The Elasticity of Demand

1. The Elasticity of Demand Chapter 6

2. The Concept of Elasticity • Elasticity is a measure of the responsiveness of one variable to another. • The greater the elasticity, the greater the responsiveness.

3. Calculating Elasticities • To determine elasticity divide the percentage change in quantity by the percentage change in price.

4. Price Elasticity • The price elasticity of demand is the percentage change in quantity demanded divided by the percentage change in price.

5. Price Elasticity ep Percentage Change in Quantity Demanded = Percentage Change in Price Change in Quantity Demanded Change in Price = ÷ Quantity Demanded Initially Initial Price P ∆Qd = * ∆P Qd Where ∆Qd = Change in Quantity Demanded ∆P = Change in Price

6. Sign of Price Elasticity • According to the law of demand, whenever the price rises, the quantity demanded falls. Thus the price elasticity of demand is always negative. • Because it is always negative, economists usually state the value without the sign.

7. Price Elasticity of Demand • From Formula Ep = % Change in Qd %Change in Price • If Price Elasticity of Demand > 1, demand is elastic • If Price Elasticity of Demand = 1, demand is unit elastic • If Price Elasticity of Demand < 1, demand is inelastic

8. Demand Elasticity • Elastic Demand – When % Change in Quantity Demanded > % Change in Price • Unit Elastic Demand – When % Change in Quantity Demanded = % Change in Price • Inelastic Demand – When % Change in Quantity Demanded < % Change in Price • Perfectly Elastic Demand – When Quantity Demanded changes by a very large percentage in response to an almost zero Change in Price • Perfectly Inelastic Demand – When the Quantity Demanded remains constant as Price changes

9. Two important points to consider: Elasticity is related (but is not the same as) slope. Elasticity changes along straight-line demand and supply curves. Elasticity and Demand Curves

10. When the curves are flat, we call the curves perfectly elastic. The quantity changes enormously in response to a proportional change in price (E =¥). Elasticity Is Not the Same as Slope

11. When the curves are vertical, we call the curves perfectly inelastic. The quantity does not change at all in response to an enormous proportional change in price (E = 0). Elasticity Is Not the Same as Slope

12. Price Perfectly elastic demand curve 0 Quantity Perfectly Elastic Demand Curve

13. Perfectly inelastic demand curve Price 0 Quantity Perfectly Inelastic Demand Curve

14. Demand Curve Shapes and Elasticity • Perfectly Elastic Demand Curve • The demand curve is horizontal, any change in price can and will cause consumers to change their consumption. • Perfectly Inelastic Demand Curve • The demand curve is vertical, the quantity demanded is totally unresponsive to the price. Changes in price have no effect on consumer demand. • In between the two extreme shapes of demand curves are the demand curves for most products.

15. Ed > 1 Ed < 1 Ed = 0 Elasticity Along a Demand Curve Ed = ∞ Elasticity declines along demand curve as we move toward the quantity axis $10 9 8 7 6 Ed = 1 Price 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 Quantity

16. Significance of Price Elasticity of Demand • Profit maximization requires that business set a price that will maximize the firm’s profit • Elasticity tells the firm how much control it has over using price to raise profit • If Ep > 1, then the % Change in Qd > % Change is Price and demand is said to be elastic • An increase in price will reduce total revenue • A decrease in price will increase total revenue

17. Significance of Price Elasticity of Demand • If Ep < 1, then the % change in Qd < % change in price, and demand is said to be inelastic • An increase in price will increase total revenue • A decrease in price will decrease total revenue • If Ep = 1, then the % change in Qd = % change in Price, and demand is said to be unit elastic • An increase in price will have no impact on total revenue • A decrease in price will have no impact on total revenue

18. Thumb rules of PED • When p rises, TR rises & vice versa, then e < 1 • When p rises, TR falls & vice versa, then e > 1 • When change in price doesn’t change TR, then e = 1.

19. The Arc price elasticity of demand • It is the percentage change differs depending on whether you view the change as a rise or a decline in price.

20. The Arc price elasticity of demand • Economists use the average of the end points to calculate the percentage change.

21. B $26 C (midpoint) 24 22 A Price 20 18 D 16 14 0 10 12 14 Quantity of software (in hundred thousands) Graphs of Elasticities Elasticity of demand between A and B = 1.27

22. Calculating Elasticity

23. Calculating Elasticity of Demand Between Two Points Elasticity of demand between A and B: $26 B 24 22 midpoint C Price 20 A 18 16 Demand 14 0 10 12 14 Quantity of software (in hundred thousands)

24. Calculating Elasticity at a Point • Let us now turn to a method of calculating the elasticity at a specific point, rather than over a range or an arc.

