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This chapter explains index numbers, which are essential for measuring changes in economic variables like prices and production.
Index Numbers – Formula & Equation Sheet
Essential formulas and equations from Statistics for Economics, tailored for Class 11 in Economics.
This one-pager compiles key formulas and equations from the Index Numbers chapter of Statistics for Economics. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Key concepts & formulas
Essential formulas, key terms, and important concepts for quick reference and revision.
Formulas
Simple Aggregative Price Index: P = (ΣP₁ / ΣP₀) × 100
P is the price index, P₁ denotes current prices, and P₀ denotes base prices. This formula computes the overall change in prices relative to a base period.
Weighted Aggregative Price Index: P = (ΣP₁q₁ / ΣP₀q₀) × 100
In this formula, P is the weighted price index, P₁ represents current prices, P₀ denotes base prices, and q represents quantities. This accounts for variances in importance among items.
Laspeyres Price Index: P = (ΣP₁q₀ / ΣP₀q₀) × 100
P represents the index, P₁ are current period prices, q₀ are base period quantities. This index uses base quantities to weigh price changes in the current period.
Paasche Price Index: P = (ΣP₁q₁ / ΣP₀q₁) × 100
P is the index, using current period quantities (q₁) to weigh current prices (P₁) against base prices (P₀). It reflects how current consumption patterns affect the price index.
Consumer Price Index (CPI): CPI = (ΣW_iP_i1 / ΣW_i) × 100
CPI measures average changes in retail prices, where W_i represents the weight and P_i1 the price of the basket of goods in the current period.
Percentage Change in Price: % Change = [(P₁ - P₀) / P₀] × 100
This formula finds the percentage increase or decrease in prices from the base period (P₀) to the current period (P₁).
Cost of Living Index = (Total Expenditure in Current Period / Total Expenditure in Base Period) × 100
This index reflects changes in the cost of living by comparing total expenditures between two distinct periods.
Index of Industrial Production: IIP = (Σ(qᵢ1/Wᵢ)) / (Σ(qᵢ0/Wᵢ)) × 100
IIP calculates the output changes across industrial sectors while considering the weight of each good produced indexed to a base year.
Inflation Rate: Inflation = [(WPI_t - WPI_(t-1)) / WPI_(t-1)] × 100
This formula calculates the inflation rate using the Wholesale Price Index (WPI) across two time points (t and t-1).
Purchasing Power = 1 / (Cost of Living Index)
This formula calculates the purchasing power of money relative to changes in the cost of living, inversely proportional to the index.
Equations
P = (ΣP_i / n)
This equation represents the average price of n commodities, where P_i is the price of each commodity.
Weighted Average Price Index: PW = Σ(W_i × P_i) / ΣW_i
In this equation, PW is the weighted index, W_i is the weight of each item, and P_i is the price of each item calculated over a specific period.
Price Relative: PR_i = (P_i1 / P_i0) × 100
This equation denotes price relatives where P_i1 is the price in the current period and P_i0 in the base period, allowing comparison across time.
CPI for Food = (CPI Food / CPI Base) × 100
This formula allows comparison of the CPI for food items relative to a base year, measuring relative price changes.
WPI = (Σ(W_iP_i1) / ΣW_i) × 100
This equation calculates the Wholesale Price Index using weights (W_i) and current prices (P_i1), important for economic analysis.
Change in Quantity: ΔQ = Q1 - Q0
The variation in production quantities identified as ΔQ is between two distinct time periods, assisting in performance analysis.
Equivalent Salary = (CPI Current / CPI Base) × Salary Base
This equation helps calculate the necessary salary adjustment to maintain purchasing power when CPI values are compared.
Wage Adjustment Factor = CPI-Current / CPI-Base
This factor shows how much wages should be adjusted based on the rise or fall in the Consumer Price Index.
Index Number Formula = (Value at Time t / Value at Base Time) × 100
This generic formula applies to various index types to determine the relative change compared to a selected base period.
Average Weighted Tax Rate = (Σ(wx)) / (Σw)
In tax contexts, this equation facilitates deriving the average tax rate by multiplying weights (expenditures) by tax rates.
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