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Elasticity as a measure of responsiveness

Elasticity as a measure of responsiveness. Y = Effect variable X = Cause variable Y = ƒ ( X ) Y = α – β X Where α & β are the coefficients. Summing UP. Introductory Economic Lecture 6. Elasticity. Definitions Computations. Recap. Y = α – β X in Y-X space. Y.

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Elasticity as a measure of responsiveness

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  1. Elasticity as a measure of responsiveness Y = Effect variable X = Cause variable Y = ƒ ( X ) Y = α – β X Where α & β are the coefficients

  2. Summing UP

  3. Introductory Economic Lecture 6

  4. Elasticity Definitions Computations

  5. Recap

  6. Y = α – βX in Y-X space Y E (elastic) C P R Q IE (inelastic) B A O X β = slope = ∆Y / ∆X CA / AB > PQ / QR

  7. Real world example Qd E ( elastic ) C P R Q IE ( inelastic ) B A P

  8. Conventional representation P IE ( inelastic ) R B C A E ( elastic ) P Q Qd

  9. Slope of a demand curve Slope of a demand curve = β Higher slope = Inelastic demand curve (Steep) Lower slope = Elastic demand curve (Flat)

  10. Price elasticity of other variables Y = ƒ ( X ) • Y = Qd & X = Price Price elasticity of demand. • Y = Qs & X = Price Price elasticity of supply. • Y = Qd & X = Income Income elasticity of demand. • Y = Qda & X = PricebCross price elasticity of demand.

  11. 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.

  12. 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%

  13. 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

  14. 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 %

  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

  16. 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%

  17. 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

  18. 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%

  19. 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%

  20. 8 0 <|Є|< (for absolute values of elasticity) Є = 0 P Є < 1 P Qd P Є = 1 Qd Є >1 P Qd P Є = α Qd Elastic Inelastic Qd Perfectly Elastic Perfectly Inelastic Unit Elastic

  21. Total revenue and elasticity Firm B Firm A O O * Not perfect competition

  22. Firm A P OAFD > OBTC TR as P Inelastic demand Curve D F 10 C T 6 A B Qd O 90 100

  23. Firm B OVZU > OYUR TR as P Elastic demand curve P R U 7 Z U 6 Y V O 100 Qd 40

  24. Numerical calculation of elasticity for firm A Є = percentage change in Qd percentage change in P = 90 – 10010 – 6 100 6 = - 0.15 P D F 10 C T 6 A B O 90 100 Qd

  25. Numerical calculation of elasticity for Firm B Є = percentage change in Qd percentage change in P = 40 – 1007 – 6 100 6 = - 3 . 6 P R U 7 Z U 6 Y V O 100 Qd 40

  26. Elastic demand between 2 points P ЄKL = percentage change in Qd percentage change in P = 16– 8÷6 – 8 8 8 = - 4 8 K L 6 Qd O 8 16 TR as the P

  27. Inelastic demand between 2 points ЄGH = percentage change in Qd percentage change in P = 36– 28 ÷ 1 – 3 28 3 = - 3 7 P G 3 H 1 Qd O 28 36 TR as the P

  28. 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

  29. 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

  30. Є = ∆ Q÷∆ P Q P Point elasticity Є = ∆ Q x P ∆ P Q d = infinitely small change in price Є = d Q x P d P Q A straight line demand curve will have a different Є at each point on it except Є = 0 or Є = α .

  31. Previous example P dP = -1 dQ 4 8 K L P at K = 8 = 1 Q 8 Є = - 4 x 1 = -4 6 Qd P at L = 6 = -3 Q 16 8 Є = - 4 x 3 = - 3 8 2 8 O 16

  32. Qd = 60 – 15P + P2

  33. Qd (000s) Price Quantity demanded

  34. PЄd = d Q x P d P 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

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