost of living for a typical household.

Key Definitions Introduced

• Consumer Price Index (CPI):
  • Measures the overall cost of a basket of goods and services bought by a typical consumer.
  • Computed and reported monthly by Statistics Canada (parallel agencies: BLS in the U.S., ONS in the U.K., etc.).
• Inflation:
  • A situation in which the economy’s overall price level is rising.
• Inflation rate:
  • The percentage change in the overall price level from the previous period.
  • Using CPI, $\text{Inflation Rate}<em>{t}=\frac{CPI</em>{t}-CPI<em>{t-1}}{CPI</em>{t-1}}\times100$.

Overview of CPI Construction

• Statistics Canada tracks prices for 600+ different goods and services each month.
• Five-step procedure (illustrated with a hot-dog–hamburger economy):
  1. Determine the fixed basket.
  2. Find the prices of each good in each year.
  3. Compute the cost of the basket in each year.
  4. Choose a base year and compute the CPI.
  5. Compute the inflation rate between years.

Detailed Walk-Through of the Five Steps

• STEP 1 – Determine the Basket
  • Survey households to identify the quantities typically purchased.
  • Example: 4 hot dogs + 2 hamburgers.
  • Weight of each item in the CPI is proportional to its budget share.
• STEP 2 – Find Prices
  • Collect market prices for each item at each point in time.
  • Example price schedule:
  • 2016: $P<em>{HD}=\$1$, $P</em>{HB}=\$2$.
  • 2017: $P<em>{HD}=\$2$, $P</em>{HB}=\$3$.
  • 2018: $P<em>{HD}=\$3$, $P</em>{HB}=\$4$.
• STEP 3 – Compute Basket Cost
  • Formula: $\text{Cost}<em>{t}=\sum</em>{i}(Q<em>{i}^{\text{fixed}}\times P</em>{i,t})$.
  • Numerical results:
  • 2016: $(4\times1)+(2\times2)=\$8$.
  • 2017: $(4\times2)+(2\times3)=\$14$.
  • 2018: $(4\times3)+(2\times4)=\$20$.
  • Holding quantities fixed isolates pure price movements.
• STEP 4 – Choose Base Year & Compute CPI
  • Base year selected arbitrarily for reference; here, 2016.
  • CPI formula: $CPI<em>{t}=\frac{\text{Cost of Basket}</em>{t}}{\text{Cost of Basket}_{\text{base}}}\times100$.
  • Example indices:
  • 2016: $(8/8)\times100=100$ (always 100 by construction).
  • 2017: $(14/8)\times100=175$.
  • 2018: $(20/8)\times100=250$.
• STEP 5 – Compute Inflation Rate
  • 2017 vs. 2016: $\frac{175-100}{100}\times100=75\%$.
  • 2018 vs. 2017: $\frac{250-175}{175}\times100=43\%$.

Interpretation & Significance

• A CPI of $175$ in 2017 tells us that the cost of the typical basket rose $75\%$ since the base year.
• A $43\%$ inflation rate between 2017 and 2018 indicates rapid erosion of purchasing power.
• Policymakers, wage negotiators, and financial markets watch CPI-based inflation closely to adjust contracts, pensions, and interest rates.
• Holding the basket fixed converts nominal price changes into a common unit, but (as later chapters will discuss) can introduce measurement bias when consumer behaviour shifts.

CPI vs. GDP Deflator (Preview)

• CPI: focuses strictly on consumer purchases, includes imported goods, uses a fixed basket.
• GDP deflator: reflects prices of all domestically produced final goods & services, excludes imports, uses current-year quantities as weights.
• Consequently, the two indices may diverge when (i) import prices move differently from domestic prices or (ii) relative quantities change substantially.

Connections to Prior & Future Material

• Prior chapter (GDP): measured quantity of output; now we measure the cost of living.
• Upcoming sections will tackle
  • Sources of CPI measurement error (substitution bias, new-goods bias, quality adjustment).
  • Converting nominal values to real values (e.g., wage indexation, Social Security adjustments).
  • Real vs. nominal interest rates: $r = i - \pi$ where $r$ is real, $i$ is nominal, $\pi$ is inflation.

Practical & Policy Relevance

• Indexation: Contracts, tax brackets, and government benefits are often linked to CPI to protect against inflation.
• Monetary policy: Central banks target low, stable inflation; accurate CPI measurement is critical for setting interest rates.
• Ethical dimension: Mis-measurement can erode purchasing power for fixed-income groups (pensioners, minimum-wage workers).

Numerical & Formula Summary

• CPI Formula: $CPI<em>{t}=\frac{\text{Cost of Basket}</em>{t}}{\text{Cost of Basket}_{\text{base}}}\times100$.
• Inflation Rate Formula: $\text{Inflation}<em>{t}=\frac{CPI</em>{t}-CPI<em>{t-1}}{CPI</em>{t-1}}\times100$.
• Real vs. Nominal (preview): $r=i-\pi$.
• Example Costs: $8,\;14,\;20$ for 2016-18 respectively.
• Example Indices: $100,\;175,\;250$.
• Example Inflation: $75\%,\;43\%$.