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Elasticity as a measure of responsiveness Y = Effect variable X = Cause variable Y=ƒ(X) Y=α–βX Where α & β are the coefficients Summing UP Introductory Economic Lecture 6 Elasticity Definitions Computations Recap Y = α – βX in Y-X space Y E (elastic) C P R Q B IE (inelastic) A O X β = slope = ∆Y / ∆X CA / AB > PQ / QR Real world example Qd E ( elastic ) C P R Q B IE ( inelastic ) A P Conventional representation P IE ( inelastic ) R B C A P E ( elastic ) Q Qd Slope of a demand curve Slope of a demand curve = β Higher slope = Inelastic demand curve (Steep) Lower slope = Elastic demand curve (Flat) Price elasticity of other variables Y=ƒ(X) 1. Y = Qd & X = Price Price elasticity of demand. 2. Y = Qs & X = Price Price elasticity of supply. 3. Y = Qd & X = Income Income elasticity of demand. 4. Y = Qda & X = Priceb Cross price elasticity of demand. Formal definition of the four combinations 1. Price elasticity of demand can be defined as PЄd = Percentage change in Quantity Demanded Percentage change in Price Where Є = Epsilon; universal notation for elasticity. PЄd = Percentage change in Quantity Demanded Percentage change in Price Example If, for example, a 20% increase in the price of a product causes a 10% fall in the Quantity demanded , the price elasticity of demand will be: PЄd = - 10% = - 0.5 20% Formal definition of the four combinations 2. Price elasticity of supply can be defined as PЄs = Percentage change in Quantity Supplied Percentage change in Price PЄs = Percentage change in Quantity Supplied Percentage change in Price Example If a 15% rise in the price of a product causes a 15% rise in the quantity supplied, the price elasticity of supply will be: PЄs = 15 % = 1 15 % Formal definition of the four combinations 3. Income elasticity of demand can be defined as YЄd = Percentage change in Quantity Demanded Percentage change in Income YЄd = Percentage change in Quantity Demanded Percentage change in Income Example If a 2% rise in the consumer’s incomes causes an 8% rise in product’s demand, then the income elasticity of demand for the product will be : YЄd = 8% = 4 2% Formal definition of the four combinations 4. Cross price elasticity of demand can be defined as PbЄda = Percentage change in Demand for good a Percentage change in Price of good b PbЄda = Percentage change in Demand for good a Percentage change in Price of good b Example If, for example, the demand for butter rose by 2% when the price of margarine rose by 8%, then the cross price elasticity of demand of butter with respect to the price of margarine will be. PbЄda = 2% = 0.25 8% PbЄda = Percentage change in Demand for good a Percentage change in Price of good b Example If, on the other hand, the price of bread (a compliment) rose, the demand for butter would fall. If a 4% rise in the price of bread led to a 3% fall in the demand for butter, the cross-price elasticity of demand for butter with respect to bread would be : PbЄda = - 3% = - 0.75 4% 8 0 < |Є|< (for absolute values of elasticity) Є=0 P P Є<1 Qd P Є=1 Qd P Є >1 Qd P Є=α Qd Inelastic Elastic Qd Perfectly Inelastic Unit Elastic Perfectly Elastic Total revenue and elasticity Firm A Firm B O O * Not perfect competition Firm A P OAFD > OBTC 10 D F TR as P Inelastic demand Curve 6C T A B O 90 100 Qd Firm B P OVZU > OYUR TR as P Elastic demand curve R U 7 U Z 6 Y V O 40 100 Qd Numerical calculation of elasticity for firm A Є = percentage change in Qd P percentage change in P 10 D F = 90 – 100 10 – 6 100 6 6C T = - 0.15 A B O 90 100 Qd Numerical calculation of elasticity for Firm B Є = percentage change in Qd percentage change in P P = 40 – 100 7–6 100 6 R U 7 =-3.6 U Z 6 Y V O 40 100 Qd Elastic demand between 2 points P 8 ЄKL = percentage change in Qd K percentage change in P 6 L = 16– 8 ÷ 6–8 8 8 = -4 O 8 16 Qd TR as the P Inelastic demand between 2 points ЄGH = percentage change in Qd P percentage change in P G = 36– 28 ÷ 1 – 3 3 28 3 =-3 H 1 7 O 28 36 Qd TR as the P Overview of previous example ЄKL = percentage change in Qd percentage change in P = 16– 8 ÷ 6 – 8 8 8 = -4 ЄLK = percentage change in Qd percentage change in P = 8 – 16 ÷ 8 – 6 16 6 = -3 2 Concept of arc elasticity As Є = ∆ Q ÷ ∆P Q P To measure arc elasticity we take average values for Q and P respectively. ЄKL = 16– 8 ÷ 6–8 =-7 12 7 3 ЄLK = 8 – 16 ÷ 8– 6 =-7 12 7 3 average elasticity along arc KL or LK is - 7/ 3 Point elasticity Є=∆Q ÷ ∆P Q P Є= ∆Q x P ∆P Q d = infinitely small change in price Є=dQ x P dP Q A straight line demand curve will have a different Є at each point on it except Є = 0 or Є = α . Previous example P dP = -1 8 K dQ 4 L P at K = 8 = 1 6 Q 8 Є = - 4 x 1 = -4 Qd O 8 16 P at L = 6 = -3 Q 16 8 Є=-4x3 =-3 8 2 Qd = 60 – 15P + P2 P 60 - 15 P P2 Qd (000s) 0 60 0 0 60 1 60 -15 1 46 2 60 -30 4 34 3 60 -45 9 24 4 60 -60 16 16 5 60 -75 25 10 6 60 -90 36 6 7 Qd (000s) 6 5 Price 4 3 2 1 0 0 20 40 60 80 Quantity demanded PЄd = d Q x P dP Q Differentiating the demand Equation Given Qd = 60 – 15P + P2 then dQ/dP = -15 + 2P Thus at a price of 3 for example, dQ/dP = -15 + ( 2 x 3 ) = -9 Thus price Elasticity of demand at Price 3 is - 9 x P/Q = - 9 x 3 / 24 = - 9 / 8