1. Slide 1 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Demand Analysis Demand Relationships The Price Elasticity of Demand »Arc and point price elasticity »Elasticity and revenue relationships »Why some products are inelastic and others are elastic Income Elasticities Cross Elasticities of Demand Combined Effects of Elasticities

2. Slide 2 Health Care & Cigarettes Raising cigarette taxes reduces smoking »In Canada, over $4 for a pack of cigarettes reduced smoking 38% in a decade But cigarette taxes also helps fund health care initiatives »The issue then, should we find a tax rate that maximizes tax revenues? »Or a tax rate that reduces smoking?

3. Slide 3 Demand Analysis An important contributor to firm risk arises from sudden shifts in demand for the product or service. Demand analysis serves two managerial objectives: (1) it provides the insights necessary for effective management of demand, and (2) it aids in forecasting sales and revenues.

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5. Slide 5 FIGURE 3.1 Demand for SUV (Ford Explorer) as Gasoline Price Doubled

6. Slide 6 Downward Slope to the Demand Curve Economists presume consumers are maximizing their utility This is used to derive a demand curve from utility maximization » income effect -- as the price of a good declines, the consumer can purchase more of all goods since his or her real income increased. So as the price falls, we typically buy more.

7. Slide 7 Downward Slope to the Demand Curve » substitution effect -- as the price declines, the good becomes relatively cheaper. A rational consumer maximizes satisfaction by reorganizing consumption until the marginal utility in each good per dollar is equal. We buy more.

8. Slide 8 FIGURE 3.2 Consumption Choice on a Business Trip

9. Slide 9 Downward Slope to the Demand Curve » targeting, switching, and positioning – marketing efforts such as loyalty programs affect demand.

10. Slide 10 The Price Elasticity of Demand Elasticity is measure of responsiveness or sensitivity Beware of using slopes bushelshundred tons price per bu. Slopes change with a change in units of measure

11. Slide 11 Price Elasticity E D = % change in Q / % change in P Shortcut notation: E D = %  Q / %  P =  Q /  P ∙ Base P / Base Q. A percentage change from 100 to 150 is 50% A percentage change from 150 to 100 is -33% For arc price elasticities, we use the average as the base, as in 100 to 150 is +50/125 = 40%, and 150 to 100 is -40% Arc Price Elasticity -- averages over the two points D arc price elasticity E D =  Q/ [(Q 1 + Q 2 )/2]  P/ [(P 1 + P 2 )/2] Average price Average quantity

12. Slide 12 Arc Price Elasticity Example Q = 1000 when the price is $10 Q= 1200 when the price is reduced to $6 Find the arc price elasticity Solution: E D = %  Q/ %  P = +200/1100 - 4 / 8 or -.3636. The answer is a number. A 1% increase in price reduces quantity by.36 percent.

13. Slide 13 Point Price Elasticity Example Need a demand curve or demand function to find the price elasticity at a point. E D = %  Q/ %  P =(  Q/  P)(P/Q) If Q = 500 - 5P, find the point price elasticity at P = 30; P = 50; and P = 80 1.E D = (  Q/  P)(P/Q) = - 5(30/350) = -.43 2.E D = (  Q/  P)(P/Q) = - 5(50/250) = - 1.0 3.E D = (  Q/  P)(P/Q) = - 5(80/100) = - 4.0

14. Slide 14 Price Elasticity (both point price and arc elasticity) If E D = -1, unit elastic If E D > -1, inelastic, e.g., - 0.43 If E D < -1, elastic, e.g., -4.0 price elastic region unit elastic inelastic region Straight line demand curve example quantity

15. Slide 15 FIGURE 3.4 Perfectly Elastic and Inelastic Demand Curves

16. Slide 16 TR and Price Elasticities If you raise price, does TR rise? Suppose demand is elastic, and raise price. TR = PQ, so, %  TR = %  P+ %  Q If elastic, P, but Q a lot Hence TR FALLS !!! Suppose demand is inelastic, and we decide to raise price. What happens to TR and TC and profit?

