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Elasticity

Elasticity. Coffee Question. Suppose two partners are arguing about a coffeeshop that is losing money. One of the partner thinks they need to raise prices - that way they will make more money on each cup of coffee they sell.

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Elasticity

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  1. Elasticity

  2. Coffee Question • Suppose two partners are arguing about a coffeeshop that is losing money. • One of the partner thinks they need to raise prices - that way they will make more money on each cup of coffee they sell. • The other partner thinks that if the lower prices they will make more money because they will sell a lot more cups of coffee. • Who was right?

  3. Coffee Question • The answer is - it depends. On what? • If you lower the price - will the new sales offset the loss in revenue on each coffee? • If you raise your price - will the loss in sales be offset by the increase in price of coffee? • In other words, how much will the quantity demanded change when price changes?

  4. Demand • We want to know just how much will quantity demanded change when price changes? That is what elasticity of demand measures.

  5. Elasticity of Demand • Elasticity of Demand (Ed) measures the responsiveness of Qd of a good to a changein its P. • Ed = % in Qd % in P • Note that means “change” • Also note that the law of demand implies Ed is negative. We will ignore the negative sign.

  6. Price Elasticity of Demand

  7. Calculating Elasticity of Demand • There are two methods for calculating elasticity - point and arc methods. • First, we will examine the point method.

  8. Point Elasticity …and let’s say we want to find the Elasticity of Demand as we move from point A to Point B... P A 6 B 5 D 0 Qd 2 3 6 7

  9. Point Elasticity • We know • Ed = % in Qd % in P • %can be calculated as the change divided by starting point

  10. Point Elasticity • The Elasticity of Demand (or Ed) is 1/2 divided by -1/6 which equals -3. But we ignore the sign and call it 3. • Ed = % in Qd = 1/2 = 0.5 = - 3 or 3 % in P -1/6 -1.67 • Demand is Elastic • Let’s try that again moving from point C to D on the same curve

  11. Point Elasticity P 6 5 C 2 D 1 0 Qd 2 3 7 8

  12. Point Elasticity • The Elasticity of Demand (or Ed) is 1/7 divided by -1/2 which equals - 0.286 But we ignore the sign and call it 0.286 • Ed = % in Qd = 1/7 = 0.143 = - 0.286 % in P -1/2 -0.50 • Demand is Inelastic

  13. Point Elasticity • Note that Ed is different at different places along the curve. • Specifically, it gets smaller as you move down the curve • Note that elasticity and slope are NOT the same thing. • One last calculation - let’s find the elasticity of demand going from point D to point C

  14. Point Elasticity P 6 5 C 2 D 1 0 Qd 2 3 7 8

  15. Point Elasticity • The Elasticity of Demand (or Ed) is -1/8 divided by 1 which equals -0.125 But we ignore the sign and call it 0.125 • Ed = % in Qd = -1/8 = -0.125 = - 0.125 % in P 1/1 1 • Demand is Inelastic • But this is a different value than before!

  16. Point Elasticity • Note that we get a different elasticity depending on which point we call the starting point. • A solution to this is by using the Arc Method for finding the Elasticity of Demand.

  17. . Change in quantity Change in price . Ed = Sum of Quantities/2 Sum of prices/2 Refinement: Midpoint Formula

  18. Calculating Ed - Arc Elasticity • Ed = % in Qd % in P • % in Qd = Qd2 - Qd1= Qd ____(Qd1 + Qd2)/2 Average Qd • % in P = P2 - P1= P___(P1 + P2)/2 Average P

  19. Arc Elasticity • As you can see from the equations, it doesn’t matter which is the starting point you will get the same number for the elasticity. • Using points C and D we get • % in Q = (1/(7+8)/2) = 1/7.5 = 0.133 • % in P = (-1/(1+2)/2) = -1/1.5 = 0.667 • The arc elasticity of demand is ED = .133/.667 = .2

  20. Price Elasticity of Demand along a Demand Curve

  21. How Do We Interpret Elasticity? • If Ed = 2, means the ratio of %  Q to the % P is 2 to 1 or: • a 1% change in price will cause a 2% change in quantity demanded. • a 2% change in price will cause a 4% change in quantity demanded, and so on.

