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Elasticity and its Application

5. Elasticity and its Application. 弹性及其应用. What is elasticity? What kinds of issues can elasticity help us understand? What is the price elasticity of demand? How is it related to the demand curve? How is it related to revenue & expenditure?

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Elasticity and its Application

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  1. 5 Elasticity and its Application 弹性及其应用

  2. What is elasticity? What kinds of issues can elasticity help us understand? What is the price elasticity of demand? How is it related to the demand curve? How is it related to revenue & expenditure? What is the price elasticity of supply? How is it related to the supply curve? What are the income and cross-price elasticities of demand? 什么是弹性？弹性能帮助我们理解什么问题？ 什么是需求价格弹性？它与需求曲线有什么联系？它与收益与支出又有什么联系？ 什么是供给价格弹性？它与供给曲线有什么联系？ 什么是需求收入弹性与需求的交叉价格弹性？ In this chapter, look for the answers to these questions: 1

  3. You design websites for local businesses. You charge $200 per website, and currently sell 12 websites per month. Your costs are rising (including the opportunity cost of your time), so you consider raising the price to $250. The law of demand says that you won’t sell as many websites if you raise your price. How many fewer websites? How much will your revenue fall, or might it increase? 你的工作是为本地企业制作网站，制作一个网站收费200美元。目前你每个月能卖出12个网站 你的成本在不断上升（包括你的时间的机会成本），因此你考虑把价格升到250美元 需求定理告诉我们：如果提高价格，你将不能卖出原来这么多的网站。你将少卖出多少网站？你的收益将会减少还是增加？减少或增加多少？ A scenario…一个故事 0 2

  4. Basic idea: Elasticity measures how much one variable responds to changes in another variable. One type of elasticity measures how much demand for your websites will fall if you raise your price. Definition: Elasticity is a numerical measure of the responsiveness of Qd or Qs to one of its determinants. 基本想法：弹性衡量一种变量对另一种变量反应程度的指标 一种弹性衡量如果你提高价格，对你网站的需求会下降多少? 定义: 弹性衡量需求量或供给量对其某种决定因素的反应程度的指标 Elasticity 弹性 0 ELASTICITY AND ITS APPLICATION

  5. Price Elasticity of Demand需求价格弹性 Price elasticity of demand measures how much Qd responds to a change in P. 需求价格弹性衡量一种物品需求量对其价格变动反应程度的指标 Percentage change in Qd Price elasticity of demand = Percentage change in P 0 • Loosely speaking, it measures the price-sensitivity of buyers’ demand. • 简单的说，它衡量卖者需求的价格敏感程度 ELASTICITY AND ITS APPLICATION

  6. Price Elasticity of Demand Price elasticity of demand equals P Percentage change in Qd Price elasticity of demand P1 = P2 Percentage change in P D Q Q1 Q2 15% = 1.5 10% 0 Example: P rises by 10% Q falls by 15% ELASTICITY AND ITS APPLICATION

  7. Price Elasticity of Demand Along a D curve, P and Q move in opposite directions, which would make price elasticity negative. We will drop the minus sign and report all price elasticities as positive numbers. 需求与价格沿着需求曲线往相反方向变化，这使需求价格弹性为负。我们去掉负号，把所有价格弹性表示为正数 P Percentage change in Qd Price elasticity of demand P1 = P2 Percentage change in P D Q Q1 Q2 0 ELASTICITY AND ITS APPLICATION

  8. Calculating Percentage Changes P end value – start value x 100% B start value D $250 A Q $200 8 12 0 Standard method of computing the percentage (%) change: Demand for your websites Going from A to B, the % change in P equals ($250–$200)/$200 = 25% ELASTICITY AND ITS APPLICATION

  9. Calculating Percentage Changes P B D $250 A Q $200 8 12 0 The standard method gives different answers depending on where you start.如果你的初始值不同，标准方法计算出来的结果也就不同 Demand for your websites From A to B, P rises 25%, Q falls 33%,elasticity = 33/25 = 1.33 From B to A, P falls 20%, Q rises 50%, elasticity = 50/20 = 2.50 ELASTICITY AND ITS APPLICATION

