Chapter 6: Elasticity and Demand McGraw-Hill/Irwin Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved.

Elasticity

Price Elasticity of Demand (E) Measures responsiveness or sensitivity of consumers to changes in the price of a good 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

Sign of Price Elasticity of Demand The coefficient of the price elasticity of demand is always negative It is intuitively more appealing to talk about price elasticity in terms of its absolute value.

Price Elasticity of Demand (E) Table 6.1 Elasticity Responsiveness E Elastic Unitary Elastic Inelastic %∆Q> %∆P E> 1 %∆Q= %∆P E= 1 %∆Q< %∆P E< 1

Elastic Demand

Inelastic Demand Demand becomes less elastic as price declines along a linear demand curve.

Price Elasticity of Demand (E) Percentage change in quantity demanded can be predicted for a given percentage change in price as: %Qd = %P x E Percentage change in price required for a given change in quantity demanded can be predicted as: %P = %Qd ÷ E

Price Elasticity & Total Revenue Table 6.2 Elastic Quantity-effect dominates Unitary elastic No dominant effect Inelastic Price-effect dominates Price rises Price falls %∆Q> %∆P %∆Q= %∆P %∆Q< %∆P TR falls No change in TR TR rises TR rises No change in TR TR falls

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

Factors Affecting Price Elasticity of Demand Necessities versus Luxuries Luxuries have a more elastic demand Definition of the market The more finely defined the market the more elastic the demand. The more aggregate the definition of the market the more inelastic the demand hamburger < beef <all meat products

Calculating Price Elasticity of Demand Price elasticity can be calculated by multiplying the slope of demand (Q/P) times the ratio of price to quantity (P/Q)

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

Calculating Price Elasticity of Demand Regression analysis provides a point estimate Arc elasticity is typically only used for teaching purposes

Computation of Elasticity Over an Interval When calculating price elasticity of demand over an interval of demand, use the interval or arc elasticity formula

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

Price Elasticity for Linear Demand

Point Elasticity When Demand is Linear Given Q = a + bP + cM + dPR, let income & price of the related good take specific values M and PR , respectively Then express demand as Q = a′ + bP , where a′ = a + cM + dPR and the slope parameter is b = ∆Q ∕ ∆P

Point Elasticity When Demand is Linear Compute elasticity using either of the two formulas below which give the same value for E Where P and Q are values of price and quantity demanded at the point of measure along demand, and A ( = –a′ ∕ b) is the price-intercept of demand

Point Elasticity When Demand is Curvilinear Compute elasticity using either of two equivalent formulas below Where ∆Q ∕ ∆P is the slope of the curved demand at the point of measure, P and Q are values of price and quantity demanded at the point of measure, and A is the price-intercept of the tangent line extended to cross the price axis

Elasticity (Generally) Varies Along a Demand Curve For linear demand, price and Evary directly The higher the price, the more elastic is demand The lower the price, the less elastic is demand For curvilinear demand, no general rule about the relation between price and quantity Special case of Q = aPb which has a constant price elasticity (equal to b) for all prices

Constant elasticity demand function

Constant Elasticity of Demand (Figure 6.3)

Constant elasticity demand function

Marginal Revenue Marginal revenue (MR) is the change in total revenue per unit change in output 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 (Table 6.3) Unit sales (Q) Price TR = P  Q MR = TR/Q $4.50 1 4.00 2 3.50 3 3.10 4 2.80 5 2.40 6 2.00 7 1.50 $ 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 (Figure 6.4) Panel A Panel B

Demand & Marginal Revenue When inverse demand is linear, P = A + BQ (A > 0, B < 0) Marginal revenue is also linear, intersects the vertical (price) axis at the same point as demand, & is twice as steep as demand MR = A + 2BQ

Proof

Marginal Revenue

Total Revenue

Linear Demand, MR, & Elasticity (Figure 6.5)

MR, TR, & Price Elasticity (Table 6.4) Marginal revenue Total revenue Price elasticity of demand MR > 0 MR = 0 MR < 0 TR increases as Q increases (P decreases) Elastic (│E│> 1) TR is maximized Unit Elastic (│E│= 1) TR decreases as Q increases (P decreases) Inelastic (│E│< 1)

Marginal Revenue & Price Elasticity For all demand & marginal revenue curves, the relation between marginal revenue, price, & elasticity can be expressed as

Proof

Marginal Revenue & Price Elasticity Note that as E - that MRP

Income Elasticity Income elasticity (EM) measures the responsiveness of quantity demanded to changes in income, holding the price of the good & all other demand determinants constant Positive for a normal good Negative for an inferior good

Normal Good

Inferior Good

Cross-Price Elasticity Cross-price elasticity (EXR) measures the responsiveness of quantity demanded of good X to changes in the price of related good R, holding the price of good X & all other demand determinants for good X constant Positive when the two goods are substitutes Negative when the two goods are complements

Substitute Good

Interval Elasticity Measures To calculate interval measures of income & cross-price elasticities, the following formulas can be employed

Point Elasticity Measures For the linear demand function Q = a + bP + cM + dPR, point measures of income & cross-price elasticities can be calculated as