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Price Elasticity of Demand: Impact and Determinants

This example explores the concept of price elasticity of demand and its impact on revenue, as well as the determinants that affect elasticity. Graphical interpretations and calculations are provided.

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Price Elasticity of Demand: Impact and Determinants

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  1. Stephen ChiuUniversity of Hong Kong Elasticity

  2. Example 4.1 • The Western tunnel, which has low travel, is now charging $50 per car. Should it reduce the toll to $40, say? Two factors for consideration. • Its travel will increase. • But the toll per car is lower. • The net impact on its revenue depends on the responsiveness of quantity demanded to the price reduction.

  3. Price Elasticity of Demand • The Price Elasticity of Demand is a measure of the responsiveness of the quantity demanded of a good to a change in the price of that good. • Formally, it is the percentage change in the quantity demanded that results from a 1 percent change in its price.

  4. Elasticity • Generally, price elasticity is a measure of the responsiveness of the quantity demanded of a good to a change in the price of that good

  5. Example 4.2 • The price of pork falls by 2% and the quantity demanded increases by 6% • Then the price elasticity of demand for pork is 6% 3 = 2%

  6. Example 4.3. • If a 1 percent rise in the price of shelter caused a 2 percent reduction in the quantity of shelter demanded, the price elasticity of demand for shelter would be 2% 2 = 1%

  7. Price Elasticity of Demand • Measuring Price Elasticity of Demand • Observations • Price elasticity of demand is always negative (i.e., an inverse relationship between price and quantity). • For convenience we often drop the negative sign. (For other types of elasticity, the sign is crucial and cannot be dropped.)

  8. Price Elasticity of Demand Unit elastic inelastic Elastic Price elasticity of demand 0 1 2 3

  9. Example 4.4.What is the elasticity of demand for sushi? • Originally • Price = $10/piece • Quantity demanded = 400 pieces/day • New • Price = $9.7/piece • Quantity demanded = 404 pieces/day, then 1 (404 - 400)/400 1% = = (9.7 - 10)/10 3% 3 Inelastic!

  10. Example 4.5.What is the elasticity of Hong Kong Disney passes? • Originally • Price = $1600 • Quantity demanded = 10,000 passes/year • New • Price = $1520 • Quantity demanded = 12,000 passes/year, then (12000 - 10000)/10000 20% = = 4 (1520 - 1600)/1600 5% Elastic!

  11. Determinants of Price Elasticity of Demand • Availability of substitutes - Elasticity increases with availability of substitutes. • Proportion of income used to buy the good - the higher the fraction of income spent on a good, the higher is elasticity. • Temporary versus permanent change in price - if the price change is temporary people react more to it. Suppose there is a one-day sale…. • Short run versus long run - elasticity increases over time. If there is a sudden price increase, individuals will take some time to find other substitutes and make suitable changes. So quantity will not respond as much in the short run.

  12. Example 4.6.Price ElasticityEstimates for Selected Products Good or service Price elasticity Green peas 2.80 Restaurant meals 1.63 Automobiles 1.35 Electricity 1.20 Beer 1.19 Movies 0.87 Air travel (foreign) 0.77 Shoes 0.70 Coffee 0.25 Theater, opera 0.18 Why is the price elasticity of demand more than 14 times larger for green peas than for theater and opera performances?

  13. A Graphical Interpretationof Price Elasticity • For small changes in price Where Q is the original quantity and P is the original price.

  14. A P P P - P Q D Q Q + Q A Graphical Interpretationof Price Elasticity • For small changes in price Price Quantity

  15. D A Example 4.7.Calculating Price Elasticity of Demand 20 16 12 Price 8 Question: What is the price elasticity of demand when P = $8? 4 1 2 3 4 5 Quantity

  16. 12 D1 6 4 D2 4 6 12 Example 4.8.Price Elasticity and the Steepness of the Demand Curve What is the price elasticity ofDemand for D1 & D2 when P = $4? Observation If two demand curves have a point in common, the steeper curve must be less elastic with respect to price at that point. Price Quantity

  17. Example 4.9. Price Elasticity Regions along a Straight-Line Demand Curve When P = $4 When P = $1 12 6 Price Observation Price elasticity varies at every point along a straight-line demand curve 4 D 1 4 6 10 12 Quantity

  18. a a/2 b/2 b Price Elasticity Regions along a Straight-Line Demand Curve Observation Price elasticity varies at every point along a straight-line demand curve Price Quantity

  19. Price Quantity Perfectly Elastic Demand Curve If the price increases a little, the quantity demanded will drop to zero. If the price drops a little, the quantity demanded will increase a lot.

