Elasticity and its Application

Definition of Elasticity Elasticity measures the responsiveness of one variable to changes in another variable How much does Y (dependent variable) change if X changes by 1% (independent variable)

Examples Price elasticity of demand Income elasticity of demand Cross price elasticity of demand Price elasticity of supply

Price Elasticity of Demand (P  D ) Responsiveness of quantity demanded to a change in price The percentage change in quantity demanded, resulting from a 1% change in price P  D = %  Q D / %  P

Quantity Price O Q3Q3 Q2Q2 Q1Q1 P1P1 P2P2 P3P3 c S2S2 S1S1 D D'D' a b The effect on price of a shift in supply depends on the responsiveness of demand to a change in price. Market supply and demand

Determinants of P  D Availability of close substitutes Necessities versus luxuries Definition of the market Time horizon

P (£) Q (000s) Demand Measuring elasticity using the arc method m n

P (£) Q (000s)  Q  P mid Q mid P  P  d = Demand m n  Q = 10  P = –2 Mid P 7 Mid Q 15 Measuring elasticity using the arc method

P (£) Q (000s)  Q  P mid Q mid P  P  d = 10   = Demand m n  Q = 10  P = –2 Mid P 7 Mid Q 15 Measuring elasticity using the arc method

P (£) Q (000s)  Q  P mid Q mid P  P  d = 10   = =  2.33 Demand m n  Q = 10  P = –2 Mid P 7 Mid Q 15 Measuring elasticity using the arc method

P  D & Consumer Expenditure Total Consumer Expenditure / Firm’s total revenue TE (TR) = P x Q Applications to pricing decisions

Elastic Demand Elasticity greater than 1 ( P  D  Effect of price change –P rises: TE falls –P falls: TE rises

P(£) Q (millions of units per period of time) 0 a D Elastic demand between two points Expenditure falls as price rises b Expenditure rises as price falls

Inelastic Demand Elasticity less than 1 ( P  D  Effects of a price change –P rises: TE rises –P falls: TE falls

a 4 20 P(£) Q (millions of units per period of time) 0 D Expenditure rises as price rises Inelastic demand between two points 8 15 c Expenditure falls as price falls

Special cases P  D = 0 (Perfectly Inelastic Demand) P  D =  (Perfectly Elastic Demand) P  D = 1 (Unit Elastic Demand)

P2P2 P Q O Q1Q1 P1P1 D b a Perfectly inelastic demand (P  D = 0)

Q2Q2 P Q O Q1Q1 P1P1 D a b Perfectly elastic demand (P  D =  )

P Q O D a Unit elastic demand (P  D = 1) b Expenditure stays the same as price changes

Price Elasticity of Supply (P  S ) Responsiveness of quantity supplied to a change in price The percentage change in quantity supplied, resulting from a 1% change in price P  S = %  Q S / %  P

Price elasticity of supply P Q O P0P0 Q0Q0 S1S1

P Q O P1P1 Q2Q2 P0P0 Q0Q0 Q1Q1 S2S2 S1S1 Price elasticity of supply

Income elasticity of demand ( Y  D ) Responsiveness of demand to a change in consumer incomes The percentage change in quantity demanded, resulting from a 1% change in consumers income Y  D = %  Q D / %  Y

Income elasticity of demand ( Y  D ) Normal goods: –Positive income elasticity –If the income increases (decreases) the quantity demanded increases (decreases) –Example: Clothing, wine Inferior goods: –Negative income elasticity –If the income increases (decreases) the quantity demanded decreases (increases) –Example: public transport

Cross-Price Elasticity of Demand ( C  Dab ) The responsiveness of demand for one good to a change in the price of another. The percentage change in quantity demanded of one good, resulting from a 1% change in price of another good. C  Dab = %  Q Da / %  P b

Cross-Price Elasticity of Demand ( C  Dab ) Substitutes: –Positive cross-price elasticity –If the price of good B increases the demand for good A increases –Example: hamburgers & burritos Complements: –Negative income elasticity –If the price of good B increases the demand for good A decreases –Example: crude oil & cars

Why are elasticity useful? Managers –Price elasticity of demand: Pricing strategy –Cross-price elasticity of demand: Defining the company’s market –Income elasticity: Forecast long-term demand Government policy –Price elasticity of demand: Decision on Tax rate –Cross-price elasticity of demand: Competitive forces in a market