25. Calculating Elasticity at a Point • Measurement of point elasticity is same as the price elasticity of demand in a limiting sense • Here changes in quantity demanded and price are infinitesimally small • Point elasticity of demand is different at different point on the demand curve

26. Calculating Elasticity at a Point • Slope of the Demand Curve dQ dP • Point Elasticity on the demand curve ep = dQ P dP Q

27. Determinants of the Price Elasticity of Demand • The degree to which the price elasticity of demand is inelastic or elastic depends on: • How many substitutes there are • How well a substitute can replace the good or service under consideration • The importance of the product in the consumer’s total budget • The time period under consideration • Habit-forming goods • Nature & Number of uses a commodity can be put to.

28. Determinants of the Price Elasticity of Demand • The larger the time interval considered, or the longer the run, the more elastic is the good’s demand curve. • There are more substitutes in the long run than in the short run. • The long run provides more options for change.

29. Relationship between ep , AR,MR ep = dQ P dP Q AR= P (Price) TR = P . Q MR = d TR d Q MR = P + Q . dP dQ MR = d P.Q d Q MR = P { 1 + Q dP } P dQ MR = AR { 1 + 1 } Ep The difference between AR and MR depends inversely on the absolute value of the elasticity of demand.

30. Income elasticity of Demand • The income elasticity of demand is defined as the rate of change in the quantity demanded of a good due to changes in the income of the consumer. • If the amount of good demanded rises as the income of the consumer increases, than value of income elasticity of demand is positive (Normal good) • If the amount of good demanded decreases as the income of the consumer increases, than value of income elasticity of demand is negative (Inferior good) • Income elasticity of demand is also used to classify goods into luxuries and necessities. If the income elasticity of good is greater than one, it is called luxury. If the income elasticity is less than one, it is called a necessity. If it is equal to one, it can be called as a semi-luxury good.

31. Income Elasticity

32. Income Elasticity E1 Q2 Income elasticity of demand is greater than one. In this case as income increases, the quantity demanded also increases. But the percentage increase in demand is more than percentage increase in income Quantity Demanded E Q1 0 Y1 Y2 Income

33. Income Inelasticity Quantity Demanded E2 Q1 Income elasticity is between zero and one. In this case, as income increases quantity demanded increases but the percentage increase in quantity demanded is less than percentage increase in income Q2 E1 0 Y1 Y2 Income

34. Income Elasticity

35. Promotional (or Advertising) Elasticity of Demand • The advertising elasticity of demand measures an extent to which the demand of a product will be influenced by advertisement and other promotional activities. • Advertising elasticity of demand measures the responsiveness of quantity demanded to changes in the expenditure on advertising and other sales promotional activities.

36. Cross Elasticity of Demand • Cross elasticity of demand is defined as the percentage change in the quantity demanded of a good due to the changes in the prices of other good, other things remaining the same. Percentage change in the price of jth good Percentage change in the demand of ith good ecji =

37. Question • JMC, a company dealing in audio systems, has been selling 500 audio systems per month on average at a price of Rs. 1,000. Its main competitor, Kilachand Sounds, plans to reduce price of its audio system from Rs. 1,050 to Rs. 900. JMC has come to know of this move and wants to know impact of this change on its own sales. It has calculated a cross-elasticity of demand between the two products as 0.7. Calculate the loss in rupees that JMC will suffer.

38. Cross Elasticity of Demand • When two goods are substitutes, than increase in the price of one good decreases its own demand and increases the demand of another good. In this case cross elasticity of demand is positive • In the case of complementary goods the increase in the price of one good decreases the demand for both the goods. In this case cross elasticity of demand is negative.

39. Determinants of Cross Elasticity of Demand The main determinant of cross elasticity of demand is the nature of the goods relatives to their usages. If two goods can satisfy equally well the same need, the cross elasticity is high and vice versa.

40. Question Q. Consider the demand equation Q = 25 - 3P, where Q represents quantity demanded and P the selling price. a. Calculate the arc-price elasticity of demand when P1 = $4 and P2 = $3. b. Calculate the point-price elasticity of demand at these prices. Is the demand for this good elastic or inelastic at these prices? c. What, if anything, can you say about the relationship between the price elasticity of demand and total revenue at these prices? d. What is the price elasticity of demand at the price that maximizes total revenue?

41. Solution

42. Solution