17. Slide 17 Another Way to Remember Linear demand curve TR on other curve Look at arrows to see movement in TR A.Increasing price in the inelastic region raises revenue B.Increasing price in the elastic region lowers revenue Elastic Unit Elastic Inelastic TR QQQQ ( Figure 3.5) A B

18. Slide 18 FIGURE 3.5 Price Elasticity over Demand Function

19. Slide 19 FIGURE 3.5 Price Elasticity over Demand Function

20. Slide 20 MR and Elasticity Marginal revenue is  TR  Q To sell more, often price must decline, so MR is often less than the price.  MR = P ( 1 + 1/E D ) equation 3.7 For a perfectly elastic demand, E D = - B. Hence, MR = P. If E D = -2, then MR =.5P, or is half of the price.

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22. Slide 22 Empirical Price Elasticities Selections from Table 3.4 Apparel (whole market) -1.1 Apparel (one firm) -4.1 Beer -.84 Wine -.55 Liquor -.50 Regular coffee -.16 Instant coffee -.36 Adult visits to dentist »Men -.65 »Women -.78 »Children -1.4 Furniture -3.04 Glassware & China -1.2 Household appliances -.64 Flights to Europe -1.25 Shoes -.73 Soybean meal -1.65 Telephones -.10 Tires -.60 Tobacco products -.46 Tomatoes -2.22 Wool -1.32

23. Slide 23 Factors Affecting the Elasticity of Demand The availability and the closeness of substitutes »more substitutes, more elastic The percentage of the consumer's budget »larger proportion of the budget, more elastic Positioning as income superior »Products that are viewed as superior goods with large income elasticities, tend to be more elastic. (Clash for Clunkers lowered prices and helped sales of larger cars more than tiny ones) The longer the time period of adjustment »more time, generally, more elastic »Predictable end-of-season discounts more elastic than unexpected “midnight madness” sales.

24. Slide 24 Income Elasticity E Y = %  Q/ %  Y = (  Q/  Y)( Y/Q) point income arc income elasticity: »suppose dollar quantity of food expenditures of families of $20,000 is $5,200; and food expenditures rises to $6,760 for families earning $30,000. »Find the income elasticity of food »%  Q/ %  Y = (1560/5980)(10,000/25,000) =.652 »With a 1% increase in income, food purchases rise.652% E Y =  Q/ [(Q 1 + Q 2 )/2] arc income  Y/ [(Y 1 + Y 2 )/2] elasticity

25. Slide 25 Income Elasticity Definitions If E Y >0, then it is a normal or income superior good »some goods are luxuries: E Y > 1 with a high income elasticity »some goods are necessities: E Y < 1 with a low income elasticity If E Y is negative, then it’s an inferior good Consider these examples: 1.Expenditures on new automobiles 2.Expenditures on new Ford Focus 3.Expenditures on 2005 Ford Focus with 150,000 miles Which of the above is likely to have the largest income elasticity? Which of the above might have a negative income elasticity?

26. Slide 26 Point Income Elasticity Problem Suppose the demand function is: Q = 10 - 2P + 3Y find the income and price elasticities at a price of P = 2, and income Y = 10 So: Q = 10 -2(2) + 3(10) = 36 E Y = (  Q/  Y)( Y/Q) = 3( 10/ 36) =.833 E D = (  Q/  P)(P/Q) = -2(2/ 36) = -.111 Characterize this demand curve, which means describe them using elasticity terms.

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28. Slide 28 Advertising Elasticity E A = %  Q/ %  ADV = (  Q/  ADV)( ADV/Q) If the Advertising elasticity is.60, then a 1% increase in Advertising Expenditures increases the quantity of goods sold by.60%.

29. Slide 29 Cross Price Elasticities E cross = %  Q A / %  P B = (  Q A /  P B )(P B /Q A ) Substitutes have positive cross price elasticities: Butter & Margarine Complements have negative cross price elasticities: DVD machines and the rental price of DVDs at Blockbuster When the cross price elasticity is zero or insignificant, the products are not related

30. Slide 30 Antitrust & Cross Price Elasticities Whether a product is a monopoly or in a larger industry is dependent on the closeness of the substitutes DuPont’s cellophane was at first viewed as a monopoly. Economists showed that the cross price elasticity with other products such as aluminum foil, waxed paper, and other flexible wrapping paper was Positive, the large, DuPont showed its cellophane was not a monopoly in this larger market.

