1 Stephen Chiu University 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. 1.Its travel will increase. 2.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. Percentage change in quantity demanded Percentage change in 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 Percentage change in quantity demanded Percentage change in price 6% 2% = 3

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% 1% = 2

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.) Percentage change in quantity demanded Percentage change in price

8 Price Elasticity of Demand 0 Price elasticity of demand Elastic Unit elastic inelastic 123

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 Inelastic! ( )/400 ( )/10 = 1% 3% = 1 3

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 Elastic! ( )/10000 ( )/1600 = 20% 5% = 4

11 Determinants of Price Elasticity of Demand 1.Availability of substitutes - Elasticity increases with availability of substitutes. 2.Proportion of income used to buy the good - the higher the fraction of income spent on a good, the higher is elasticity. 3.Temporary versus permanent change in price - if the price change is temporary people react more to it. Suppose there is a one-day sale…. 4.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 Elasticity Estimates for Selected Products Good or servicePrice elasticity Green peas2.80 Restaurant meals1.63 Automobiles1.35 Electricity1.20 Beer1.19 Movies0.87 Air travel (foreign)0.77 Shoes0.70 Coffee0.25 Theater, opera0.18 Why is the price elasticity of demand more than 14 times larger for green peas than for theater and opera performances?

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

14 A Graphical Interpretation of Price Elasticity For small changes in price Quantity Price P D A Q P - P Q + Q Q P

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

16 Example 4.8. Price Elasticity and the Steepness of the Demand Curve D1D1 D2D Quantity Price What is the price elasticity of Demand for D 1 & D 2 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.

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

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

19 Perfectly Elastic Demand Curve Quantity Price 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 Perfectly Inelastic Demand Curve Quantity Price 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 Example The Demand Curve for Movie Tickets 12 Quantity (100s of tickets/day) Price ($/ticket) Total expenditure ($/day) 12 Price ($/ticket)

23 Total Expenditure as a Function of Price 1,800 Price ($/ticket) Total expenditure ($/day) ,600 1, Quantity (100s of tickets/day) Price ($/ticket) Total revenue is at a maximum at the midpoint on a straight-line demand curve.

24 Example 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 Elasticity and Total Expenditure Should a rock band raise or lower its price to increase total revenue? Assume P=$20, Q=5,000, and  =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 Q P Unitary elastic: PxQ=k

28 Example 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  P/P = 1%,  Q/Q = 0.2%. Elasticity = (  Q/Q)/(  P/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 Example A Supply Curve for Which Price Elasticity Declines as Quantity Rises 2 8 A 3 10 B Quantity Price 0 4 S 8 2 Observations: 1.Elasticity >0 2.Elasticity >1 for linear supply curve that has a positive Y-intercept. 3.Elasticity decreases as quantity increases.

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

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

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

36 Determinants of Supply Elasticity 1.Flexibility of inputs 2.Mobility of inputs 3.Ability to produce substitute inputs 4.Time

37 End