Managerial Economics & Business Strategy

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

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

3. The Elasticity Concept • How responsive is variable “G” to a change in variable “S” If EG,S > 0, then S and G are directly related. If EG,S < 0, then S and G are inversely related. If EG,S = 0, then S and G are unrelated.

4. The Elasticity Concept Using Calculus • An alternative way to measure the elasticity of a function G = f(S) is If EG,S > 0, then S and G are directly related. If EG,S < 0, then S and G are inversely related. If EG,S = 0, then S and G are unrelated.

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

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

7. 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.

8. Elasticity, Total Revenue and Linear Demand P TR 100 30 40 50 Q Q 0 10 20 0

9. Elasticity, Total Revenue and Linear Demand P TR 100 80 800 30 40 50 Q Q 0 10 20 10 30 40 50 0 20

10. Elasticity, Total Revenue and Linear Demand P TR 100 80 1200 60 800 30 40 50 Q Q 0 10 20 30 40 50 0 10 20

11. Elasticity, Total Revenue and Linear Demand P TR 100 80 1200 60 40 800 30 40 50 Q Q 0 10 20 30 40 50 0 10 20

12. Elasticity, Total Revenue and Linear Demand P TR 100 80 1200 60 40 800 20 30 40 50 Q Q 0 10 20 30 40 50 0 10 20

13. Elasticity, Total Revenue and Linear Demand P TR 100 Elastic 80 1200 60 40 800 20 30 40 50 Q Q 0 10 20 30 40 50 0 10 20 Elastic

14. Elasticity, Total Revenue and Linear Demand P TR 100 Elastic 80 1200 60 Inelastic 40 800 20 30 40 50 Q Q 0 10 20 30 40 50 0 10 20 Elastic Inelastic

15. Elasticity, Total Revenue and Linear Demand P TR 100 Unit elastic Elastic Unit elastic 80 1200 60 Inelastic 40 800 20 30 40 50 Q Q 0 10 20 30 40 50 0 10 20 Elastic Inelastic

16. Demand, Marginal Revenue (MR) and Elasticity • For a linear inverse demand function, MR(Q) = a + 2bQ, where b < 0. • When • MR > 0, demand is elastic; • MR = 0, demand is unit elastic; • MR < 0, demand is inelastic. P 100 Elastic Unit elastic 80 60 Inelastic 40 20 Q 40 50 0 10 20 MR

17. Total Revenue Test • TRT can help manage cash flows. • Should a company increase prices to boost cash flow or cut prices and make it up in volume?

18. TRT • If elasticity of Demand = -2.3 • Cut prices by 10% • Will sales increase enough to increase revenues? • Qd will increase by 23%. • Since the % decrease in price is< % increase in Qd, TR will increase.

19. Factors Affecting the Own-Price Elasticity • Available Substitutes • Broad or narrowly defined categories • Time • Expenditure Share

20. Mid-Point Formula • For consistency when working from a function whether it is Demand or Supply an average approximation of elasticity is used. • Ep = Q2-Q1/[(Q2+Q1/2]/P2-P1/[(P2+P1/2]

21. Cross-Price Elasticity of Demand If EQX,PY > 0, then X and Y are substitutes. If EQX,PY < 0, then X and Y are complements.

22. Cross-Price Elasticity Examples • Transportation and recreation = -0.05 • Food and Recreation = 0.15 • Clothing and food = -0.18

23. Predicting Revenue Changes from Two Products Suppose that a firm sells two related goods. If the price of X changes, then total revenue will change by:

24. Example • Suppose a diner earns $5000/wk selling egg salad sandwiches and $3000/wk selling French fries. If own price elasticity for egg salad is -3.2 and cross price elasticity between egg salad and French fries is -0.5 what happens to the firms total revenue if it increased the price of egg salad sandwiches by 5%?