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32. Slide 32 Combined Effect of Demand Elasticities Most managers find that prices and income change every year. The combined effect of several changes are additive. %  Q = E D (%  P) + E Y (%  Y) + E cross (%  P R ) »where P is price, Y is income, and P R is the price of a related good. If you knew the price, income, and cross price elasticities, then you can forecast the percentage changes in quantity. The forecast for period 2 is: Q 2 = Q 1 [ 1 + E D (%  P) + E Y (%  Y) + E cross (%  P R )

33. Slide 33 Example: Combined Effects of Elasticities Toro has a price elasticity of -2 for snow blowers Toro snow blowers have an income elasticity of 1.5 The cross price elasticity with professional snow removal for residential properties is +.50 What will happen to the quantity sold if you raise price 3%, income rises 2%, and professional snow removal companies raises its price 1%? »%  Q = E P %  P +E Y %  Y + E cross %  P R = -2 3% + 1.5 2% +.50 1% = -6% + 3% +.5% »%  Q = -2.5%. We expect sales to decline 2.5%. Q: Will Total Revenue for your product rise or fall?

34. Slide 34 Example: Combined Effects of Elasticities A:Total revenue will rise slightly (about +.5%), as the price rises 3% and the quantity of snow- blowers sold falls 2.5%.

35. Slide 35 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Estimating Demand A chief uncertainty for managers is the future. Managers fear what will happen to their product. »Managers use forecasting, prediction & estimation to reduce their uncertainty. »The methods that they use vary from consumer surveys or experiments at test stores to statistical procedures on past data such as regression analysis. Objective : Learn how to interpret the results of regression analysis based on demand data.

36. Slide 36 Demand Estimation Using Marketing Research Techniques Consumer Surveys »ask a sample of consumers their attitudes Consumer Focus Groups »experimental groups try to emulate a market (but beware of the Hawthorne effect = people often behave differently in when being observed) Market Experiments in Test Stores »get demand information by trying different prices Historical Data - what happened in the past is guide to the future using statistics is an alternative Consumer Surveys »ask a sample of consumers their attitudes Consumer Focus Groups »experimental groups try to emulate a market (but beware of the Hawthorne effect = people often behave differently in when being observed) Market Experiments in Test Stores »get demand information by trying different prices Historical Data - what happened in the past is guide to the future using statistics is an alternative

37. Slide 37 Statistical Estimation of Demand Functions: Plot Historical Data Look at the relationship of price and quantity over time Plot it »Is it a demand curve or a supply curve? »The problem is this does not hold other things equal or constant. quantity Price 2004 2009 2008 2006 2010 2007 2005 Is this curve demand or supply?

38. Slide 38 Steps to take: »Specification of the model -- formulate the demand model, select a Functional Form linearQ = a + bP + cY double loglog Q = a + blog P + clog Y quadraticQ = a + bP + cY+ dP 2 »Estimate the parameters -- determine which are statistically significant try other variables & other functional forms »Develop forecasts from the model Statistical Estimation of Demand Functions

39. Slide 39 Specifying the Variables Dependent Variable -- quantity in units, quantity in dollar value (as in sales revenues) Independent Variables -- variables thought to influence the quantity demanded Tastes Time Trend »Instrumental Variables -- proxy variables for the item wanted which tends to have a relatively high correlation with the desired variable: e.g., Tastes Time Trend

40. Slide 40 Functional Forms: Linear Linear Model Q = a + bP + cY »The effect of each variable is constant, as in  Q/  P = b and  Q/  Y = c, where P is price and Y is income. »The effect of each variable is independent of other variables »Price elasticity is: E D = (  Q/  P)(P/Q) = bP/Q »Income elasticity is: E Y = (  Q/  Y)(Y/Q)= cY/Q »The linear form is often a good approximation of the relationship in empirical work.