  22. Degrees of Ed • Inelastic • Ed = % in Qd % in P • Ed < 1 • % in Qd < % in P • For every 1% change in P, • Qd changes by less than 1%

  23. Degrees of Ed • Unitary Elastic • Ed = % in Qd % in P • Ed = 1 % in Qd = 1 % in P • Ed = 1 • For every 1% change in P, • Qd changes by 1% (in opposite direction)

  24. Degrees of Ed • Elastic • Ed = % in Qd % in P • Ed > 1 • % in Qd > % in P • For every 1% change in P, • Qd changes by more than 1% (in opposite direction)

  25. Degrees of Ed • Perfectly Elastic • Ed = % in Qd % in P • Ed = % in Qd 0 • The price of the good never changes, no matter how much consumers purchase of the good.

  26. Elasticity P Perfectly Elastic 0 Qd

  27. Elasticity P Perfectly Inelastic 0 Qd

  28. Generalizing about Elasticity • Notice that the vertical D curve has an elasticity of zero and the flat D curve has an elasticity of infinity. • As the demand curve goes from vertical to horizontal the elasticity is going from 0 to infinity • In other words, the flatter the demand curve, the greater the elasticity

  29. Elasticity P Relatively Elastic 0 Qd

  30. Elasticity Relatively Inelastic P Relatively Elastic 0 Qd

  31. The Coffee Problem • Back to the Coffeehouse question - should they raise or lower price? • We said that depended on how much sales will change when they change price • In other words, it depends on the elasticity

  32. Total Revenue • Total Revenue = P x Q • The coffeehouse is interested in how TR (total revenue) changes as p and q change

  33. Total Revenue Calculation - Example • Price $1 Qd = 100 TR = $100 • Price $2 Qd = 70 TR = $140

  34. Total Revenue and Elasticity • Let’s say demand is inelastic. Then if the coffeehouse raises prices 10%, the sales will drop by less than 10% • In other words, the gain in revenue from higher prices is greater than the loss in revenue from lost sales.Therefore, Total Revenue will rise

  35. Total Revenue and Elasticity • If they lowered prices, though, the loss of revenue from higher prices would be greater than the gain from increased sales, so Total Revenue will fall

  36. Elasticity and Total Revenue P Loss in Revenue Gain in Revenue Relatively Inelastic 0 Qd

  37. Total Revenue Test If P and TR or P and TR Demand is Inelastic

  38. Total Revenue and Elasticity • Let’s say demand is elastic. Then if the coffeehouse raises prices 10%, the sales will drop by more than 10% • In other words, the gain in revenue from higher prices is less than the loss in revenue from lost sales.Therefore, Total Revenue will fall

  39. Total Revenue and Elasticity • If they lowered prices, though, the loss of revenue from higher prices would be less than the gain in revenue from increased sales, so Total Revenue will rise

  40. Elasticity and Total Revenue P P TR Loss in Revenue Relatively Elastic Gain in Revenue 0 Qd

  41. Total Revenue Test If P and TR or P and TR Demand is Elastic

  42. Total Revenue and Elasticity Elastic Unitary Inelastic

  43. Total Revenue and Demand Elastic Elasticity = 1 $ Inelastic Demand Q $ Total Revenue Q

  44. Elasticity and Total Revenue P Loss in Revenue Gain in Revenue Unitary Elastic 0 Qd

  45. Total Revenue Test If P and TR is unchanged Demand is Unitary

  46. Elasticity and Total Revenue Elastic Inelastic Unitary

  47. Determinants of Ed • Availability of Substitutes • As there are more substitutes, demand is more elastic (and vice versa) • Example: • Insulin has no substitutes if diabetic and demand is very inelastic. • Wal-Mart Brand Cola has many substitutes and hence, demand is very elastic

  48. Determinants of Ed • Amount of Consumers Budget • The less expensive a good is as a fraction of our total budget, the more inelastic the demand for the good is (and vice versa). • Example: • Price of cars go up 10% (from $20,000 to $22,000) • Price of soda goes up 10% (from $0.50 to $0.55) • Demand is more effected by the price of cars increasing.

  49. Determinants of Ed • Time • The longer the time frame is, the more elastic the demand for a good is (and vice versa). • Example - Price of Gasoline Increases • Immediately: can’t do much, still need to get to work, school, etc. • Short-run: find a car pool, ride bike, etc. • Long-run: next car you buy uses less gas.

  50. Determinants of Ed • Necessities vs. Luxuries • The more necessary a good is, the more inelastic the demand for the good (and vice versa). • Example: Insulin

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