Measuring the Price Level and Inflation Study Notes

Measuring the Price Level and Inflation

Learning Objectives

• Explain how the consumer price index (CPI) is constructed and use it to calculate the inflation rate.

• Show how the CPI is used to adjust dollar amounts to eliminate the effects of inflation.

• Discuss the two most important biases in the CPI.

• Distinguish between inflation and relative price changes to find the true costs of inflation.

• Summarize the connections among inflation, nominal interest rates, and real interest rates.

Measuring the Price Level

• The consumer price index (CPI) is a measure of the cost of living during a particular period.

Components of CPI

• 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 of goods and services in the base year.

  • Base year changes periodically.

Calculating the CPI

Example of Monthly Cost Calculation

CPI Formula and Explanation

• The CPI is the ratio of the cost of the basket of goods in the current year to the cost in the base year:

  • Formula:
    CPI = rac{ ext{Cost in Current Year}}{ ext{Cost in Base Year}} imes 100

  • Example Calculation of CPI for given years:

  • Base year cost: $940

  • Current year (2020) cost: $1,175

  • Calculation:
    CPI = rac{1,175}{940} imes 100 = 125

  • Interpretation: Cost of living in 2020 is 25% higher than in 2015.

• The CPI for the base year is always 100, and for any given period, the CPI reflects the cost of living relative to the base year costs.

• The Bureau of Economic Analysis (BEA) uses CPI as a percentage, expressed as the ratio times 100.

Cost of Living Details

• Calculation of new CPI:
  CPI = rac{1,375}{1,060} = 1.30

Price Index and Inflation

• A price index measures the average price of a given quality of goods and services relative to the price of the same goods and services in a base year.

• The CPI measures the change in consumer prices.

• Other indices include:

  • Core inflation (CPI without energy and food).

  • Producer price index (PPI).

  • Import/export price index.

Understanding Inflation

• Inflation is the rate of inflation measured as the annual percentage change in the price level.

• Example:
  ext{Inflation in 2016} = rac{(CPI{2016} - CPI{2015})}{CPI_{2015}} = rac{(2.40 - 2.37)}{2.37} = 0.0126 ext{ or } 1.3 ext{%}

• Historical example from the Great Depression:

  • Period of falling output and prices indicates deflation, which occurs when inflation rates are negative.

Historical CPI and Inflation Data

Adjusting for Inflation

• A nominal quantity is measured in terms of its current dollar value, while a real quantity is measured in physical terms (quantities of goods and services).

• To compare values over time, real quantities should be used.

• Deflating a nominal quantity converts it to a real quantity:

  • Formula:
    ext{Real Quantity} = rac{ ext{Nominal Quantity}}{ ext{Price Index}}

Family Income Comparison Example

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• Analysis: Can a family buy more with $40,000 in income in 2015 or with $44,000 in 2020?

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• 2015 is the base year for the CPI; therefore, both nominal incomes must be converted to real income for comparison:
  

  Year	Nominal Income	CPI	Real Income
  2015	$40,000	1.00	$40,000
  2020	$44,000	1.25	rac{44,000}{1.25} = 35,200
  Conclusion: $40,000 in 2015 has the greater purchasing power.
  Comparing Historical Salaries

  Example: Babe Ruth vs. Stephen Strasburg

  • Requires a CPI series that includes 1930 data.

  • CPI using 1982-1984 as the base year:

    Player	Year	Nominal Salary	Real Salary	CPI
    Babe Ruth	1930	$80,000	$479,042	0.167
    Stephen Strasburg	2019	$38,300,000	$14,902,724	2.57

  • Note: Despite higher nominal salaries, real income fluctuations are prevalent due to inflation and economic conditions.

  Understanding Real Wages

  • The real wage is defined as the wage paid to the worker measured in terms of purchasing power.

  • Real wage is calculated by dividing the nominal wage by the CPI for that period.

  Historical Average Wages for U.S. Production Workers

  Year	Average Wage	CPI	Real Average Wage
  1970	$3.40	0.388	rac{3.40}{0.388} = 8.76
  2019	$23.51	2.56	rac{23.51}{2.56} = 9.18

  Indexing

  • Indexing involves increasing a nominal quantity each period by the percentage increase in a specified price index.

  • Purpose: Prevents the purchasing power of the nominal quantity from being eroded by inflation.

  • Example: Social Security payments adjust automatically by the inflation rate without the need for Congressional action.

  Example of Indexed Labor Contract

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  • Given an indexed contract:
    

    Year	Real Wage	Price Index	Nominal Wage
    1	$12.00	1.00	$12.00
    2	$12.24	1.05	$12.85
    3	$12.48	1.10	$13.73
    Minimum Wage Considerations

    • The national minimum wage is set in nominal terms and debated periodically for increases.

    • Indexing minimizes the complexity of these debates; however, politics often influence adjustments.

    • Notably, the real minimum wage has decreased almost 30% since 1970 despite nominal increases.

    CPI and Inflation

    • CPI and other price indices have significant implications on policy decisions and wage increases.

    • Potential overstatements of inflation may increase government spending unnecessarily while underestimating standard of living increases.

    Example Scenario

    • If CPI indicates 3% inflation but the actual cost of living only increases by 2%, the real income increase may only be 1%.

    • The Bureau of Labor Statistics endeavors to improve CPI calculations rigorously.

    CPI Quality Adjustment Bias

    • One significant bias within the CPI is its measurement of price changes without accounting for corresponding quality changes.

      • Example: A PC might cost 20% more due to increased memory; however, the quality improvement isn’t reflected without adjustments, falsely inflating CPI contributions.

    Adjustments for Quality

    • Adjusting for quality is challenging because:

      • A vast number of goods need consideration.

      • Subjective differences complicate quality comparisons.

      • Incorporating new goods is problematic due to a lack of historical pricing.

    CPI Substitution Bias

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    • CPI traditionally employs a fixed basket of goods and services.

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    • Consumer behavior in response to price changes isn't accounted for, leading to overstated inflation figures.

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    • Example of Base Year Cost
      

      Item	2015 Price	2015 Spending
      Coffee	$1.00	$50.00
      Tea	$1.00	$50.00
      Scones	$1.00	$100.00
      Total		$200.00
      Example of 2020 Prices with Substitution

      Item	2020 Price	2020 Spending
      Coffee	$2.00	$100.00
      Tea	$1.00	$50.00
      Scones	$1.50	$150.00
      Total		$300.00

      • According to CPI, the basket’s value would be inflated to 1.50 due to perceived increased costs.

      • However, with the substitution of goods (tea instead of coffee), the total spending reflects 1.25, indicating a misunderstanding of consumer experience.

      The Costs of Inflation

      • The price level serves as a measure of the overall level of prices at a given moment, as assessed through indices like the CPI.

      • The relative price of a specific good refers to a comparison of its price against those of other goods and services, calculated as a ratio.

      • A one-time doubling of gas prices impacts inflation minimally while significantly raising gasoline's relative price.

      Relative Prices and Inflation

      • Changes in relative prices can happen independently of overall inflation.

      • Examples of relative price changes:

        • Higher: Beach hotels, cruises, gas prices.

        • Lower: Fresh fruit and vegetables, heating oil.

      Inflation Data Summary

      Year	CPI	Inflation
      2018	1.20
      2019	1.32	10%
      2020	1.40	6%

      Noisy Prices and Information Transfer

      • Prices signal crucial information about production costs and consumer valuation.

      • Inflation introduces ambiguity, hindering clear interpretation of price changes, complicating market interactions.