Revision: Demand and Supply: Basic Concepts >> Elasticity of Demand Economic Applications (English Medium) ICSE Class 10 CISCE

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.

 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

• "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.

• 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.

• "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

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

Where,

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

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

• 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.

• 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:
  \[\mathrm{Ed}=\frac{\text{Percentage change in Quantity demanded}}{\text{Percentage change in Price}}\]
  \[\mathrm{Ed}=\frac{\%\triangle\mathrm{Q}}{\%\triangle\mathrm{P}}\]

• 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.

• 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.