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Demand and Elasticities

Demand and Elasticities. Microeconomic Analysis 1-808-07 Tuesday September 8 th 2009. Recap. jbgrou@umich.edu (subject: “HEC”) Office hours Monday 14:00 -15:00 Tuesday 15:30 – 16:30 First Quiz: Tuesday Sept 22 nd HWs: see syllabus for suggested exercises. In-class survey.

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Demand and Elasticities

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  1. Demand and Elasticities Microeconomic Analysis 1-808-07 Tuesday September 8th 2009

  2. Recap • jbgrou@umich.edu (subject: “HEC”) • Office hours • Monday 14:00 -15:00 • Tuesday 15:30 – 16:30 • First Quiz: Tuesday Sept 22nd • HWs: see syllabus for suggested exercises

  3. In-class survey • Reason for choosing HEC: • Top school, good reputation • Trilingual program • Cheap • International student body • Background in Economics • None • French Bacc

  4. In-class survey • Grade objective: • Average answer  A • 10 years from now: • CEO • Travel • Sustainable development • Intl organisation • HR • Consulting • My own firm

  5. In-class survey • Interesting about you: • Many different origins (France, Columbia, Tahiti, etc.) • Small business owner • Skydiver • Drum player • Touched a shark • Speaks four languages • …

  6. Today • Review of last week • Demand • From MV(q) to qid(p) • Elasticities

  7. So far… • Valuation • V(q) vs. MV(q) • Buyer’s decision: P ≤ MV(q) • Seller’s decision: MC(q) ≤ P • Gains from trade  Surplus • Efficiency / Pareto Optimality • MC(q) = MV(q)

  8. Demand

  9. Goals • To go from the behavior of individuals to that of an entire population • To analyze the determining factors of an economy • Being able to understand and to react appropriately to various economic circumstances p D Q

  10. Individual demand

  11. Recall: marginal valuation Quantity Marginal Valuation MV(q) Price 4 0 4 2,53 52 7,51 10 0 3 2 1 MV(q) q 0 5 10

  12. Recall: marginal valuation How many units would this person buy for a price of $2.50? q MV(q) P < MV(q)? 0 4 2,53 52 7,51 10 0

  13. Recall: marginal valuation How many units would this person buy for a price of $2.50? q MV(q) P < MV(q)? 0 4 Yes  Buy! 2,53 Yes  Buy! 52 No  Stop! 7,51 No 10 0 No

  14. From MV(q) to qid(p) • For each price, correspond a quantity demanded by the consumer. • In the previous example, a price of $2.50 corresponds to a demand of 2 units.

  15. Consumer behavior At a given unit price, the consumer will choose the quantity, q, which maximizes her surplus: MV(q) = P. Prix 4 3 surplus P = 2 expenses 1 MV(q) q 0 q = 5 10

  16. Valuation and individual demand MV(q) = P : the consumer’s demand curve coincides with her marginal valuation curve. Price 4 3 P = 2 d = MV 1 q 0 q = 5 10

  17. Market demand

  18. Market demand The aggregate demand of an entire population. Market quantity demanded is the sum of quantities demanded by all individuals:

  19. Market demand PriceInd. quantity Market (4 identical consumers) ($) (q) (Q = 4xq) 0 10 __ 1 7,5__ 2 5__ 3 2,5__ 4 0__

  20. Market demand PriceInd. quantity Market (4 identical consumers) ($) (q) (Q = 4xq) 0 10 40 1 7,5 30 2 5 20 3 2,5 10 4 0 0

  21. Market demand Price The market demand curve is thehorizontal sum of individual demand curves… 5 4 Draw the demand curve of a population made up of 4 consumers with individual market demand, d. 3 2 Quantity demanded 1 d 0 5 10 15 20 25 30 35 40

  22. Market demand Price The market demand curve is thehorizontal sum of individual demand curves… 5 4 3 2 D Quantity demanded 1 d 0 5 10 15 20 25 30 35 40

  23. The demand function Demand for Coca-Cola (undiluted syrup): Qd = 26.17 - 3.98 Pc + 2.25 Pp + 2.60 Ac – 0.62 Ap + 9.58 S + 0.99 Y With: Qd = quantity demanded of Coca-Cola syrup Pc, Pp = prices of Coca-Cola and Pepsi syrups Ac, Ap = advertisement expenditures of Coca-Cola and Pepsi S = seasonal indicator (=1 if spring or summer, =0 otherwise) Y = household income

  24. Factors affecting demand Quantity demanded, Qd, generally depends on… : • …the price of the good (falls when the price rises) • …the price of other goods, Po: • If Po ↑  Qd↑, the goods are substitutes • If Po ↑  Qd ↓, the goods are complements • … household income: • If Y ↑  Qd ↑, the good is normal • If Y ↑  Qd ↓, the good is inferior • …other factors. (Examples?)

