Managerial Economics & Business Strategy Chapter 3 Quantitative Demand Analysis

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

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

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

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

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

Own Price Elasticity of Demand - Mid-point

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

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

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

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)

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

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

Own-Price Elasticity and Total Revenue 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.

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

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.

Own Price Elasticity Implications 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

Own Price Elasticity Implications If demand is elastic: Raise price revenue down volume down  total costs down profits ??? Lower price revenue up volume up  total costs up

Cross Price Elasticity of Demand + Substitutes - Complements

Income Elasticity + Normal Good - Inferior Good

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

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

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?

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?

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.

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?

Answer Calls would increase by 25.92 percent!

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?

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

Specific Demand Functions Linear Demand Own Price Elasticity Cross Price Elasticity Income Elasticity

Log-Linear Demand

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

P P Q D D Q Linear Log Linear

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

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

An Example - Data

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

An Example - Regression Results

An Example - Regression Results

An Example - Regression Results

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

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

An Example - Log-linear Data

An Example - Log-linear Data

An Example - Log-linear Data

An Example - Log-linear Data

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

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

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.