Managerial Economics & Business Strategy

1. Managerial Economics & Business Strategy Chapter 3 Quantitative Demand Analysis

2. Overview I. Elasticities of Demand • Own Price Elasticity • Elasticity and Total Revenue • Cross-Price Elasticity • Income Elasticity II. Demand Functions • Linear • Log-Linear III. Regression Analysis

3. Elasticities of Demand • How responsive is variable “G” to a change in variable “S” % means “percent change If eG,S > 0 then S and G are directly related If eG,S < 0 then S and G are inversely related

4. Own Price Elasticity of Demand • Calculation method depends on available data • Basic formula if you have % • Mid-point formula: if you have 2 price:quantity observations • Calculus method if you have a general expression

5. Own Price Elasticity of Demand -Mid-point • Be careful to be consistent in subtraction • Always negative

6. Own Price Elasticity of Demand -Mid-point • Consider 2 sales points • P = 5, Qd = 6 and • P = 4, Qd = 7.5 P 5 4 6 7.5 Q

7. Own Price Elasticity of Demand -Mid-point

8. Own Price Elasticity of Demand -Continuous or Point Estimate • If changes in Q and P are small then the average approaches the observation • The ratio of changes is simply the inverse of the slope

9. Own Price Elasticity of Demand -Continuous or Point Estimate • Consider the same 2 sales points • Develop a more general estimate of elasticity • Steps: • Find demand function • Find elasticity

10. Own Price Elasticity of Demand -Continuous or Point Estimate • Consider 2 sales points • P = 5, Qd = 6 and P = 4, Qd = 7.5 • General equation is: • P = 9 - 2/3 Q or • Q = 27/2 - 3/2 P

11. Own Price Elasticity of Demand -Continuous or Point Estimate Q/ P is the slope so Q/ P = -3/2 d = -3/2 (P/Q) Substituting in: d = -3/2 (P/Q) = -3P/(27-3P) or d = -3/2 (P/Q) = 1 - (27/2Q) Picking one of the points: P = 5, Qd = 6 gives d = -5/4 P = 4, Qd = 7.5 gives d = -4/5 Average of the two = -1 (compare to other method)

12. Own Price Elasticity of Demand • Negative according to the “law of demand” Elastic: Inelastic: Unitary:

13. Perfectly Elastic & Inelastic Demand Price Price D D Quantity Quantity Perfectly Elastic Perfectly Inelastic

14. Own-Price Elasticity and Total Revenue • Elastic • Increase (a decrease) in price leads to a decrease (an increase) in total revenue. • Inelastic • Increase (a decrease) in price leads to an increase (a decrease) in total revenue. • Unitary • Total revenue is maximized at the point where demand is unitary elastic.

15. Price 10 Elastic 8 6 Inelastic 4 2 D 1 2 3 4 5 Quantity Elasticity, TR, and Linear Demand

16. Factors Affecting Own Price Elasticity • Available Substitutes • The more substitutes available for the good, the more elastic the demand. • Time • Demand tends to be more inelastic in the short term than in the long term. • Time allows consumers to seek out available substitutes. • Need vs. Luxury • Demand tends to be less elastic the more we “need” the good. • Expenditure Share • Goods that comprise a small share of consumer’s budgets tend to be more inelastic than goods for which consumers spend a large portion of their incomes.

17. Own Price ElasticityImplications • If demand is inelastic: • Raise price - • revenue up • volume down  total costs down • profits up • Lower price • revenue down • volume up  total costs up • profits down

18. Own Price ElasticityImplications • If demand is elastic: • Raise price • revenue down • volume down  total costs down • profits ??? • Lower price • revenue up • volume up  total costs up • profits ???