  10. Calculating Percentage Changes So, we instead use the midpoint method: end value – start value x 100% midpoint中点 0 • The midpoint is the number halfway between the start & end values, the average of those values.中点是初始值与终值的平均值 • It doesn’t matter which value you use as the “start” and which as the “end” – you get the same answer either way!哪一点看作初始值还是终值并不重要---你都会得到相同的结果 ELASTICITY AND ITS APPLICATION

  11. Calculating Percentage Changes Using the midpoint method, the % change in P equals = 40.0% x 100% 12 – 8 $250 – $200 10 = 22.2% x 100% $225 40/22.2 = 1.8 0 • The % change in Q equals • The price elasticity of demand equals ELASTICITY AND ITS APPLICATION

  12. A C T I V E L E A R N I N G 1Calculate an elasticity Use the following information to calculate the price elasticity of demand for hotel rooms: if P = $70, Qd = 5000 if P = $90, Qd = 3000 11

  13. 50% = 2.0 25% A C T I V E L E A R N I N G 1Answers Use midpoint method to calculate % change in Qd (5000 – 3000)/4000 = 50% % change in P ($90 – $70)/$80 = 25% The price elasticity of demand equals 12

  14. To learn the determinants of price elasticity, we look at a series of examples. Each compares two common goods. In each example: Suppose the prices of both goods rise by 20%. The good for which Qd falls the most (in percent) has the highest price elasticity of demand. Which good is it? Why? What lesson does the example teach us about the determinants of the price elasticity of demand? 为了找到需求价格弹性的决定因素，我们看下面的这些例子。每个例子都比较了两种物品。 在每个例子中: 假设两种物品的价格都上升了20% 需求数量下降最大(百分比)的物品有最大的需求价格弹性。它是哪种物品？为什么？ 这个例子告诉我们什么是决定需求价格弹性的因素 What determines price elasticity? 0 ELASTICITY AND ITS APPLICATION

  15. The prices of both of these goods rise by 20%. For which good does Qd drop the most? Why? Breakfast cereal has close substitutes (e.g., pancakes, Eggo waffles, leftover pizza), so buyers can easily switch if the price rises. Sunscreen has no close substitutes, so consumers would probably not buy much less if its price rises. Lesson: Price elasticity is higher when close substitutes are available. 这两种物品的价格都上升20%。哪种物品的需求数量下降的最多？为什么？ 谷类早餐有很多相近的替代品（比如，煎饼，Eggo华夫饼，剩余的皮萨等），如果价格上升买者可以很容易购买其他物品 防晒霜没有类似的替代品，如果价格上升，消费者不可能少买太多 总结：有相近替代品的物品的需求往往较富有弹性 EXAMPLE 1: Breakfast cereal vs. Sunscreen谷类早餐vs.防晒霜 0 ELASTICITY AND ITS APPLICATION

  16. The prices of both goods rise by 20%. For which good does Qd drop the most? Why? For a narrowly defined good such as blue jeans, there are many substitutes (khakis, shorts, Speedos). There are fewer substitutes available for broadly defined goods. (There aren’t too many substitutes for clothing, other than living in a nudist colony.) Lesson: Price elasticity is higher for narrowly defined goods than broadly defined ones. 如果两种物品的价格都上涨20%，哪种物品的需求量下降的最多？为什么？ 定义范围狭窄的物品比如蓝色牛仔裤有很多的替代品（卡其，短裤，Speedos等） 定义范围宽泛的物品很少有替代品（衣服没有什么替代品，除非是流行裸体的殖民地） 总结：范围小的市场的需求弹性往往大于范围大的市场的需求弹性 EXAMPLE 2:“Blue Jeans” vs. “Clothing” “蓝色牛仔裤”与 “衣服” 0 ELASTICITY AND ITS APPLICATION