  20. Price Quantity Perfectly Inelastic Demand Curve The quantity demanded is not responsive to any change in price.

  21. Elasticity and Total Expenditure • Total Expenditure = P x Q • Market demand measures the quantity (Q) at each price (P) • Total Expenditure = Total Revenue

  22. 12 10 8 6 Price ($/ticket) 4 2 0 1 2 3 4 5 6 Quantity (100s of tickets/day) Example 4.10. The Demand Curve for Movie Tickets Price ($/ticket) Total expenditure ($/day) 12 0 10 1000 8 1600 6 1800 4 1600 2 1000 0 0

  23. 12 10 1,800 1,600 8 6 Price ($/ticket) 1,000 Total expenditure ($/day) 4 2 0 2 4 6 8 10 12 0 1 2 3 4 5 6 Price ($/ticket) Quantity (100s of tickets/day) Total Expenditure as a Function of Price Total revenue is at a maximum at themidpoint on a straight-line demand curve.

  24. Example 4.11. • What happens to total expenditure on shelter when the price is reduced from $12/sq yd to $10/sq yd? When price goes down, total expenditure will rise [fall] if the gain from sale of additional units is larger [smaller] than the loss from the sale of existing units at the lower price.

  25. Example 4.12.Elasticity and Total Expenditure • Should a rock band raise or lower its price to increase total revenue? • Assume P=$20, Q=5,000, and e=3. • Total revenue = $20 x 5,000 = $100,000/week • If P is increased 10%, • Q will decrease 30% • Total revenue = $22 x 3,500 = $77,000/week • If P is lowered 10%, • Q will increase 30% • Total revenue = $18 x 6,500 = $177,000/week Note: Cost does not change with Q. Maximizing total revenue is the same as maximizing total profit.

  26. Elasticity and Total Expenditure

  27. A demand curve with constant elasticity P Unitary elastic: PxQ=k Q

  28. Example 4.13. • A director of a big bus company said, "For each 1 percent fare hike, we lose 0.2 percent of our riders." We can conclude that: a. a fare increase will increase total revenue. b. demand for bus service will go up as fares increase. c. demand is price elastic. d. a 10 percent fare hike will produce a 20 percent reduction in riders. e. the price elasticity is 5. • We are told that when DP/P = 1%, DQ/Q = 0.2%. • Elasticity = (DQ/Q)/(DP/P) = 0.2. (inelastic) So answer a is correct. A fare increase will increase total revenue.

  29. Cross-Price Elasticity of Demand • The percentage by which quantity demanded of the first good changes in response to a 1 percent change in the price of the second good • Substitute Goods • When the cross-price elasticity of demand is • positive • Complement Goods • When the cross-price elasticity of demand is • Negative • Now keeping the sign is important!

  30. Income Elasticity of Demand • The percentage by which quantity demanded changes in response to a 1 percent change in income • Normal Goods • Income elasticity is • positive • Inferior Goods • Income elasticity is • negative

  31. The Price Elasticity of Supply • Price Elasticity of Supply • The percentage change in the quantity supplied that occurs in response to a 1 percent change in price

  32. S A 8 4 2 Example 4.14. A Supply Curve for Which Price Elasticity Declines as Quantity Rises B 10 8 • Observations: • Elasticity >0 • Elasticity >1 for linear supply curve that has a positive Y-intercept. • Elasticity decreases as quantity increases. Price 0 2 3 Quantity

  33. S B 5 A 4 P Q Price 0 12 15 Quantity Example 4.15. A Supply Curve for Which Price Elasticity is unity The price elasticity of supply will always equal 1 at any point along a straight-line supply curve that passes through the origin.

  34. S Elasticity = 0 at every point along a vertical supply curve A Perfectly Inelastic Supply Curve What is the price elasticity of supply of land within Central? Price ($/acre) 0 Quantity of land in Central (1,000s of acres)

  35. If MC is constant, then the price elasticity of supply at every point along a horizontal supply curve is infinite S A Perfectly Elastic Supply Curve Price (cents/cup) 14 0 Quantity of lemonade (cups/day)

  36. Determinants of Supply Elasticity • Flexibility of inputs • Mobility of inputs • Ability to produce substitute inputs • Time

  37. End

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