19. Cross Price Elasticity of Demand + Substitutes - Complements

20. Income Elasticity + Normal Good - Inferior Good

21. Uses of Elasticities • Pricing • Impact of changes in competitors’ prices • Impact of economic booms and recessions • Impact of advertising campaigns

22. For own price changes: For related product price changes (Y): Uses of Elasticities -Calculating Revenue Changes

23. Uses of Elasticities -Calculating Revenue Changes Two products drinks and chips TRdrinks = $600 TRchips = $400 edrinks = -1.5 echips,drinks = 0.5 What happens to TR if you raise the price of drinks by 2%? Is it profitable?

24. Example 1: Pricing and Cash Flows • According to an FTC Report by Michael Ward, AT&T’s own price elasticity of demand for long distance services is -8.64. • AT&T needs to boost revenues in order to meet it’s marketing goals. • To accomplish this goal, should AT&T raise or lower it’s price?

25. Answer: Lower price! • Since demand is elastic, a reduction in price will increase quantity demanded by a greater percentage than the price decline, resulting in more revenues for AT&T.

26. Example 2: Quantifying the Change • If AT&T lowered price by 3 percent, what would happen to the volume of long distance telephone calls routed through AT&T?

27. Answer • Calls would increase by 25.92 percent!

28. Example 3: Impact of a change in a competitor’s price • According to an FTC Report by Michael Ward, AT&T’s cross price elasticity of demand for long distance services is 9.06. • If MCI and other competitors reduced their prices by 4 percent, what would happen to the demand for AT&T services?

29. Answer • AT&T’s demand would fall by 36.24 percent!

30. Specific Demand Functions • Linear Demand Income Elasticity Own Price Elasticity Cross Price Elasticity

31. Log-Linear Demand

32. Example of Log-Linear Demand • log Qd = 10 - 2 log P • Own Price Elasticity: -2

33. P Q P D D Q Log Linear Linear

34. Regression Analysis • Used to estimate demand functions • Important terminology • Least Squares Regression: Y = a + bX + e • Confidence Intervals • t-statistic • R-square or Coefficient of Determination • F-statistic

35. An Example Use a spreadsheet to estimate demand Use a spreadsheet to estimate elasticity

36. An Example - Data

37. An Example Using the data to find a general demand curve: Q = a0 + a1*PX There will be errors but we want to minimize them Find elasticity estimate: ed = Q/ P * P/Q ed = a1 * P/Q (use average) Or with logs: ed = a1

38. An Example -Regression Results

39. An Example -Regression Results

40. An Example -Regression Results

41. An Example • Equation is: • Qd = 1631.47 - 2.60*P • Average P = 455 • Average Q = 450.50 • Average elasticity of demand: • -2.6 * 455/450.5 = -2.63

42. Interpreting the Output • Estimated demand function: • Qx = 1631.47 - 2.60*Px • Own price elasticity: -2.63 (elastic) • How good is our estimate? • t-statistics of -4.89 indicates that the estimated coefficient is statistically different from zero • R-square of .75 indicates we explained 75 percent of the variation in quantity

43. An Example -Log-linear Data

44. An Example -Log-linear Data

45. An Example -Log-linear Data

46. An Example -Log-linear Data

47. An Example -Log-linear Data • Equation is: • ln(Qd) = 23.78 - 2.91*ln(P) • Average ln(P) = 6.11 • Average ln(Qd) = • Elasticity of demand: • -2.91172627898845 compared to -2.63

48. Interpreting the Log Output • Estimated demand function: • ln(Qx)= 23.78 - 2.91*ln(Px) • Own price elasticity: -2.91 (elastic) • How good is our estimate? • t-statistics of -4.34 indicates that the estimated coefficient is statistically different from zero • R-square of .70 indicates we explained 70 percent of the variation

49. Summary • Elasticities are tools you can use to quantify the impact of changes in prices, income, and advertising on sales and revenues. • Given market or survey data, regression analysis can be used to estimate: • Demand functions • Elasticities • A host of other things, including cost functions • Managers can quantify the impact of changes in prices, income, advertising, etc.