2010 Managerial Economics Lecture 3: Elasticity PDF

Managerial Economics Lecture 3: Quantitative Demand and Supply Analysis Elasticity and its Applications McGraw-Hill/Irwin Copyright © 2010 by the McGraw-Hill Companies, Inc. All rights reserved.  Overview ▪ The Elasticity Concept –...

Managerial Economics Lecture 3: Quantitative Demand and Supply Analysis Elasticity and its Applications McGraw-Hill/Irwin Copyright © 2010 by the McGraw-Hill Companies, Inc. All rights reserved.  Overview ▪ The Elasticity Concept – Own Price Elasticity – Elasticity and Total Revenue – Cross-Price Elasticity – Income Elasticity ▪ Demand Functions – Linear – Log-Linear ▪ Regression Analysis 1-2 Elasticity Concept 1-3  Elasticity Concept Quantitative Questions ▪ Our previous two lectures addressed qualitative method of tackling managerial issues. This lecture will look at ‘detailed’ quantitative answers to questions like: ▪ How much do we have to cut our price to achieve 3.2 percent sales growth? ▪ If we cut prices by 6.5 percent, how many more units will we sell? ▪ How much will our sales change if rivals cut their prices by 2 percent or a recession hits and household incomes decline by 2.5 percent? 1-4  Elasticity Concept Scenario ▪ Suppose some variable, such as the price of a product, reduced by 10 percent. What would happen to the quantity demanded of the good? – Based on our previous lecture and the law of demand, a fall in price will lead to a rise in quantity demanded. – However, it will be useful for a manager to know the magnitude of the rise in quantity demanded, whether it will be 5% 10% or any amount rise. – We primarily use the concept of elasticity to establish such a magnitude. 1-5  The Elasticity Concept ▪ How responsive is variable “G” to a change in variable “S” – For instance: the elasticity of your grade with respect to studying is the percentage change in your grade that will result from a given percentage change in the time you spend studying. In other words. %G EG,S = %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. 1-6  The Elasticity Concept The Elasticity Concept Using Calculus BEAR IN MIND: If the absolute value of the elasticity is greater than 1, the numerator is larger than the denominator in the elasticity formula, and we know that a small percentage change in S will lead to a relatively large percentage change in G and the reverse is true. ▪ An alternative way to measure the elasticity of a function G = f(S) is dG S EG,S = dS G 1-7  The Elasticity Concept The Elasticity Concept Using Calculus NOTE: Two aspects of an elasticity are important: (1) its sign and (2) whether it is greater or less than 1 in absolute value. 1-8 Types of Elasticity 1-9  Types of Elasticity of Demand ▪ There are three main types of elasticity: – Point/Own Price Elasticity of Demand – Cross-Elasticity of Demand – Income Elasticity of demand 1-10 Point/Own Price Elasticity of Demand 1-11  Point/Own Price Elasticity of Demand ▪ Businesses cannot directly control demand. ▪ They can seek to influence demand by utilizing a variety of strategies and tactics but ultimately the consumer decides whether to buy a product or not. ▪ One important way in which consumer behavior can be influenced is through a firm changing the price of its good. ▪ Thus, an understanding of the price elasticity of demand is important in anticipating the likely effects of changes in price on demand. ▪ Price elasticity of demand measures how much the quantity demanded responds to change in price. ▪ This means that an elasticity of 0.7 implies that a 1 percent change in price leads to 0.7 percent change in quantity demanded. 