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Learning Objectives • Define and measure elasticity • Apply concepts of price elasticity, cross-elasticity, and income elasticity • Understand determinants of elasticity • Show how elasticity affects revenue Price Elasticity of Demand (E) • Measures responsiveness or sensitivity of consumers to changes in the price of a good • %Q E %P • P & Q are inversely related by the law of demand so E is always negative – The larger the absolute value of E, the more sensitive buyers are to a change in price Calculating Price Elasticity of Demand • Price elasticity can be measured at an interval (or arc) along demand, or at a specific point on the demand curve – If the price change is relatively small, a point calculation is suitable – If the price change spans a sizable arc along the demand curve, the interval calculation provides a better measure Computation of Elasticity Over an Interval • When calculating price elasticity of demand over an interval of demand, use the interval or arc elasticity formula Q Average P E P Average Q So, arc price elasticity of demand = Q2 Q1 P2 P1 Ep (Q1 Q2 ) / 2 ( P1 P2 ) / 2 • • • • • Ep = Coefficient of arc price elasticity Q1 = Original quantity demanded Q2 = New quantity demanded P1 = Original price P2 = New price Computation of Elasticity at a Point • When calculating price elasticity at a point on demand, multiply the slope of demand (Q/P), computed at the point of measure, times the ratio P/Q, using the values of P and Q at the point of measure • Method of measuring point elasticity depends on whether demand is linear or curvilinear The Price Elasticity of Demand • Point elasticity: measured at a given point of a demand (or a supply) curve. dQ P1 εP = x dP Q1 The Price Elasticity of Demand The point elasticity of a linear demand function can be expressed as: Q P1 p P Q1 The Price Elasticity of Demand • Some demand curves have constant elasticity over the relevant range • Such a curve would look like: Q = aP-b where –b is the elasticity coefficient • This equation can be converted to linear by expressing it in logarithms: log Q = log a – b(log P) The Price Elasticity of Demand • Elasticity differs along a linear demand curve. Price Elasticity of Demand (E) Elasticity Responsiveness E Elastic %Q%P E 1 Unitary Elastic %Q%P E 1 Inelastic %Q%P Perfect elasticity: E = ∞ Perfect inelasticity: E = 0 E 1 Factors Affecting Price Elasticity of Demand • Availability of substitutes – The better & more numerous the substitutes for a good, the more elastic is demand • Percentage of consumer’s budget – The greater the percentage of the consumer’s budget spent on the good, the more elastic is demand • Time period of adjustment – The longer the time period consumers have to adjust to price changes, the more elastic is demand The Price Elasticity of Demand • A long-run demand curve will generally be more elastic than a short-run curve. • As the time period lengthens consumers find way to adjust to the price change, via substitution or shifting consumption The Price Elasticity of Demand • There is a relationship between the price elasticity of demand and revenue received. – Because a demand curve is downward sloping, a decrease in price will increase the quantity demanded – If elasticity is greater than 1, the quantity effect is stronger than the price effect, and total revenue will increase Price Elasticity & Total Revenue Elastic Unitary elastic Inelastic Quantity-effect dominates No dominant effect Price-effect dominates Price rises TR falls No change in TR TR rises Price falls TR rises No change in TR TR falls • As price decreases – Revenue rises when demand is elastic. – Revenue falls when it is inelastic. – Revenue reaches its peak when elasticity of demand equals 1. • Marginal Revenue: The change in total revenue resulting from changing quantity by one unit. Total Revenue MR Quantity • Since MR measures the rate of change in total revenue as quantity changes, MR is the slope of the total revenue (TR) curve Demand & Marginal Revenue Unit sales (Q) Price 0 $4.50 1 4.00 2 3.50 3 3.10 4 2.80 5 2.40 6 2.00 7 1.50 TR = P Q $ MR = TR/Q -- 0 $4.00 $4.00 $7.00 $3.00 $9.30 $2.30 $11.20 $1.90 $12.00 $0.80 $12.00 $0 $10.50 $-1.50 Demand, MR, & TR Panel A Panel B • For a straight-line demand curve the marginal revenue curve is twice as steep as the demand. • At the point where marginal revenue crosses the X-axis, the demand curve is unitary elastic and total revenue reaches a maximum. Linear Demand, MR, & Elasticity • Some sample elasticities – – – – – Coffee: short run -0.2, long run -0.33 Kitchen and household appliances: -0.63 Meals at restaurants: -2.27 Airline travel in U.S.: -1.98 Beer: -0.84, Wine: -0.55 MR, TR, & Price Elasticity Marginal Total revenue revenue MR > 0 TR increases as Q increases MR = 0 MR < 0 (P decreases) Price elasticity of demand Elastic Elastic (E> 1) (E> 1) Unit Unitelastic elastic TR is maximized (E= 1) (E= 1) TR decreases as Inelastic Inelastic (E< 1) Q increases (P decreases) (E< 1) Marginal Revenue & Price Elasticity • For all demand & marginal revenue curves, the relation between marginal revenue, price, & elasticity can be expressed as 1 MR P 1 E The Cross-Elasticity of Demand • Cross-elasticity of demand: The percentage change in quantity consumed of one product as a result of a 1 percent change in the price of a related product. % Q A EX % PB The Cross-Elasticity of Demand • Arc Elasticity Q2 A Q1 A P2 B P1B Ex (Q1 A Q2 A ) / 2 ( P1B P2 B ) / 2 The Cross-Elasticity of Demand • Point Elasticity QA PB EX QA PB The Cross-Elasticity of Demand • The sign of cross-elasticity for substitutes is positive. • The sign of cross-elasticity for complements is negative. • Two products are considered good substitutes or complements when the coefficient is larger than 0.5. Predicting Revenue Changes from Two Products Suppose that a firm sells to related goods. If the price of X changes, then total revenue will change by: R RX 1 EQX , PX RY EQY , PX %PX Income Elasticity • Income Elasticity of Demand: The percentage change in quantity demanded caused by a 1 percent change in income. %Q EY %Y Income Elasticity • Arc Elasticity Q2 Q1 Y2 Y1 EY (Q1 Q2 ) / 2 (Y1 Y2 ) / 2 Income Elasticity • Categories of income elasticity – Superior goods: EY > 1 – Normal goods: 0 >EY >1 – Inferior goods – demand decreases as income increases: EY < 0 Other Elasticity Measures • Elasticity is encountered every time a change in some variable affects quantities. – Advertising expenditure – Interest rates – Population size 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! 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! EQX , PX % Q X 8.64 % PX d % Q X 8.64 3% d 3% 8.64 % QX d % Q X 25.92% d 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? Answer • AT&T’s demand would fall by 36.24 percent! EQX , PY %QX 9.06 %PY %QX 9.06 4% d 4% 9.06 %QX d %QX 36.24% d d Elasticity of Supply • Price Elasticity of Supply: The percentage change in quantity supplied as a result of a 1 percent change in price. % Quantity Supplied ES % Price • If the supply curve slopes upward and to the right, the coefficient of supply elasticity is a positive number. Elasticity of Supply • Arc elasticity Q2 Q1 P2 P1 Es (Q1 Q2 ) / 2 ( P1 P2 ) / 2 Elasticity of Supply • When the supply curve is more elastic, the effect of a change in demand will be greater on quantity than on the price of the product. • With a supply curve of low elasticity, a change in demand will have a greater effect on price than on quantity. Interpreting Demand Functions • Mathematical representations of demand curves. • Example: d QX 10 2 PX 3PY 2M • X and Y are substitutes (coefficient of PY is positive). • X is an inferior good (coefficient of M is negative). Linear Demand Functions • General Linear Demand Function: QX 0 X PX Y PY M M H H d P EQX , PX X X QX Own Price Elasticity EQ X , PY PY Y QX Cross Price Elasticity M EQX , M M QX Income Elasticity 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. Log-Linear Demand • General Log-Linear Demand Function: ln QX d 0 X ln PX Y ln PY M ln M H ln H X Cross Price Elasticity : Y Income Elasticity : M Own Price Elasticity : Example of Log-Linear Demand • ln(Qd) = 10 - 2 ln(P). • Own Price Elasticity: -2. Graphical Representation of Linear and Log-Linear Demand P P D Linear D Q Log Linear Q