DEMAND ELASTICITY Overview Context: Product manager wants to - PowerPoint PPT Presentation

DEMAND ELASTICITY

Overview • Context: Product manager wants to estimate impact of price change on sales (quantity and revenue). How sensitive is demand to price? How important is the pricing of competing products? • Concepts: demand elasticity, cross-elasticity • Economic principle: sometimes reducing price attracts many more customers, sometimes very few

How sensitive is demand to price changes? • Example 1: world oil demand decreases by 1.3 million barrels a day when price increases from $50 to $60 dollars per barrel. Would you consider the demand for oil very sensitive or not very sensitive to price? • Example 2: demand for sugar in Europe decreases by 1 million tones per day when average retail price increases from e .80 to e .90 per kilo. Can you compare the demand for sugar in Europe to the worldwide demand for oil? • Problem: by measuring the slope of the demand curve, we are stuck with units: barrels, dollars, kilos, euros, and so on.

Demand elasticity: definition d q d log q d q p q = = ✏ ≡ d p d p q d log p p

Demand elasticity: definition d q d log q d q p q = = ✏ ≡ d p d p q d log p p ∆ q % ∆ quantity q = ≈ ∆ p % ∆ price p

Demand elasticity: definition d q d log q d q p q = = ✏ ≡ d p d p q d log p p ∆ q % ∆ quantity q = ≈ ∆ p % ∆ price p ∆ log quantity ≈ ∆ log price

Demand elasticity: notes • Elasticity and slope are not the same • Elasticity is independent of units • Knowing price change, quantity change may be estimated based on elasticity: ∆ q ✏ ∆ p ≈ q p

Examples Product Elasticity Milk -0.5 Cigarettes -0.5 Beer -0.8 Apples -1.3 US luxury cars in US -1.9 Foreign luxury cars in US -2.8

Elasticity illustrated: linear demand p ✏ = −∞ • | ✏ | > 1 | ✏ | = 1 • | ✏ | < 1 ✏ = 0 q •

Elasticity illustrated: constant elasticity p ✏ = −∞ | ✏ | > 1 | ✏ | < 1 ✏ = 0 q

Elasticity, price, and revenue Revenue ≡ R = p × q . Therefore: ∆ R ∆ ( p × q ) q ∆ p + p ∆ q = ≈ ( p × q ) ( p × q ) R ∆ p + ∆ q ∆ p + ✏ ∆ p ∆ p = = = p (1 + ✏ ) p q p p If price falls, then: • Revenue rises if ✏ < − 1 (that is, | ✏ | > 1) • Revenue falls if ✏ > − 1 (that is, | ✏ | < 1) • Revenue is unchanged if ✏ = − 1

Elasticity, price, and revenue Examples: for a 1% decrease in price, • Cigarettes: revenue falls approx 0.5% = − .1% × ( 1+( − .5) ) • U.S. luxury cars: revenue rises approx 0.9% • Foreign luxury cars: revenue rises approx 1.8%

Revenue change from price decrease p Loss L = q ( − ∆ p ), Gain G = p ∆ q G > L i ff p ∆ q > q ( − ∆ p ) ∆ q p i ff q < − 1 ∆ p E 1 ∆ p E 2 q p q ∆ q

Cross-price elasticity • Idea: How sensitive is demand for your product to prices of competing products? Answer: Cross-price elasticity. d q i q i ✏ ij = d p j p j • Jargon: − If ✏ ij > 0, we say i and j are substitutes − If ✏ ij < 0, we say i and j are complements − If ✏ ij = 0, we say i and j are independent • Examples?

Income elasticity • Idea: How sensitive is demand for your product to consumer income? Answer: income elasticity. d q q ✏ y = d y y • Jargon: − Inferior good: ✏ y < 0 − Normal good: ✏ y > 0 − Necessity: 0 < ✏ y < 1 − Luxury: ✏ y > 1 • Examples?

Example: U.S. gasoline demand (cont)

Example: gasoline demand • Based on U.S. data from 1953–2004, ln q = − 16.1 − 0.03 ln p + 1.17 ln y − 0.33 ln c + 0.85 ln n where q : gasoline consumption p : gasoline price y : per capita income c : price of cars n : population • What is the gasoline demand elasticity? Income elasticity? Cross price elasticity w.r.t. cars? How do you classify the good “gasoline”?

Example: gasoline demand • From 1953 to 2004, p , y , c and n increased at the following annual rates: 3.9, 2.2, 2.0, 1.2%. How much do you expect demand to have grown? • Recall that d z z = ✏ zx d x x , for any z and x . Hence, ∆ q = − .03 × 3.9% + 1.17 × 2.2% − 0.33 × 2 + .85 × 1.2% q = − .117% + 2.574% − 0.66% + 1.02% = 2.817% • Note: actual growth rate was 2.7%

Takeaways • The elasticity (of demand) measures sensitivity of buyers to changes in price • It’s useful for computing impact of price changes on quantity and revenue • Cross-price and income elasticities measure sensitivity to other factors