1-12  Point/Own Price Elasticity of Demand Computing the Price Elasticity of Demand ▪ The price elasticity of demand is computed as the percentage change in the quantity demanded divided by the percentage change in the price. That is, d %QX EQX ,PX = %PX ▪ It can also be expressed as dQx Px EQx,Px = dPx Qx ▪ It is always Negative because of the ‘law of demand’. Elastic: EQX ,PX 1 Inelastic: EQ X ,PX  1 Unitary: EQ ,P = 1 X X 1-13  Demand Curves according to their Elasticity Fairly elastic demand Demand is described as fairly elastic when a small percentage change in price leads to larger percentage in quantity demanded. P E P1 B Po D Q1 Q0 Qty In the figure, price increases from Po to P1 (a relatively small margin) and quantity demanded decreases from Qo to Q1 (a bigger margin). Here the absolute value of the elasticity is greater than 1. An example of such a good is a good that has close substitutes. For instance, Milo, Ideal Milk, Uncle Sam, Geisha Mackerel and so on. 1-15  Demand Curves according to their Elasticity Fairly Inelastic demand Demand is described as fairly inelastic when a large percentage change in price leads to a small percentage in quantity demanded. P E P1 Po B D Q1 Q0 Qty In the figure, price increases from Po to P1 (a relatively large margin) and quantity demanded decreases from Qo to Q1 (a smaller margin). Here the absolute value of the elasticity is less than 1 but greater than zero. An example of such a good is a good that has no close substitutes. For instance, Petrol, Diesel, Alcohol and so on. 1-16  Demand Curves according to their Elasticity Unitary elastic demand With unitary elastic demand, quantity demanded changes by exactly the same percentage change in price. The demand curve is rectangular hyperbola. P P1 Po Q1 Qo Qty In the figure, price increases from Po to P1 (a relatively small or large margin) and quantity demanded decreases from Qo to Q1 (a same margin). Here the absolute value of the elasticity is equal to 1. 1-16  Demand Curves according to their Elasticity Perfectly Elastic & Inelastic Demand Price Price D D Quantity Quantity PerfectlyElastic(EQ X ,PX = −) PerfectlyInelastic(EQ X ,PX = 0) When demand is perfectly elastic, when demand is perfectly inelastic, a manager who raises price even consumers do not respond at all to slightly will find that none of the changes in price. good is purchased. 1-18  Demand Curves according to their Elasticity Problem: ▪ Suppose that the own price elasticity of demand for a product is -2. If the price of this product fell by 5%, by what percentage would the quantity demanded for a product change? ▪ The demand equation for a product is Qd = 500-225P. Calculate the own-price elasticity of demand if P= 2. Interpret the result. 1-19 Factors Influencing Price Elasticity 1-20  Factors that Influence Price Elasticity of Demand ▪ Availability of close substitutes – The more substitutes available to a good, the more elastic the demand and vise versa. For instance, ideal milk, pork, Toyota cars, Geisha mackerel ▪ Time – Demand tends to be more inelastic in the short term than in the long term. – Time allows consumers to seek out available substitutes. ▪ Expenditure Share – Goods that attract a small share of consumer’s budgets tend to be more inelastic than goods for which consumers spend a large portion of their incomes. For example, spending on salt, pepper, matches (inelastic) and Cars (elastic). 1-21  Factors that Influence Price Elasticity of Demand ▪ Number of uses of the Good – The greater the number of possible uses of a product, the greater the elasticity of demand. – This is because a price reduction in price will lead to a greater proportionate change in quantity demanded for the various uses. – For instance, palm oil, which can be used for soap making, margarine, cooking and so on will tend to have higher elasticity than butter. ▪ Number of New Buyers – Goods that a person normally requires only one at a time (for instance, television), it is new buyers instead of additional demand by existing users that has a major effect on the market demand curve. – Thus when the prices of such goods fall within the reach of numerous lower income groups, demand will increase, and demand will tend to be elastic. 