41. Slide 41 Functional Forms: Multiplicative or Double Log Multiplicative Exponential Model Q = A P b Y c »The effect of each variable depends on all the other variables and is not constant, as in  Q/  P = bAP b-1 Y c and  Q/  Y = cAP b Y c-1 »It is double log (log is the natural log, also written as ln) Log Q = a + bLog P + cLog Y »the price elasticity, E D = b »the income elasticity, E Y = c »This property of constant elasticity makes this approach easy to use and popular among economists.

42. Slide 42 A Simple Linear Regression Model Y t = a + b X t +  t time subscripts & error term Find “best fitting” line  t = Y t - a - b X t  t 2 = [Y t - a - b X t ] 2. min  t 2 =  [Y t - a - b X t ] 2. Solution: slope b = Cov(Y,X)/Var(X) and intercept a = mean(Y) - bmean(X) _X_X Y _Y_Y a XX YY

43. Slide 43 Simple Linear Regression: Assumptions & Solution Methods 1.The dependent variable is random. 2.A straight line relationship exists. 3.The error term has a mean of zero and a finite variance: the independent variables are indeed independent. Spreadsheets - such as »Excel, Lotus 1-2-3, Quatro Pro, or Joe Spreadsheet Statistical calculators Statistical programs such as »Minitab »SAS »SPSS »For-Profit »Mystat

44. Slide 44 Assumption 2: Theoretical Straight-Line Relationship

45. Slide 45 Assumption 3: Error Term Has A Mean Of Zero And A Finite Variance

46. Slide 46 Assumption 3: Error Term Has A Mean Of Zero And A Finite Variance

47. Slide 47 FIGURE 4.4 Deviation of the Observations about the Sample Regression Line

48. Slide 48 Sherwin-Williams Case Ten regions with data on promotional expenditures (X) and sales (Y), selling price (P), and disposable income (M) If look only at Y and X: Result: Y = 120.755 +.434 X One use of a regression is to make predictions. If a region had promotional expenditures of 185, the prediction is Y = 201.045, by substituting 185 for X The regression output will tell us also the standard error of the estimate, s e. In this case, s e = 22.799 Approximately 95% prediction interval is Y ± 2 s e. Hence, the predicted range is anywhere from 155.447 to 246.643.

49. Slide 49 Sherwin-Williams Case

50. Slide 50 Figure 4.5 Estimated Regression Line Sherwin-Williams Case

51. Slide 51 T-tests Different samples would yield different coefficients Test the hypothesis that coefficient equals zero »H o : b = 0 »H a : b  0 RULE: If absolute value of the estimated t > Critical-t, then REJECT H o. »We say that it’s significant! The estimated t = (b - 0) /  b The critical t is: »Large Samples, critical t  2 N > 30 »Small Samples, critical t is on Student’s t Distribution, page B-2 at end of book, usually column 0.05, & degrees of freedom. D.F. = # observations, minus number of independent variables, minus one. N < 30

52. Slide 52 Sherwin-Williams Case In the simple linear regression: Y = 120.755 +.434 X The standard error of the slope coefficient is.14763. (This is usually available from any regression program used.) Test the hypothesis that the slope is zero, b=0. The estimated t is: t = (.434 – 0 )/.14763 = 2.939 The critical t for a sample of 10, has only 8 degrees of freedom »D.F. = 10 – 1 independent variable – 1 for the constant. »Table B2 shows this to be 2.306 at the.05 significance level Therefore, |2.939| > 2.306, so we reject the null hypothesis. We informally say, that promotional expenses (X) is “significant.”

53. Slide 53 USING THE REGRESSION EQUATION TO MAKE PREDICTIONS A regression equation can be used to make predictions concerning the value of Y, given any particular value of X. A measure of the accuracy of estimation with the regression equation can be obtained by calculating the standard deviation of the errors of prediction (also known as the standard error of the estimate).

54. Slide 54 Correlation Coefficient We would expect more promotional expenditures to be associated with more sales at Sherwin-Williams. A measure of that association is the correlation coefficient, r. If r = 0, there is no correlation. If r = 1, the correlation is perfect and positive. The other extreme is r = -1, which is negative.

