Consumer Price Index (CPI) and Inflation Calculation Notes

Consumer Price Index (CPI)

• Definition: CPI represents the average change over time in the prices paid by urban consumers for a market basket of consumer goods and services.
• Calculation of CPI:
  • Formula:
    \text{CPI} = \frac{\text{Cost of basket in current year}}{\text{Cost of basket in base year}} \times 100
  • Example Calculation: If the cost today is 1.2 multiplied by 100, the CPI is 120, indicating costs are 20% higher than in the base year.

Understanding Inflation Rate

• Inflation Calculation:
  • Inflation is the percentage change in CPI from one year to the next.
  • Formula:
    \text{Inflation Rate} = \frac{\text{CPI this year} - \text{CPI last year}}{\text{CPI last year}} \times 100
  • Steps to Calculate:
  1. Determine quantity of goods consumed.
  2. Determine price of each good.
  3. Multiply quantity by price to get total cost.
  4. Compare current year cost to base year cost to establish an index where the base year = 100.
  5. Calculate the percentage change to find inflation rate.

Example of Calculating CPI with Two Goods

• Consumption Basket:

  • Define Year 1 as the base year.
  • Goods:
  • Grapes: 50 units
  • Oranges: 100 units

• Prices:

  • Price of grapes: $4 per unit
  • Price of oranges: $3 per unit

• Total Cost Calculation:

  • Grapes cost:
    50 \times 4 = 200
  • Oranges cost:
    100 \times 3 = 300
  • Total cost for the basket:
    200 + 300 = 500

• Base Year CPI Calculation:

  • Since this is the base year, the CPI for this year is:
    \text{CPI} = \frac{500}{500} \times 100 = 100

Consistency of the Consumption Basket

• Important Note:
  • The consumption basket must remain constant over time for accurate CPI calculations. After defining the basket in the base year, calculations are repeated for subsequent years to determine how much it costs to buy the same basket of goods.