1-22  Factors that Influence Price Elasticity of Demand ▪ Addictiveness of a product – When a product is addictive, its elasticity is inelastic ▪ Necessities verses Luxury – Necessities tend to have relatively inelastic demands For instance if the price of gas and electricity rose together, people will not demand dramatically less of them. They might try and be more energy efficient and reduce their demand a little. – Luxuries such as pizza are highly elastic in nature in that, when their prices rise the quantities demanded fall substantially. 1-23 Price Elasticity and Total Revenue 1-24  Price elasticity and Total Revenue ▪ Suppose a firm sells ideal milk at Ȼ3.00 and it is able to sell 100 tins, what will be its total revenue? ▪ Do you know why? ▪ What will happen to total revenue if price reduces to Ȼ2.50 and sales increase to 150 tins? ▪ What did you get? ▪ What will happen to total revenue if price increases to Ȼ4.00 and sales fall to 50 tins? 1-25  Price elasticity and Total Revenue ▪ What do these scenarios inform you? It means the extent to which quantity demanded changes as a result of price changes (elasticity of demand) influence revenue. 1-26  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. 1-27  The Relationship between Price Changes and Changes in Total Revenue /Ep/ ΔP ΔQ ΔTR Absolute terms >1 - + + >1 + - - ˂1 - + _ ˂1 + - + 1-28 Demand, Elasticity and Total Revenue 1-29 Demand, Elasticity and Total Revenue 1-30  Demand, Marginal Revenue (MR) and Elasticity MR = P   P 40 1+ E Elastic 35 Unit elastic E 30 Inelastic ▪ When 25 – MR > 0, demand is elastic; 20 – MR = 0, demand is unit elastic; 40 50 Q – MR < 0, demand is 0 10 20 inelastic. MR 1-31 Cross-Price Elasticity of Demand 1-32  Cross-Price Elasticity of Demand It reveals the responsiveness of the demand for a good to changes in the price of a related good. This elasticity helps managers ascertain how much its demand will rise or fall due to a change in the price of another firm’s product. d %QX dQx Py E QX EQx,Py = ,PY %Py dPy Qx If EQX,PY > 0, then X and Y are substitutes. If EQX,PY < 0, then X and Y are complements. 1-33  Examples of Cross-Price Elasticity Cross-Price Elasticity Transportation and Recreation -0.05 Food and Recreation 0.15 Clothing and Food -0.18 1-34 Problem You have just opened a new grocery store. Every item you carry is generic (generic beer, generic bread, generic chicken and so on). You recently read an article in the Daily Graphic reporting that the price of recreation is expected to increase by 15%. How will this affect your store’s sales of generic food products. 1-35  Cross-Price Elasticity of Demand Scenario: Cross-price elasticities play an important role in the pricing decisions of firms that sell multiple products. Indeed, many drinking bars offer lime for under Ȼ1.00 because their managers realize that Herb Afrik and lime are complements: When consumers buy Herb Afrik, lime typically accompanies the purchase. Thus, by lowering the price of Herb Afrik, a drinking bar affects its revenues from both Herb Afrik sales and lime sales. The precise impact on these revenues depends on the own price and cross-price elasticities of demand. 1-36  Predicting Revenue Changes from Two Products Suppose that a firm sells two related goods. If the price of X (Herb Afrik) changes, then total revenue will change by: ( (1+ E R = R X Q X ,PX )+ R Y E QY ,PX )%P X 1-37  Cross-Price Elasticity of Demand Example: Suppose a drinking bar earns Ȼ4,000 per week in revenues from Herb Afrik sales ( product X) and Ȼ2,000 per week from lime sales (product Y). Thus, Rx = Ȼ4,000 and Ry = Ȼ2,000. If the own price elasticity of demand for Herb Afrik is -1.5 and the cross-price elasticity of demand between lime and Herb Afrik is -4.0, what would happen to the firm’s total revenues if it reduced the price of Herb Afrik by 1 percent? 1-38  Cross-Price Elasticity of Demand Note ▪ Lowering the price of Herb Afrik by 1% increases total revenues by Ȼ100. – Notice that Ȼ20 of this increase comes from increased Herb Afrik revenues. – In addition, Ȼ80 of the increase is from extra lime sales. 