Measuring the Cost of Living

• Measuring the Cost of Living was presented on March 4, 2025.

Introduction to Inflation

• GDP measures total production.
• The GDP deflator measures overall prices.
• Consumer prices and purchasing power will be focused on.
• The key questions are:
  • How to measure changes in the cost of living
  • What is the difference between CPI and GDP deflator
  • How to compare dollar amounts across time
  • Does inflation reduce real wages

The Consumer Price Index (CPI)

• The CPI measures the overall cost of goods and services bought by a typical consumer.
• Government statisticians identify a market basket of goods and services.
• Prices are tracked to see how they change.
• The CPI is the basis for calculating the inflation rate.

Calculating CPI

• The five steps to calculate the CPI are:
  • Fix the basket
  • Find prices
  • Compute basket's cost
  • Choose base year and compute index
  • Compute inflation rate

Step 1: Fix the Basket

• Determine which goods/services are most important based on consumer surveys.
• For example, Food 15%, Housing 40%, Transportation 15%, etc.

Step 2: Find Prices

• Collect prices for each item in the basket from multiple locations like supermarkets and department stores at specific times each month.

Step 3: Compute Basket Cost

• Use quantities from the base year of the fixed basket.
• Multiply by current prices.
• The formula is ∑(Qbase × Pcurrent)

Step 4: Compute CPI

• CPI = (Cost in Current Year / Cost in Base Year) × 100
• The base year CPI is always 100.
• A 2024 CPI of 260 means 160% inflation since the base year.

Step 5: Compute Inflation Rate

• Inflation rate = (CPIyear2 - CPIyear1) /CPIyear1 × 100%
• It measures the percentage change in price level.

Other measures

• Core CPI excludes food and energy; these are volatile.
• Producer Price Index (PPI) measures the prices of the output of domestic producers and was formerly known as the wholesale price index.

Quiz 1

• If the CPI was 240 in 2023 and 250 in 2024, the inflation rate was 4.17%.

CPI vs. GDP Deflator: Key Differences

• Scope of goods:
  • CPI uses a fixed basket of consumer goods.
  • GDP deflator includes all domestically produced goods.
• Basket updating:
  • CPI uses fixed quantities.
  • GDP deflator uses current quantities.

Formula Comparison

• CPI = (Current Basket Cost / Base Basket Cost) × 100
• GDP deflator = (Nominal GDP / Real GDP) × 100

Quiz 2

• If the price of imported oil increases, that affects the CPI but not the GDP deflator.

Adjusting for Inflation

• Nominal variables are measured in current dollars.
• Real variables are adjusted for inflation.
• Real Value = (Nominal Value / Price Index) × 100

Indexation Examples

• COLA: Cost-of-living adjustments
• Social Security benefits.
• Tax brackets.
• Union contracts.

Quiz 3

• If salary increases from $50,000 to $55,000 while CPI increases from 200 to 210, real salary increases by 4.76%.

Problems with CPI: Measurement Challenges

• Substitution bias.
• Introduction of new goods.
• Quality changes.

Substitution Bias

• Consumers substitute toward cheaper goods.
• CPI uses a fixed basket.
• The CPI overstates cost of living increase.

Quiz 4

• If the CPI overstates inflation by 1% annually, a COLA pegged to CPI will overcompensate recipients.

Interest Rates and Inflation: Real vs. Nominal Interest Rates

• Nominal rate: Stated rate, no inflation adjustment.
• Real rate = Nominal rate - Inflation rate

Quiz 5

If $1000 is lent at 7% interest and inflation is 4%, the real return is $30.

Summary and Implications

• CPI measures cost of living using fixed basket.
• Inflation rate =
• Real values adjust for inflation.
• CPI overstatement has significant economic impacts.

Policy Considerations

• Indexed contracts reduce inflation risk.
• Social Security adjustments protect retirees.
• Monetary policy targets inflation.

Future Challenges

• Improving measurement accuracy.
• Incorporating digital economy.
• Addressing hedonic adjustments.

Book Quiz 1

• The CPI measures approximately the same economic phenomenon as the GDP deflator.

Book Quiz 2

• The largest component in the basket of goods and services used to compute the CPI is housing.

Book Quiz 3

• If a Pennsylvania gun manufacturer raises the price of rifles it sells to the U.S. Army, its price hike will increase the GDP deflator but not the CPI.

Book Quiz 4

• Because consumers can sometimes substitute cheaper goods for those that have risen in price, the CPI overstates inflation.

Book Quiz 5

• If the CPI is 200 for the year 2010 and 300 today, then $600 in 2010 has the same purchasing power as $900 has today.

Book Quiz 6

• The main reason the cost of living varies across regions of the country is differences in the price of housing.

Book Quiz 7

• $2,000 is deposited in a savings account.
• A year later, there is $2,100.
• The CPI rises from 200 to 204.
• In this case, the nominal interest rate is 5 percent, and the real interest rate is 3 percent.