Revision: Elasticity of Demand Eco HSC Commerce (English Medium) 12th Standard Board Exam Maharashtra State Board

• "Elasticity of demand may be defined as the percentage change in quantity demanded to the percentage change in price." - Alfred Marshall
• "The elasticity of demand for a commodity is the rate at which quantity bought changes as the price changes." - A.K. Cairncross
• "Elasticity of demand is a technical term used by the economists to describe the degree of respensiveness of demand of a commodity to a change in its price." -Stonier and Hague
• Elasticity of demand refers to the degree of responsiveness of quantity demanded of a commodity to a change in any of its determinants.

 Cross elasticity of demand is the measure of the responsiveness of demand for a good to a change in the price of a related good.

`"Ec" = ("Proportionate change in quantity demanded of good X")/("Proportionate change in price of good Y")`

It is the measure of the degree of responsiveness of the demand for a good to the changes in its price. It is defined as the percentage change in the demand for a good divided by the percentage change in its price.

e_d = `"Percentage change in demand for good"/"Percentage change in price of that good"`

e_d = `(ΔQ)/(ΔP) xx P/Q`

Where ΔQ = Q₂ − Q₁, change in demand

ΔP = P₂ − P₁, change in price

P₁ = Initial price

Q₁ = Initial quantity

Price elasticity of demand tells us the amount of the change in the quantity demanded of a commodity in response to change in its price. In other words, it measures the degree of change of demand in response to changes in price.

• "Income elasticity of demand means the ratio of the percentage change in the quantity demanded to the percentage change in income." - Watson
• "The responsiveness of demand to change in income is termed as income elasticity of demand." - R.G. Lipsey

• "The Cross elasticity of demand is the proportional change in the quantity of X good demanded resulting from a given relative change in the price of a related good Y ." - Ferguson
• "The Cross elasticity of demand is a measure of the responsiveness of the purchase of Y to a change in the price of X." -Leibafsky

• Prof. Marshall’s Definition:
  PED is the ratio of the percentage change in quantity demanded of a commodity to the percentage change in its price.

• Price elasticity of demand measures the responsiveness or sensitivity of the quantity demanded to changes in the price of a commodity. In simple words, it tells us how much the demand changes when the price changes.

E_y = `"Proportionate change in Quantity Demanded"/"Proportionate change in income"`

\[E_y=\frac{\frac{\Delta Q}{Q}}{\frac{\Delta Y}{Y}}\quad=\frac{\Delta Q}{Q}\div\frac{\Delta Y}{Y}=\frac{\Delta Q}{Q}\times\frac{Y}{\Delta Y}\]

Where:

E_y = Income elasticity of demand
ΔQ = Change in the quantity demanded
Q = Initial demand
ΔY = Change in income
Y = Initial Income

\[e_{xy}=\frac{\Delta Q_X}{Q_X}\times\frac{P_Y}{\Delta P_Y}\]

Where:

• e_xy: Cross elasticity of demand between X & Y
• ΔQ_X: Change in quantity demanded of X
• Q_X: Initial quantity demanded of X
• P_Y: Initial price of Y
• ΔP_Y: Change in price of Y

\[\mathrm{Ed}=\frac{\%\Delta Q}{\%\Delta P}\]

Where,

• Q = original quantity demanded
• ΔQ = change in quantity demanded
• P = original price
• ΔP = change in price
• Alternate Formula:
                                   \[\mathrm{Ed}=\frac{\Delta Q}{Q}\div\frac{\Delta P}{P}=\frac{\Delta Q}{\Delta P}\times\frac{P}{Q}\]

• Law of demand only shows direction (more or less), elasticity shows the degree (how much more or less).
• Some things (necessities) have inelastic demand; luxuries or goods with many substitutes have elastic demand.
• Alfred Marshall introduced this concept and the popular measurement formula.

• YED shows how demand changes with income.
• Luxury goods: YED > 1 → demand grows faster than income.
• Necessities: 0 < YED < 1 → demand grows slower than income.
• Essential goods: YED = 0 → demand stays the same.
• Inferior goods: YED < 0 → demand drops as income rises.

• Measures responsiveness of demand of one good to price changes of another.
• Positive elasticity for substitutes, negative for complements, and zero for unrelated.
• Useful for practical decision-making in business, policy, and trade.

• PED shows the sensitivity of demand to price changes.
• Values: <1 (Inelastic), 1 (Unitary), >1 (Elastic), 0 (Perfectly Inelastic), ∞ (Perfectly Elastic).
• Essential for business pricing, government taxes, and policy planning.

• Perfectly elastic demand means infinite change in quantity due to no or very small change in price.
• It is a theoretical concept.
• Elasticity of demand (Ed) = ∞.
• Demand curve is a horizontal straight line parallel to X-axis.

• Perfectly inelastic demand means quantity demanded does not change despite price change.
• Elasticity of demand (Ed) = 0.
• Rare in practice (e.g., salt, milk).
• Demand curve is a vertical straight line parallel to Y-axis.

• Relatively elastic demand means quantity changes more than proportionately to price.
• Elasticity of demand (Ed) > 1.
• Small price change causes large change in quantity demanded.
• Demand curve is flatter.

• Relatively inelastic demand means quantity changes less than proportionately to price.
• Elasticity of demand (Ed) < 1.
• Large price change causes small change in quantity demanded.
• Demand curve is steep.

• Total Expenditure Formula:
  Total Expenditure (TE) = Price (P) × Quantity Demanded (Q)
• Revenue Method Formula:
  Ed = AR / (AR - MR)
  or
  Ed = Average Revenue / (Average Revenue - Marginal Revenue)
• Arc Elasticity Demand Formula:
  \[\mathrm{E=\frac{Q_{2}-Q_{1}}{Q_{2}+Q_{1}}\div\frac{P_{1}-P_{2}}{P_{1}+P_{2}}}\]
• Proportionate Method Formula:
  \[\mathrm{Ed}=\frac{\text{Percentage change in Quantity demanded}}{\text{Percentage change in Price}}\]
  \[\mathrm{Ed}=\frac{\%\triangle\mathrm{Q}}{\%\triangle\mathrm{P}}\]

• For a non-linear (convex) demand curve, elasticity is measured using a tangent.
• Ed = Lower segment / Upper segment of the tangent at a point.