1-39 Income Elasticity of Demand 1-40  Income Elasticity of Demand It is a measure of the responsiveness of consumer demand to changes in income. d dQx M EQ ,M = %QX EQx,M = X %M dM Qx If EQX,M > 0, then X is a normal good. If EQX,M < 0, then X is an inferior good. 1-41  Income Elasticity of Demand Problem Your firm’s research department has estimated the income elasticity of demand for electric heater to be -1.94. You have just read in the papers that due to an upturn in the economy, consumer incomes are expected to rise by 10 percent over the next three years. As a manager of an electrical shop, how will this forecast affect your purchases of electric heater? 1-42  Income Elasticity of Demand Solution Since electric heater has an income elasticity of -1.94 and consumer income is expected to rise by 10 percent, you can expect to sell 19.4 percent less electric heater over the next three years. Therefore, you should decrease your purchases of electric heater by 19.4 percent, unless something else changes. 1-43 Linear Demand Function and Elasticities 1-44  Linear Demand Function and Elasticities ▪ General Linear Demand Function and Elasticities: Q X = 0 +  X PX +  Y PY +  M M +  H H d PX PY M EQX ,PX =  X EQX ,PY = Y EQ X ,M =  M QX QX QX Own Price Cross Price Income Elasticity Elasticity Elasticity 1-45  Linear Demand Function and Elasticities Problem: The daily demand for ODIKE Ventures shoes is estimated to be QX = 100− 3PX + 4PY − 0.01M + 2AX d Where Ax represents the amount of advertising spent on shoes (X), Px is the price of good X, Py is the price of good Y, and M is average income. Suppose good X sells at Ȼ25 a pair, good Y sells at Ȼ35, the company utilizes 50 units of advertising, and average consumer income is Ȼ20,000. Calculate and interpret the own price, cross-price, and income elasticities of demand. 1-46  Uses of Elasticities ▪ Pricing ▪ Managing cash flows ▪ Impact of changes in competitors’ prices ▪ Wage negotiations by Trade Unions ▪ Impact of advertising campaigns. 1-47  Example 1: Pricing and Cash Flows ▪ According to an IEA Report by Mrs. Mensah, Vodafone’s own price elasticity of demand for long distance services is -8.64. ▪ Vodafone needs to boost revenues in order to meet it’s marketing goals. ▪ To accomplish this goal, should Vodafone raise or lower it’s price? 1-48  Answer: Lower price! Since demand for Vodafone services is elastic, a reduction in price will increase quantity demanded by a greater percentage than the price decline, resulting in more revenues for Vodafone. 1-49  Example 2: Quantifying the Change ▪ If Vodafone lowered price by 3 percent, what would happen to the volume of long distance telephone calls routed through Vodafone? 1-50  Answer: Calls Increase! Calls would increase by 25.92 percent! d %Q X EQ X ,PX = −8.64 = %PX d %Q X − 8.64 = − 3% − 3%  (− 8.64 ) = %Q X d d %QX = 25.92% 1-51 Example 3: Impact of a Change in a Competitor’s Price ▪ According to an IEA Report by Mrs. Mensah, Vodafone’s cross price elasticity of demand for long distance services is 9.06. ▪ If competitors (MTN, Airtel, Glo and so on) reduced their prices by 4 percent, what would happen to the demand for Vodafone’s services? 1-52  Answer: Vodafone’s Demand Falls! Vodafone’s demand would fall by 36.24 percent! 1-53  How does elasticity influence wage negotiation and advertising? ▪ When the demand for a good or service produced by labor has inelastic demand, unions could negotiate for high wages. ▪ Firms will try to make their products more inelastic using advertisements for instance, so that they are ensured a decent quantity demanded regardless of their set price. For instance, Alomo bitters 1-54  Interpreting Demand Functions ▪ Mathematical representations of demand curves. ▪ Example: QX = 10 − 2PX + 3PY − 2M d – 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). 1-55  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. 