  25. Factors affecting demand Quantity demanded, Qd, generally depends on… : • Giffen goods

  26. Exercise Consider the demand for minivans in the U.S.: Qd = 12 – 0,6 P + 0,2 Ps – 3 Pg + 0,2 Y With: Qd = qty demanded (in hundreds of thousands) P = price of a minivan (in thousand $) Ps = price of a station wagon(in thousand $) Pg = price of gasoline (in $ per gallon) Y = household income (in thousand $ per year)

  27. Exercise (cont.) A. Draw the demand curve for Ps = $16,000, Pg = $3/gal, and Y = $25,000/yr. P Qd

  28. Exercise (cont.) B. Are minivans a normal good? They can be a normal good over a certain range of income (lower) and become an inferior after a certain range (higher), where rich people would substitute away from minivan once they start getting wealthy enough. C. Are minivans and station wagons substitutes or complements? D. Are minivans and gasoline substitutes or complements?

  29. Effect of a fall in income (crisis): Effect of an increase in the price of station wagons: Exercise (end) P P D D Qd Qd

  30. Effect of a fall in income (crisis): Effect of an increase in the price of station wagons: Exercise (end) P P D D Qd Qd

  31. Summary A change in the price of a good leads to a movement alongthe demand curve for that good. A change in a factor other than the price of the good leads to a shift of the demand curve.

  32. Elasticities

  33. Price-elasticity of demand Elasticity : A number representing the sensitivity of one variable (e.g., Qd) to changes in another variable (e.g., P). Interpretation: The price-elasticity of demand is the percentage change in Qd when P changes by 1%. % change in Qd∆Qd/QdEp = --------------------------- = ---------------- % change in P ∆P/P

  34. Computation: local method Hence, with Qd = 280 – 20P, we get ∆Qd/∆P = -20 everywhere. At P = 3$, we get Qd = 220 and Ep = - 20 x 3/220 = - 0.27. At P = 4$, we get Qd = 200 and Ep = - 20 x 4/200 = - 0.4. Note: The value of the elasticity of demand depends on where we are on the demand curve.

  35. We say that D is: Ep = - ∞: perfectly elastic Ep = 0: perfectly inelastic Ep = -1: unit elastic -∞ < Ep < -1: relatively elastic -1 < Ep < 0: relatively inelastic Ep on a linear D: P Ep = __ Ep < __ Ep = __ __ < Ep< __ D Q Ep= ___

  36. Ep = ____ Examples? Special cases P P D D Qd Qd Ep = ____ Examples?

  37. Ep = 0 Examples? Drug Special cases P P D D Qd Qd Ep = ∞ Examples? Bottled water

  38. Ep and producer revenue R = p x QdA price increase does not necessary lead to an increase in revenue. Hence, the percentage change in revenue in response to a 1% change in price is: Question: When is it profitable for a producer to raise prices? % change in R ∆R/R----------------------------- = ---------------- = … = 1+Ep % change in p ∆p/p

  39. Ep and producer revenue • Graphically • Rectangles vs. squares • Concave revenue graphs • Maximizing a concave function

  40. Other elasticities (1) The income elasticity of demand is the relative change in Qd in response to a 1% change in income (Y). • If EY > 0, we say the good is ____________, • If EY < 0, the good is ______________. Examples? % change in Qd∆Qd/QdEY = ------------------------- = ---------------- % change in Y ∆Y/Y

  41. Other elasticities (1) The income elasticity of demand is the relative change in Qd in response to a 1% change in income (Y). • If EY > 0, we say the good is normal • If EY < 0, the good is inferior. Examples? % change in Qd∆Qd/QdEY = ------------------------- = ---------------- % change in Y ∆Y/Y

  42. Other elasticities (2) The cross-price elasticity is the percentage change in Qd of a good X in response to a 1% change in the price of another good, PY. • If EcXY < 0, the goods X and Y are ________________. • If EcXY > 0, they are ____________________________. Examples? % change in QdX∆QdX/QdXEcXY = ----------------------- = ---------------- % change in PY∆PY/PY

  43. Other elasticities (2) The cross-price elasticity is the percentage change in Qd of a good X in response to a 1% change in the price of another good, PY. • If EcXY < 0, the goods X and Y are Substitutes • If EcXY > 0, they are Complements Examples? % change in QdX∆QdX/QdXEcXY = ----------------------- = ---------------- % change in PY∆PY/PY

  44. Conclusion We now know: • How to derive the purchasing behavior of an individual and of a population • How demand is affected by economic circumstance • How to predict changes and react accordingly

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