Chapter 6 Elasticities of Demand

1. Chapter 6 Elasticities of Demand

2. Contents: • Elasticity of Demand • Classification of Elasticities of Demand • Price Elasticity of Demand • Price Elasticity & Demand Curve • Price Elasticity of Demand, Total Revenue & Total Expenditure • Income Elasticity of Demand • Cross Elasticity of Demand

3. Contents: • Advanced Material 6.1: Price Consumption Curve and Price Elasticity • Advanced Material 6.2: Income Consumption Curve and Income Elasticity

4. Elasticity of Demand

5. Elasticity of demand • Elasticity of demand (需求彈性, Ed) • is a measure of theresponsivenessof the quantity demandedof a good toa change in an exogenous variable. • % change in X_________ • % change in exogenous variable Why?

6. Classification of Elasticities of Demand

7. Classification according to the exogenous variable concerned Price of the good Income Price of related good

8. Classification according to the formula adopted in calculation Pointelasticity of demand % Δ= X2 – X1 x 100% X1 Situations applied: when the % change are _________ Arc elasticity of demand % Δ= X2 – X1 x 100% (X1+ X2)/2 Situations applied: when the % change are _________ very small significant

9. Px 0 X Classification according to the size of the elasticity • Perfectly inelastic (Ed = 0) • The exogenous variable changes but X remains unchanged i.e. % Δ in X =_______. • In the case of price elasticity, the demand curve is _________. 0 D vertical vertical

10. Classification according to the size of the elasticity 2. Inelastic(Ed < 1) %  in X ____ %  in exogenous variable  3. Unitarily elastic (Ed = 1) %  in X ____ %  in exogenous variable  4. Elastic(Ed > 1) %  in X ____ %  in exogenous variable 

11. Classification according to the size of the elasticity Px D 0 X • 5. Perfectly elastic (Ed = infinity) • A negligible change in the exogenous variable brings an infinite change in Qd • i.e. % Δ in X =_________. • In the case of price elasticity, • the demand curve is ___________. infinity horizontal horizontal

12. Price Elasticity of Demand

13. What is price elasticity? Price elasticity of demand (價格需求彈性, pEd) is equal to the percentage change in quantity demanded of a good divided by the percentage change in its own price.

14. What is price elasticity? (Con’t) According to the first law of demand, pEd is________. negative • However, if Giffen good existed, • its pEd would be ________. positive

15. Point elasticity of demand -- on a linear demand curve (DC) • Mathematical measure: • Graphical measure: ΔPx pEd at point A: ΔX Px C A P1  DC X 0 B X1

16. Point elasticity of demand – on a non-linear DC • Mathematical measure: • Graphical measure: pEd at point A: ΔPx ΔX Px C A P1  DC X 0 X1 B

17. Price Elasticity & Demand Curve

18. Px Demand curve 0 X Point elasticity of demand -- on a linear DC |pEd| > 1 (elastic) M (mid-point): |pEd|= 1 (unitarily elastic)  |pEd| < 1 (inelastic)

19. Price elasticity at points on different DCs If two linear DCs have the same y-intercept OPPC EDDC = = • they will have the same pEdat every price. Px BAAC pEd at point A on d1= C =pEd at point D on d2 D P A d1 d2 X O B E

20. Price elasticity at points on different DCs Px F BAAC OPPC = = = C OPPF EDDF P d2 d1 X O B E If 2 linear DCs have different y-intercepts • The curve with a smaller y-intercept will have a larger price elasticity than the curve with a larger y-interceptat every price. pEd at point A on d1 (with a smaller y-intercept) > =pEd at point D on d2(with a larger y-intercept) A D

21. Price elasticity of points on different DCs BAAC OPPC = = OPPF EDDF = Px If 2 linear DCs intersect, • the one witha gentler slopewill have a larger price elasticityat the intersection point. pEd at point A on a d1 (with a larger slope) C < F = pEd at point D on d2 (with a smaller slope) D (on d2) P  A on (d1) d1 d2 X O B E

22. Price Elasticity of Demand, Total Revenue &Total Expenditure

23. Price elasticity, total expenditure (TE) and total revenue(TR) Total expenditure paid by a consumer = PricexQuantity transacted(or P x Q) = Total revenue received by a producer

24. Change in TE and TR • When demand or supply changes, • price & quantity transacted vary. • Subsequently, total expenditure • & total revenue are affected.