25. Solution • [5000 x (1+(-3.2)) +((3000 x (-0.5))] x +5% • [5000 x (-2.2) – (1500)) x +5% • [-550 – 75] = -$ 625

26. Income Elasticity If EQX,M> 0, then X is a normal good. If EQX,M < 0, then X is a inferior good.

27. Income Elasticities • Transportation 1.80 • Food 0.80 • Ground beef, non-fed -1.94

28. Uses of Elasticities • Pricing. • Managing cash flows. • Impact of changes in competitors’ prices. • Impact of economic booms and recessions. • Impact of advertising campaigns. • And lots more!

29. 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?

30. 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.

31. 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?

32. Answer: Calls Increase! Calls would increase by 25.92 percent!

33. 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 competitors reduced their prices by 4 percent, what would happen to the demand for AT&T services?

34. Answer: AT&T’s Demand Falls! AT&T’s demand would fall by 36.24 percent!

35. Interpreting Demand Functions • Mathematical representations of demand curves. • Example: • Law of demand holds (coefficient of PX is negative). • X and Y are substitutes (coefficient of PY is positive). • X is an inferior good (coefficient of M is negative).

36. Linear Demand Functions and Elasticities • General Linear Demand Function and Elasticities: Income Elasticity Own Price Elasticity Cross Price Elasticity

37. Example of Linear Demand • Qd = 10 - 2P. • Own-Price Elasticity: (-2)P/Q. • If P=1, Q=8 (since 10 - 2 = 8). • Own price elasticity at P=1, Q=8: (-2)(1)/8= - 0.25.

38. Log-Linear Demand • General Log-Linear Demand Function:

39. Example of Log-Linear Demand • ln(Qd) = 10 - 2 ln(P). • Own Price Elasticity: -2.

40. P Q Graphical Representation of Linear and Log-Linear Demand P D D Q Linear Log Linear

41. Regression Analysis • One use is for estimating demand functions. • Econometrics – statistical analysis of economic phenomena • Important terminology and concepts: • Least Squares Regression model: • Y = a + bX + e. • Least Squares Regression line: • Confidence Intervals. • t-statistic. • R-square or Coefficient of Determination. • F-statistic. • Causality versus Correlation

42. Regression Analysis • Standard error is a measure of how much each estimated coefficient would vary in regressions based on the same underlying true demand relation, but with different observations. • LSE are unbiased estimators of the true parameters whenever the errors have a zero mean and are iid. • If that is the case then C.I.s can be constructed

43. Evaluating Statistical Significance • Confidence intervals: • 90% C.I.  a +/- 1 SE of the estimate • 95% C.I.  a +/- 2 SE of the estimate • 99% C.I.  a +/- 3 SE of the estimate • T statistic: ratio of the value of the parameter estimate to its SE. • When the absolute value of the t-statistic is >2 one can be 95% confident that the true value of the underlying parameter is not zero.

44. Evaluating Statistical Significance • R-squared – coefficient of determination. Fraction of the total variation in the dependent variable explained by the regression. • R2 = Explained variation/total variation • R2 = SSregression / SStotal • Subjective measure of goodness of fit. • Remember! degrees of freedom • Adjusted R2 better indicator of GOF. • AdjR2 = 1 – (1 – R2) [(n-1)/(n-k)]

45. Evaluating Statistical Significance • F statistic – alternative measure of GOF. Provides a measure of total variation explained by the regression relative to the total unexplained variation. • Larger the F-stat the better the overall fit of the regression line to the data.

46. An Example • Use a spreadsheet to estimate the following log-linear demand function.

47. Summary Output

48. Interpreting the Regression Output • The estimated log-linear demand function is: • ln(Qx)= 7.58 - 0.84 ln(Px). • Own price elasticity: -0.84 (inelastic). • How good is our estimate? • t-statistics of 5.29 and -2.80 indicate that the estimated coefficients are statistically different from zero. • R-square of 0.17 indicates the ln(PX) variable explains only 17 percent of the variation in ln(Qx). • F-statistic significant at the 1 percent level.

49. Multiple Regression • MR – regressions of a dependent variable on multiple independent variables. • Caveat: beware of using regression indiscriminately. • Issues: Heteroskedacity, Multi-colinearity, etc.

50. Conclusion • 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.