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Elasticity

Elasticity. A unit free measure of responsiveness of changes in one variable to changes in another variable. Own price elasticity of demand: a measure of responsiveness of quantity demanded to a change in the price of the good. Slope is not a good measure.

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Elasticity

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  1. Elasticity A unit free measure of responsiveness of changes in one variable to changes in another variable. Own price elasticity of demand: a measure of responsiveness of quantity demanded to a change in the price of the good

  2. Slope is not a good measure. The demand for apples (measured in pounds) as a function of their price (in dollars) is given by Qd = 10 - 2P If the price is expressed in cents the equation becomes Qd = 10 - 200P

  3. Elasticity

  4. Interpreting elasticity The price elasticity of demand for DVD players is equal to 2. A 1% increase in the price results in a 2% decrease in the quantity demanded.

  5. Limiting case 1. Perfectly elastic demand.Perfectly elastic supply.

  6. Limiting case 2.Perfectly inelastic demand.Perfectly inelastic supply.

  7. The demand is elastic if the elasticity greater than one. The demand is inelastic if the elasticity is smaller than one. The demand is unit-elastic if the elasticity is equal to one.

  8. 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.

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

  10. Example. Parking service . • Imagine that the goal of the parking service is to maximize revenue • Imagine that the cost of providing parking for an additional day is zero • What is the price elasticity of demand for illegal parking?

  11. 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. • 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.

  12. Who pays the tax? • An application of the concept of elasticity • The price of a gallon of gas is $1.53 • This price includes 23 cents of tax • What would be the price is the tax were removed?

  13. ΔP T Effect of a sales tax (tax) on the equilibrium.Price in the market goes up but not by the full amount of the tax.

  14. Tax Revenue Effect of a sales tax (tax) on the equilibrium.A tax causes a decrease in the total surplus:

  15. Consumer’s share of lost surplus Producer’s share of lost surplus Who pays the tax?The burden of a sales tax is carried by the sellers or the buyers depending who loses more surplus as a result of the tax.

  16. The more inelastic the demand the greater share of the tax is paid buy the consumers.Think of cigarettes, gasoline, or alcoholic beverages.

  17. The more elastic the supply the greater share of the tax is paid by consumers.

  18. What about a situation in which supply is inelastic?Think of real estate.

  19. Cross Price Elasticity of Demand + Substitutes - Complements

  20. Income Elasticity + Normal Good - Inferior Good

  21. 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!

  22. 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?

  23. 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.

  24. 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?

  25. Answer • Calls would increase by 25.92 percent!

  26. 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?

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

  28. P 50 40 30 20 10 Q 0 M • The following graph represents demand for illegal parking in the town of Parkdale. • A)    What price maximizes revenue from parking tickets? • B)     What price minimizes illegal parking? • C)    What is the equation of the demand curve? • D)    Population of the Parkdale doubled as a result of increased enrollment at a local university. What can we say about the revenue maximizing price?

  29. Demand Functions • Mathematical representations of demand curves • Example: • X and Y are substitutes (coefficient of PY is positive) • X is an inferior good (coefficient of M is negative)

  30. Specific Demand Functions • Linear Demand Income Elasticity Own Price Elasticity Cross Price Elasticity

  31. 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

  32. Log-Linear Demand

  33. Example of Log-Linear Demand • ln Qd = 10 - 2 ln P • Own Price Elasticity: -2

  34. P Q P D D Q Log Linear Linear

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