  17. The prices of both of these goods rise by 20%. For which good does Qd drop the most? Why? To millions of diabetics, insulin is a necessity. A rise in its price would cause little or no decrease in demand. A cruise is a luxury. If the price rises, some people will forego it. Lesson: Price elasticity is higher for luxuries than for necessities. 如果两种物品的价格都上涨20%，哪种物品的需求量下降的最多？为什么？ 对数以百万计的糖尿病患者来说，胰岛素是必需品。胰岛素价格的上升基本上不会引起需求的下降 游轮是奢侈品，如果价格上升，有些人会放弃购买 总结：奢侈品的需求弹性要大于必需品的需求弹性 EXAMPLE 3:Insulin vs. Caribbean Cruises胰岛素与加勒比游轮 0 ELASTICITY AND ITS APPLICATION

  18. The price of gasoline rises 20%. Does Qd drop more in the short run or the long run? Why? There’s not much people can do in the short run, other than ride the bus or carpool. In the long run, people can buy smaller cars or live closer to where they work. Lesson: Price elasticity is higher in the long run than the short run. 汽油价格上涨20%，短期还是长期的汽油需求量会下降更多？为什么？ 短期内，人们除了坐公交或者自己开车之外，并没有什么其他办法 长期中，人们可以购买省油的小排量汽车或搬到上班地方附近居住 总结：相对于短期，物品的需求往往在长期更富有弹性 EXAMPLE 4:Gasoline in the Short Run vs. Gasoline in the Long Run短期的汽油与长期的汽油 0 ELASTICITY AND ITS APPLICATION

  19. The price elasticity of demand depends on: the extent to which close substitutes are available whether the good is a necessity or a luxury how broadly or narrowly the good is defined the time horizon – elasticity is higher in the long run than the short run 需求价格弹性取决于： 相近替代品的可获得性 物品是必需品还是奢侈品 物品的定义是宽泛还是狭义 时间框架—长期比短期更富有弹性 The Determinants of Price Elasticity: A Summary 0 ELASTICITY AND ITS APPLICATION

  20. The price elasticity of demand is closely related to the slope of the demand curve. Rule of thumb: The flatter the curve, the bigger the elasticity. The steeper the curve, the smaller the elasticity. Five different classifications of D curves.… 需求价格弹性与需求曲线的斜率密切相关 拇指规则：通过某一点的需求曲线越平坦，需求的价格弹性就越大通过某一点的需求曲线越陡峭，需求的价格弹性就越小 需求曲线的五种不同分类.… The Variety of Demand Curves各种需求曲线 0 ELASTICITY AND ITS APPLICATION

  21. “Perfectly inelastic demand” (one extreme case) “完全无弹性的需求” (一个极端例子) % change in Q Price elasticity of demand = = % change in P P D P1 P2 Q Q1 0 0% = 0 10% D curve: vertical Consumers’ price sensitivity:消费者的价格敏感度 none P falls by 10% Elasticity: 0 Q changes by 0% ELASTICITY AND ITS APPLICATION

  22. “Inelastic demand” “缺乏弹性的需求” % change in Q Price elasticity of demand = = % change in P P P1 P2 Q D Q1 Q2 0 < 10% < 1 10% D curve: relatively steep相对陡峭 Consumers’ price sensitivity: relatively low P falls by 10% Elasticity: < 1 Q rises less than 10% ELASTICITY AND ITS APPLICATION

  23. “Unit elastic demand” “单位弹性需求” % change in Q Price elasticity of demand = = % change in P P P1 D P2 Q Q1 Q2 0 10% = 1 10% D curve: intermediate slope Consumers’ price sensitivity: intermediate P falls by 10% Elasticity: 1 Q rises by 10% ELASTICITY AND ITS APPLICATION

  24. “Elastic demand” “富有弹性的需求” % change in Q Price elasticity of demand = = % change in P P P1 D P2 Q Q1 Q2 0 > 10% > 1 10% D curve: relatively flat Consumers’ price sensitivity: relatively high P falls by 10% Elasticity: > 1 Q rises more than 10% ELASTICITY AND ITS APPLICATION