1-56  Regression Analysis ▪ Demand and Supply functions are not fictitious textbook constructs—they are equations that managers may actually obtain by using appropriate econometric techniques and data. ▪ Analysis of a bivarate demand and supply regression is quite simple to do ▪ Quantity function is specified as: ▪ Q = a + bp 𝑛 σ 𝑃𝑄 − σ 𝑃 σ 𝑄 ▪ where b = 𝑛 σ 𝑝2 − (σ 𝑃)2 ▪ where a= Q − b  P n n 1-57  Example As the division manager of BEANTO Company Ltd., a firm that deals in White Marker Boards, your marketing department has compiled the following data on the price and quantity of White Marker Boards for the last 10 months: Observation Quantity Price(GH¢) 1 28 250 2 69 400 3 43 450 4 32 550 5 42 575 6 72 375 7 66 375 8 49 450 9 70 400 10 60 375 1-58  Example continued... 1.Estimate the function describing the information on the table making Q the dependent variable. 2. What type of economic function did you obtain in (1) above? 3. Your consultant has estimated another function to be Q = -30.10 + 0.06P. Identify this function in terms of demand or supply. 4. Find the market clearing price and quantity of White Marker Boards. 5.Estimate the price elasticity of demand for White Marker Boards at the equilibrium price and quantity. Interpret your answer. 6.Based on the price elasticities of demand, what will you advise the management of BEANTO Company Limited to do to the price of White Marker Boards in order to increase total sales? 1-59  Suggested solution Obs Quantity Price PQ P2 1 28 250 7000 62500 2 69 400 27600 160000 3 43 450 19350 202500 4 32 550 17600 302500 5 42 575 24150 330625 6 72 375 27000 140625 7 66 375 24750 140625 8 49 450 22050 202500 9 70 400 28000 160000 10 60 375 22500 140625 531 4200 220000 1842500 1-60  Suggested solution continued 1. Q = a + bp 𝑛 σ 𝑃𝑄 − σ 𝑃 σ 𝑄 10(220000) − (4200)(531) ▪ where b = = = -0.04 2 𝑛 σ 𝑝 − (σ 𝑃) 2 10(1842500) − (4200) 2 ▪ where a=  Q − b  P 531 = − (−0.04) 4200 = 69.9 n n 10 10 ▪ Therefore the demand function is specified as: ▪ Qd = 69.9 - 0.04P 1-61  Suggested solution continued 2. The estimated function is a demand function. 3.The second function is a supply function since it shows a positive relationship between price and quantity. 4. At Equilbirum, Qd= QS 69.9 - 0.04P = -30.10 + 0.06P 69.9 + 30.10 = 0.06P + 0.04P 100 = 0.1P P = 1000 Qe= Qs = Qd Qe = 69.9 - 0.04(1000) = 29.9 units 1-62  Suggested solution continued Qd P 5. P.E.D =  = − 0.04  1000 = -1.34 P Q 29.9 The good is fairly elastic. A 1% reduction in price will lead to an increase in demand for marker boards by 1.34% and vice versa 6. The management of BEANTO should reduce the price of marker to increase revenue. 1-63 Computing consumer and producer surplus When Qd = 0 0 = 69.9 – 0.04P P = 1747.5 CS = 0.50 x 29.9 x (1747.5 – 1000)= GHS 11,175.13 When Qs = 0 0 = -30.10 + 0.06P P = 501.67 PS = 0.50 x 29.9 x (1000 – 501.67) = GHS 7450.03  Multiple Regression Analysis ▪ It is important to stress, to do multiple regression analysis, it requires some knowledge in econometrics, a specialized field of economics that takes years of study to master ▪ It is far beyond the scope of this course to teach you how to estimate multiple demand or supply regression functions, but it is possible to convey the basic ideas econometricians use to obtain such information ▪ Suppose the following equation: ▪ Qx = βo + β1X1 + β2X2 + β3X3 + β4X4 +...... βnXn 1-66  Multiple Regression Analysis ▪ The t-Statistic: The t-statistic of a parameter estimate is the ratio of the value of the parameter estimate to its standard error. b ▪ T Statistics = se ▪ In practice, we employ sample data for analysis. Thus we need to be sure that even the estimated coeffecient for the sample is still significant or not equal to zero when it comes to the whole population. ▪ A useful rule of thumb is that if the absolute value of a t- statistic is greater than or equal to 2, then the corresponding parameter estimate is statistically different from zero. 1-67  Multiple Regression Analysis ▪ Regression packages report P-values, which are a much more precise measure of statistical significance. ▪ The rule of thumb is if the P-value is less than 0.05, we say that the estimated coefficient is statistically significant. ▪ In addition to evaluating the statistical significance of one or more coefficients, one can also measure the precision with which the overall regression line fits the data. ▪ The R-square (also called the coefficient of determination) tells the fraction of the total variation in the dependent variable that is explained by the regression. 