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Goals

Lecture Notes: Econ 203 Introductory Microeconomics Lecture/Chapter 5: Elasticity and its applications M. Cary Leahey Manhattan College Fall 2012. Goals. Explain the concept of elasticity as an extension of supply and demand analysis of earlier chapters

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Goals

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  1. Lecture Notes: Econ 203 Introductory MicroeconomicsLecture/Chapter 5: Elasticity and its applicationsM. Cary LeaheyManhattan CollegeFall 2012

  2. Goals • Explain the concept of elasticity as an extension of supply and demand analysis of earlier chapters • Note that is is a short-hand way of categorizing supply and demand responsiveness • Investigate the distinction between short-run and long run (elasticity's) • Look at various kinds of elasticity –own price and cross-price, etc

  3. Understanding elasticity via a direct example Running a business selling websites at $200 per site Currently selling 12 websites Costs are rising What should you do, hike charges to $250 per site? What will happen to my business if I hike prices? 3

  4. Elasticity – First pass Elasticity measures how much one variable (y) responds to a change in another variable (x) In this example, we are interested in one type of elasticity, how much the demand for websites responds to changes in their prices. Formal definition: elasticity is a numerical measure of the responses of Qd or Qs to one of its determinants, e.g. the price elasticity of quantity demands or Qd. 4

  5. Determinants of price elasticity Price elasticity of demand depends on: extent of “close” substitutes whether good is necessity or luxury how homogenous is the good time horizon – how long do participants have to adjust? 5

  6. Price elasticity of demand – most common “kind” Price elasticity of demand = % change in Qd/ % change in P Price elasticity measures how much Qd responds to change in P 6

  7. 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%

  8. Calculating percentage changes (1) 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%

  9. Calculating percentage changes (2) P B D $250 A Q $200 8 12 0 Problem: The standard method gives different answers depending on where you start. 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

  10. Calculating percentage changes (3) So, we instead use the midpoint method: end value – start value x 100% midpoint 0 • The midpoint is the number halfway between the start and end values, the average of those values. • It doesn’t matter which value you use as the start and which as the end—you get the same answer either way!

  11. Calculating percentage changes (4) 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

  12. Gasoline demand in the short run vs. long run 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. Price elasticity is higher in the long run than short run Example from the fist 1973 OPEC price shock 0

  13. Kinds of demand curves • Price elasticity of demand is closely related to the slope of the curve. • Rule of thumb: • The flatter the curve, the larger the elasticity. • The steeper the curve, the smaller the elasticity. • Some nomenclature: • Unitary elasticity = 1 or % change in Qd = % change in price • Elastic demand > 1 or % change in Qd > % change in price • Inelastic demand > 1 or % change in Qd < % change in price Some examples to follow

  14. Perfectly inelastic demand” (one extreme case) % 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: none P falls by 10% Elasticity: 0 Q changes by 0%

  15. Inelastic demand % 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 Consumers’price sensitivity: relatively low P falls by 10% Elasticity: < 1 Q rises less than 10%

  16. Unit elastic demand % 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%

  17. Elastic demand % 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%

  18. Perfectly elastic demand (the other extreme) % change in Q Price elasticity of demand = = % change in P P D Q Q2 Q1 0 any % = infinity 0% D curve: horizontal P1 P2 = Consumers’price sensitivity: extreme P changes by 0% Elasticity: infinity Q changes by any %

  19. Price elasticity and total revenue Returning to the initial example/problem, if you raise your price of websites from $200 to $250, would revenue rise or fall? Total revenue (TR) = P x Q A rise in P increases per unit revenue, TR/P But lowers Q The ultimate effect depends on the price elasticity of demand Price elasticity = % change in Q / % change in P If demand is elastic, then % change in Q > % change in P Revenue falls as revenue per unit increase (P) is smaller than the change in Q 19

  20. Price elasticity and total revenue, comparing the “boxes” 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 increased revenue due to higher P lost revenue due to lower Q When D is elastic, a price increase causes revenue to fall. Demand for your websites

  21. Price elasticity and total revenue, comparing the “boxes” 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 lost revenue due to lower Q When D is inelastic, a price increase causes revenue to rise. Demand for your websites

  22. Price elasticity of supply Price elasticity of supply = % change in Qs / % change in P Price elasticity measures how much Qs responds to change in P It measures sellers price sensitivity 22

  23. Determinants of price elasticity Price elasticity of supply depends on: extent of “close” substitutes whether good is necessity or luxury how homogenous is the good time horizon – how long do participants have to adjust? In long-run, all inputs are variable (auto transplant example) 23

  24. Kinds of supply curves Price elasticity of supply is closely related to the slope of the curve. Rule of thumb: The flatter the curve, the larger the elasticity. The steeper the curve, the smaller the elasticity. Some nomenclature: Unitary elasticity = 1 or % change in Qs = % change in price Elastic supply > 1 or % change in Qs > % change in price Inelastic supply > 1 or % change in Qs < % change in price Some examples to follow 24

  25. 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%

  26. 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%

  27. 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%

  28. 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%

  29. 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%

  30. 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 %

  31. Other elasticities • Income elasticity of demand, % change in Qd / % change in income • Cross price elasticity of demand, % change in Qd for good 1 / % change in price of good 2 • Beef/chicken or tomato/pizza is a good example • For substitutes, cross price elasticity is positive • For complements the cross price elasticity is negative.

  32. Summary Elasticity measures the responsive of Qs and Qd to change in one of its determinants, usually price. Defines as the % change in Qs or Qd / % change in P Unitary elasticity = % change in Q = % change in P Elastic = % change in Q > % change in P Inelastic = % change in Q < % change in P Elasticities tend to rise from the short-run to the long-run Cross price elasticity of demand measures responsiveness of Qd of good 1 to change in price of good 2 Substitutes have a positive elasticity Complements have a negative elasticity 32

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