25. Increase in demand D P  & Q TR  Px S1 P2 P1 D2 D1 X 0 X1 X2  in TR

26. Decrease in demand D P  & Q TR  Px S1 in TR P1 P2 D1 D2 0 X X2 X1

27. Increase in supply Px S1 • Pbut X  S2 • Δ in TR depends on • the relative % Δ in • P & Q, i.e., the pEd. P1 P2 D 0 X1 X2 X

28. S2 P2  in TR  in TR X2 a. Demand is elastic • When supply increases, if demand is elastic, • %in X  % in P • TR  Px S1 P1 M  D X 0 X1

29. Px S1 S2 P1 M  P2  in TR D 0 X  in TR X1 X2 b. Demand is unitarily elastic • %in X %in P • TR remains constant

30. S2  in TR P2  in TR X2 c. Demand is inelastic Px • %in X % in P • TR  S1 M  P1 D X 0 X1

31. Decrease in supply • Pbut X  Px S2 S1 • Δ in TR depends on • the relative % Δ in • P & Q, i.e., the pEd P2 P1 D X 0 X2 X1

32. S2 P2 X2 a. Demand is elastic • When supply decreases, if demand is elastic, • % in X  % in P • Δ in TR  Px S1 P1 M   in TR D X1  in TR X

33. S2 P2  in TR  in TR X2 b. Demand is unitarily elastic • % in X = % in P • TR remains constant Px S1 M  P1 D X X1

34. S2 P2  in TR  in TR X2 c. Demand is inelastic • %in X  % in P • Δin TR  Px S1 M  P1 D X X1

35. Q6.6: (a) If the demand is inelastic, to increase the TR, should a producer raise the price or should he cut the price? (b) After raising the price of a good, a producer finds that the total revenue falls. What is the reason?

36. Unit elasticity and total revenue For a unitarily elastic demand: • % Δin X = % Δ in P • TR remains constant despite a change in P or Q. • If one spends the whole amount (or a fixed amount)of his income on a good no matter what its price is, its pEdmust beequalto / greater than /smaller thanone. equal to

37. X x

38. Factors affecting price elasticity • Number of close substitutes: • moreclose substitutes • more elastic demand. Why? 2.Degree of necessity: necessities & habit-forming goods less elastic demand. Why?

39. Factors affecting price elasticity (Con’t) 3. Number of possible uses: more different usesmore elastic demand. Why? 4. Durability: more durablemore elastic demand. Why? 5. Proportion of income spent: a larger proportion of one’s expenditure more elastic demand. Why?

40. Px P0 P1 Shift of DC as time passes 0 X X0 X1 X2 X3 X4 6. Time of adjustment: longer time for adjustmentmore elasticdemand (Second law of demand) Why?

41. Q6.7: The demand for salt is inelastic. List all possible reasons.

42. Income Elasticity of Demand

43. What is income elasticity? • Income elasticity of demand (所得需求彈性, iEd) • is equal to the percentage change in quantity demanded • divided by the percentage change in income.

44.   • iEd 1 •  • iEd 1 •  • Superior good • X is _________ related to income. • iEd is ________. positively positive necessities luxuries (Options: positive / negative / luxuries / necessities / positively / negatively )

45. Inferior good • X is _________ related to income. • iEd is __________. negatively negative (Options: positive / negative / luxuries / necessities positively / negatively)

46. Mathematical measure: • Graphical measure: X X Good X is a superior good Good X is an inferior good B ΔX A X1 Δ I  Δ I X1  A ΔX B C I I 0 C 0 I1 I1

47. Cross Elasticity of Demand

48. What is cross elasticity? • Cross elasticity of demand (交叉需求彈性, cEd) • is equal to the percentage change in quantity demanded • of a good (e.g., good X) divided by the percentage • change in price of another good (e.g., good Y).

49. Cross elasticity of demand • The cross elasticity of substitutes is positive, why? • The cross elasticity of complementsis negative, why? when PY Y and X (substitute of Y)thus, PY and X are positively related. when PY Y and X (complement of Y)thus, PY and X are negatively related.

50. Mathematical measure: • Graphical measure: PY PY Good X and good Y are substitutes Good X and good Y are complements C A A PY1  PY1  ΔPY ΔPY ΔX 0 ΔX X B X1 X 0 C X1 B