1-68  Example ▪ A recent study of BMW production found that the following regression predicted BMW output : Regression Variable Coefficient t-Statistic Constant 23.0 4.5 Disposable Income 12.9 3.6 Prime Rate -97.8 -1.2 Advertisement 19.9 5.1 BMW Price -230.0 -5.0 Non-auto Price 6.0 2.1 ▪ The R-square was 0.862, and the standard error of the estimate was 532. Answer the following questions using this table. 1-69 a. Specify the estimable equation which represent the table. Qx = B0 + B1DI + B2PR + B3ADV + B4Px + B5NAP b.Which of the coeffeceint(s) is(are) not significant and why? PR is statistically not signficant. Since its t-statistics in absolute terms is less than the rule of thumb of 2. c.Based on your answer in (b), specify the final estimated equation Qx = 23 + 12.9 DI + 19.9ADV -230 Px + 6.0 NAP d.Does the equation specified in (c) above remind you of a demand curve or a supply curve? Explain. Demand function. This is because it shows a negative relationship between the output (Q) of BMW and the Price of BMW. Again, the intercept is positive which mostly applies to demand curve. 1-70 e. Interpret the relevance of the coefficients to the manager of BMW. ▪ When all variables are set to zero, there will still be quantity demanded of 23. ▪ A unit increase in disposable income will lead to a 12.9 unit increase in the Quantity Demanded of BMW and vice versa ▪ A unit increase in advertisement cost will lead to a 19.9 unit increase in Quantity Demanded of BMW and vice versa ▪ A unit increase in BMW price will lead to a 230 unit decrease in Quantity demanded BMW and vice versa ▪ A unit increase in non-auto price will lead to a 6.0 unit increase in Quantity demanded of BMW and vice versa 1-71 f.Given another function of the form , 0= -47 - Q + 170P where P is the price of BMW and Q is the quantity of BMW respectively. What will be the market clearing price and quantity of BMW given that Non-Auto price is GHS 0.2m ; Prime rate is 0.02, Advertisement cost is GHS 2m and disposable income is GHS10m. Qd = 23 +12.9(10) + 19.9(2) - 230Px +6(0.2) Qd = 193 - 230Px Qs = -47 +170p At equilibrium : Qd = Qs 193 - 230Px = -47 + 170Px 193 +47 = 170Px + 230Px 240 = 400Px Px = GHS 0.6m 1-72 ▪ Qe = Qs=Qd ▪ Qe = -47 + 170(0.6) = 55 units f. Estimate and interpret all possible elasticities of Demand Qd P 0.6 PED =  = − 230 P Q 55 = -2.51 This means that a percentage increase in BMW Price will lead to a 2.51% decrease in Quantity Demanded of BMW. The good has fairly price elastic Demand Qd M  10 = 2.35 MED =  M Q = 12.9 55 This means that a percentage increase in diposable income of customers will will lead to a 2.35% increase in Quantity Demanded of BMW. The good is a normal good. 1-73   Q d BM W NA 0.20 ▪ C.P.E.D=  = 6.0 = 0.02 N A P 55 ▪ This means that a percentage increase in NAP will lead to a 0.02% increase in Quantity Demanded of BMW. Non-Auto and BMW are therefore substitutes Qd Adv 2 ▪ A.E.D =  = 19.9 = 0.73 Adv Qd 55 ▪ This means that a percentage increase in Advertisment cost will lead to a 0.73% increase in Quantity Demanded of BMW. Even though it is not reducing quantity demanded, the advertisement could do much better than this. 1-74  An Example ▪ Use a spreadsheet to estimate the following log-linear demand function. ln Qx = 0 + x ln Px + e 1-75  Summary Output Regression Statistics Multiple R 0.41 R Square 0.17 Adjusted R 0.15 Square Standard Error 0.68 Observations 41.00 ANOVA df SS MS F Significance F Regression 1.00 3.65 3.65 7.85 0.01 Residual 39.00 18.13 0.46 Total 40.00 21.78 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 7.58 1.43 5.29 0.000005 4.68 10.48 ln(P) -0.84 0.30 -2.80 0.007868 -1.44 -0.23 1-76  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. 1-77  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. 1-78