  25. “Perfectly elastic demand” (the other extreme) “完全有弹性的需求” (另一个极端例子) % change in Q Price elasticity of demand = = % change in P P D Q Q1 Q2 0 any % = infinity无穷大 0% D curve: horizontal P1 P2 = Consumers’ price sensitivity: extreme P changes by 0% Elasticity: infinity Q changes by any % ELASTICITY AND ITS APPLICATION

  26. Elasticity of a Linear Demand Curve线性需求曲线的弹性 The slope of a linear demand curve is constant, but its elasticity is not.线性需求曲线的斜率为常数，但它的弹性不是常数 67% 200% 40% E= E= E= = 1.0 = 0.2 = 5.0 P 67% 40% 200% $30 20 10 $0 Q 0 20 40 60 0 ELASTICITY AND ITS APPLICATION

  27. Continuing our scenario, if you raise your pricefrom $200 to $250, would your revenue rise or fall? Revenue = P x Q A price increase has two effects on revenue: Higher P means more revenue on each unit you sell. But you sell fewer units (lower Q), due to Law of Demand. Which of these two effects is bigger? It depends on the price elasticity of demand. 继续我们的故事，如果你把价格从$200上升到$250，你的收益会增加还是减少？ 收益 = P x Q 价格上升对收益有两种影响： 更高的价格意味着你在售出的每单位物品上会有更多的收益 但根据需求定理，你售出的物品数量会减少 两种影响哪种更大？这要取决于需求价格弹性 Price Elasticity and Total Revenue总收益与需求价格弹性 0 ELASTICITY AND ITS APPLICATION

  28. Price Elasticity and Total Revenue If demand is elastic, then price elast. of demand > 1 如果需求是有弹性的，那需求价格弹性> 1 % change in Q > % change in P 需求量变动百分比 > 价格变动百分比 The fall in revenue from lower Q is greater than the increase in revenue from higher P, so revenue falls.需求量减少使收益减少的幅度大于价格上升使收益增加的幅度，总收益减少 Percentage change in Q Price elasticity of demand = Percentage change in P 0 Revenue = P x Q ELASTICITY AND ITS APPLICATION

  29. Price Elasticity and Total Revenue Elastic demand(elasticity = 1.8) P If P = $200, Q = 12 and revenue = $2400. $250 $200 If P = $250, Q = 8 and revenue = $2000. D Q 12 8 0 Demand for your websites lost revenue due to lower Q increased revenue due to higher P When D is elastic, a price increase causes revenue to fall. ELASTICITY AND ITS APPLICATION

  30. Price Elasticity and Total Revenue If demand is inelastic, then price elast. of demand < 1 % change in Q < % change in P The fall in revenue from lower Q is smaller than the increase in revenue from higher P, so revenue rises.需求量减少使收益减少的幅度小于价格上升使收益增加的幅度，总收益增加 In our example, suppose that Q only falls to 10 (instead of 8) when you raise your price to $250. Percentage change in Q Price elasticity of demand = Percentage change in P 0 Revenue = P x Q ELASTICITY AND ITS APPLICATION

  31. Price Elasticity and Total Revenue Now, demand is inelastic: elasticity = 0.82 P If P = $200, Q = 12 and revenue = $2400. $250 $200 D If P = $250, Q = 10 and revenue = $2500. Q 12 10 0 increased revenue due to higher P Demand for your websites lost revenue due to lower Q When D is inelastic, a price increase causes revenue to rise. ELASTICITY AND ITS APPLICATION

  32. A. Pharmacies raise the price of insulin by 10%. Does total expenditure on insulin rise or fall? B. As a result of a fare war, the price of a luxury cruise falls 20%. Does luxury cruise companies’ total revenue rise or fall? A. 药店将胰岛素的价格提高10%，对胰岛素的总支出会增加还是减少？ B. 作为价格战的结果，游轮价格下降了20%。游轮制造公司的收益会增加还是下降？ A C T I V E L E A R N I N G 2Elasticity and expenditure/revenue弹性与支出/收益 31

  33. A C T I V E L E A R N I N G 2Answers • Pharmacies raise the price of insulin by 10%. Does total expenditure on insulin rise or fall? 药店将胰岛素的价格提高10%，对胰岛素的总支出会增加还是减少？ Expenditure = P x Q Since demand is inelastic, Q will fall less than 10%, so expenditure rises. 胰岛素的需求缺乏弹性，需求量下降幅度不超过10%，因此支出增加 32

  34. A C T I V E L E A R N I N G 2Answers B. As a result of a fare war, the price of a luxury cruise falls 20%. Does luxury cruise companies’ total revenue rise or fall? 作为价格战的结果，游轮价格下降了20%。游轮制造公司的收益会增加还是下降？ Revenue = P x Q The fall in P reduces revenue, but Q increases, which increases revenue. Which effect is bigger? Since demand is elastic, Q will increase more than 20%, so revenue rises. 33

  35. One side effect of illegal drug use is crime: Users often turn to crime to finance their habit. We examine two policies designed to reduce illegal drug use and see what effects they have on drug-related crime. For simplicity, we assume the total dollar value of drug-related crime equals total expenditure on drugs. Demand for illegal drugs is inelastic, due to addiction issues. 使用毒品的一个不利影响是犯罪：吸毒上瘾的人往往会有暴力犯罪，以得到吸毒所需要的钱 我们比较两种旨在减少吸毒的政策，并观察它们对与毒品相关的犯罪的影响 为简化起见，我们假定与毒品相关的犯罪的美元价值等于购买毒品的总支出 由于吸毒成瘾，非法毒品的需求是缺乏弹性的 APPLICATION: Does Drug Interdiction Increase or Decrease Drug-Related Crime?禁毒增加还是减少了与毒品相关的犯罪 0 ELASTICITY AND ITS APPLICATION

  36. Policy 1: Interdiction禁毒 new value of drug-related crime与毒品相关的犯罪的新价值 Price of Drugs S2 D1 S1 P2 initial value of drug-related crime P1 Quantity of Drugs Q1 Q2 0 Interdiction reduces the supply of drugs. Since demand for drugs is inelastic, P rises propor-tionally more than Q falls. Result: an increase in total spending on drugs, and in drug-related crime在毒品上的总支出和与毒品相关的犯罪都会增加 ELASTICITY AND ITS APPLICATION

  37. Policy 2: Education new value of drug-related crime Price of Drugs D2 D1 S initial value of drug-related crime P1 P2 Quantity of Drugs Q2 Q1 0 Education reduces the demand for drugs. P and Q fall. Result:A decrease in total spending on drugs, and in drug-related crime.结果：在毒品上的总支出和与毒品相关的犯罪都减少 ELASTICITY AND ITS APPLICATION

  38. Price Elasticity of Supply Price elasticity of supply measures how much Qs responds to a change in P. 供给价格弹性衡量一种物品供给量对其价格变动反应程度的指标 Percentage change in Qs Price elasticity of supply = Percentage change in P 0 • Loosely speaking, it measures sellers’ price-sensitivity. • Again, use the midpoint method to compute the percentage changes.继续使用中点法计算变动的百分比 ELASTICITY AND ITS APPLICATION

  39. Price Elasticity of Supply Price elasticity of supply equals P S Percentage change in Qs Price elasticity of supply = P2 Percentage change in P P1 Q Q1 Q2 16% = 2.0 8% 0 Example: P rises by 8% Q rises by 16% ELASTICITY AND ITS APPLICATION

  40. The slope of the supply curve is closely related to price elasticity of supply. Rule of thumb: The flatter the curve, the bigger the elasticity. The steeper the curve, the smaller the elasticity. Five different classifications.… 供给价格弹性与供给曲线的斜率密切相关 拇指规则：通过某一点的供给曲线越平坦，供给的价格弹性就越大通过某一点的供给曲线越陡峭，供给的价格弹性就越小 五种不同的分类.… The Variety of Supply Curves 0 ELASTICITY AND ITS APPLICATION

  41. “Perfectly inelastic” (one extreme) % change in Q Price elasticity of supply = = % change in P P S P2 Q 0 0% = 0 10% S curve: vertical Sellers’ price sensitivity: P1 none P rises by 10% Elasticity: Q1 0 Q changes by 0% ELASTICITY AND ITS APPLICATION

  42. “Inelastic” % change in Q Price elasticity of supply = = % change in P P S P2 Q Q2 0 < 10% < 1 10% S curve: relatively steep Sellers’ price sensitivity: P1 relatively low P rises by 10% Elasticity: Q1 < 1 Q rises less than 10% ELASTICITY AND ITS APPLICATION

  43. “Unit elastic” % change in Q Price elasticity of supply = = % change in P P S P2 Q Q2 0 10% = 1 10% S curve: intermediate slope Sellers’ price sensitivity: P1 intermediate P rises by 10% Elasticity: Q1 = 1 Q rises by 10% ELASTICITY AND ITS APPLICATION

  44. “Elastic” % change in Q Price elasticity of supply = = % change in P P S P2 Q Q2 0 > 10% > 1 10% S curve: relatively flat Sellers’ price sensitivity: P1 relatively high P rises by 10% Elasticity: Q1 > 1 Q rises more than 10% ELASTICITY AND ITS APPLICATION

  45. “Perfectly elastic”(the other extreme) % change in Q Price elasticity of supply = = % change in P P S Q Q2 Q1 0 any % = infinity 0% S curve: horizontal P1 P2 = Sellers’ price sensitivity: extreme P changes by 0% Elasticity: infinity Q changes by any % ELASTICITY AND ITS APPLICATION

  46. The more easily sellers can change the quantity they produce, the greater the price elasticity of supply. Example: Supply of beachfront property is harder to vary and thus less elastic than supply of new cars. For many goods, price elasticity of supply is greater in the long run than in the short run, because firms can build new factories, or new firms may be able to enter the market. 卖者越容易改变他们的生产数量，供给价格弹性越大 例如：海滨别墅的供给较难改变，因此其供给弹性要低于新汽车的供给弹性 对许多物品而言，长期供给价格弹性都要大于短期供给价格弹性。这是因为企业在长期能建更多的工厂，或者新的企业能够进入市场 The Determinants of Supply Elasticity ELASTICITY AND ITS APPLICATION

  47. A C T I V E L E A R N I N G 3Elasticity and changes in equilibrium • The supply of beachfront property is inelastic. The supply of new cars is elastic.海滨别墅的供给缺乏弹性的，而新汽车的供给是富有弹性的 • Suppose population growth causes demand for both goods to double (at each price, Qd doubles).假设人口数量的增长使对两种物品的需求都翻了一番（就是在在每种价格水平上，需求量加倍） • For which product will P change the most?哪种物品的价格变动更大？ • For which product will Q change the most?哪种物品的产量变动更大？ 46

  48. P S D1 D2 B P2 P1 A Q Q1 Q2 A C T I V E L E A R N I N G 3Answers Beachfront property海滨别墅(inelastic supply): When supply is inelastic, an increase in demand has a bigger impact on price than on quantity. 供给缺乏弹性时，需求增加使价格上升的比例要大于产量增加的比例 47

  49. P D1 D2 S B P2 A P1 Q Q2 Q1 A C T I V E L E A R N I N G 3Answers New cars(elastic supply): When supply is elastic, an increase in demand has a bigger impact on quantity than on price.供给富有弹性时，需求增加使产量增加的比例要大于价格上升的比例 48

  50. How the Price Elasticity of Supply Can Vary供给价格弹性会如何变动 Supply often becomes less elastic as Q rises, due to capacity limits.由于生产能力限制，当供给量越大时，供给价格弹性越小 P S $15 12 4 $3 Q 100 200 500 525 0 elasticity < 1 elasticity > 1 ELASTICITY AND ITS APPLICATION

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