55. Slide 55 Analysis of Variance R-squared is the percentage of the variation in dependent variable that is explained As more variables are included, R-squared rises Adjusted R-squared, however, can decline »Adj R 2 = 1 – (1-R 2 )[(N-1)/(N-K)] »As K rises, Adj R 2 may decline. _X_X Y _Y_Y ^Yt^Yt Y t predicted ^ X

56. Slide 56 FIGURE 4.7 Partitioning the Total Deviation

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58. Slide 58 Association and Causation Regressions indicate association, but beware of jumping to the conclusion of causation Suppose you collect data on the number of swimmers at a local beach and the temperature and find: Temperature = 61 +.04 Swimmers, and R 2 =.88. »Surely the temperature and the number of swimmers is positively related, but we do not believe that more swimmers CAUSED the temperature to rise. »Furthermore, there may be other factors that determine the relationship, for example the presence of rain or whether or not it is a weekend or weekday. Education may lead to more income, and also more income may lead to more education. The direction of causation is often unclear. But the association is very strong.

59. Slide 59 Multiple Linear Regression Most economic relationships involve several variables. We can include more independent variables into the regression. To do this, we must have more observations (N) than the number of independent variables, and no exact linear relationships among the independent variables. At Sherwin-Williams, besides promotional expenses (PromExp), different regions charge different selling prices (SellPrice) and have different levels of disposable income (DispInc) The next slide gives the output of a multiple linear regression, multiple, because there are three independent variables

60. Slide 60 Figure 4.8 Computer Output: Sherwin-Williams Company Dep var: Sales (Y) N=10 R-squared =.790 Adjusted R 2 =.684 Standard Error of Estimate = 17.417 VariableCoefficient Std error T P(2 tail) Constant310.245 95.075 3.263.017 PromExp.008 0.204 0.038.971 SellPrice -12.202 4.582 -2.663.037 DispInc 2.677 3.160 0.847.429 Analysis of Variance Source Sum of Squares DFMean Squares F p Regression6829.8 32276.6 7.5.019 Residual1820.1 6 303.4

61. Slide 61 Interpreting Multiple Regression Output Write the result as an equation: Sales = 310.245 +.008 ProExp -12.202 SellPrice + 2.677 DispInc Does the result make economic sense? »As promotion expense rises, so does sales. That makes sense. »As the selling price rises, so does sales. Yes, that’s reasonable. »As disposable income rises in a region, so does sales. Yup. That’s reasonable. Is the coefficient on the selling price statistically significant? »The estimated t value is given in Figure 4.8 to be -2.663 on SellPrice. »The critical t value, with 6 ( which is 10 – 3 – 1) degrees of freedom in table B2 is 2.447 »Therefore |-2.663| > 2.447, so reject the null hypothesis, and assert that the selling price is significant!

62. Slide 62 Soft Drink Demand Estimation A Cross Section Of 48 States CoefficientsStandard Errort Stat Intercept159.1794.161.69 Price-102.5633.25-3.08 Income1.001.770.57 Temperature3.940.824.83 Regression Statistics Multiple R0.736 R Square0.541 Adjusted R Square0.510 Standard Error47.312 Observations48 Linear estimation yields:

63. Slide 63 Find The Linear Elasticities Cans = 159.17 -102.56 Price + 1.00 Income + 3.94 Temp (Q/  P)(P/Q) = -102.56(2.19/200)= -1.123 The price elasticity in Alabama is = (  Q/  P)(P/Q) = -102.56(2.19/200)= -1.123 The price elasticity in Nevada is = (Q/  P)(P/Q) = -102.56(2.19/166) = -1.353 The price elasticity in Nevada is = (  Q/  P)(P/Q) = -102.56(2.19/166) = -1.353 (Q/  P)(P/Q) = -102.56(2.38/97)= -2.516 The price elasticity in Wisconsin is = (  Q/  P)(P/Q) = -102.56(2.38/97)= -2.516 The estimated elasticities are elastic for individual states. The estimated elasticities are elastic for individual states. We can estimate the elasticity from the whole samples as: We can estimate the elasticity from the whole samples as: (  Q/  P)  (Mean P/Mean Q) =  102.56 x ($2.22/160) = -1.423, which is also elastic. Linear Specification write as an equation: