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Elasticity Chapter 4 Elasticity 1 Example 4.1 Will the China’s trade balance (export – import) deteriorate if RMB appreciates (say, from 1USD=8.1RMB to 1USD=7.8RMB)? 1. China’s imports become less expensive. Quantity demanded for import may increase. 2. China’s Exports become more expensive. Quantity demanded for export may decrease. The impact of RMB appreciation on the trade balance depends on the responsiveness of import demand and export demand to the appreciation. 2 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 3 Elasticity Generally, elasticity is a measure of the responsiveness of the quantity demanded of a good to a change in the price of that good 4 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% -2% = -3 Percentage change in quantity demanded Percentage change in price 5 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 6 Price Elasticity of Demand Measuring Price Elasticity of Demand Percentage change in quantity demanded Percentage change in price Observations Price elasticity of demand will always be negative (i.e., an inverse relationship between price and quantity). For convenience sometimes we drop the negative sign. 7 Price Elasticity of Demand Percentage Change in Quantity Demanded Percentage Change in Price Unit elastic inelastic Elastic -3 -2 -1 Price elasticity 0 of demand 8 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 (404 - 400)/400 (9.7 - 10)/10 = 1% -3% = -1 3 Inelastic! 9 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 (1520 - 1600)/1600 = 20% -5% = -4 Elastic! 10 Determinants of Price Elasticity of Demand 1. Availability of substitutes - the higher the number of substitutes, the more responsive people are to price changes. 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 - the response of quantity demanded that day will be much greater than the response to quantity when prices are expected to decrease permanently. 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 much in the short run. 11 Example 4.6. Price Elasticity Estimates 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? 12 A Graphical Interpretation of Price Elasticity For small changes in price ΔQ Q Price elasticity ( ΔQ / ΔP )( P / Q) ΔP P Where Q is the original quantity and P is the original price. 13 A Graphical Interpretation of Price Elasticity For small changes in price ΔQ Q ΔP P P 1 Pr ice elasticity at A Q slope A P Price Price elasticity P P- P Q D Q Q+ Quantity Q 14 Example 4.7. Calculating Price Elasticity of Demand slope 20 D vertical intercept 20 4 horizontal intercept 5 16 8 1 8 2 A x 3 4 12 3 Price 12 A 8 Question: What is the price elasticity of demand when P = $8? 4 1 2 3 4 5 Quantity 15 Example 4.8. Price Elasticity and the Steepness of the Demand Curve What is the price elasticity of Demand for D1 & D2 when P = $4? 12 D1 1 4 1 D1 12 2 4 6 4 1 D2 2 6 4 12 Price 6 Observation If two demand curves have a point in common, the steeper curve must be less elastic with respect to price at that point. 4 D2 4 6 Quantity 12 16 Example 4.9. Price Elasticity Regions along a Straight-Line Demand Curve 12 When P = $4 When P = $1 4 1 D 2 6 4 12 1 1 1 D 5 10 6 12 Price 6 4 Observation Price elasticity varies at every point along a straight-line demand curve D 1 4 6 10 12 Quantity 17 Price Elasticity Regions along a Straight-Line Demand Curve Observation Price elasticity varies at every point along a straightline demand curve a 1 Price 1 1 a/2 b/2 Quantity b 18 Perfectly Elastic Demand Curve Perfectly elastic Price demand (elasticit y - ) Quantity If the price increases a little, the quantity demanded will drop to zero. If the price drops a little, the quantity demanded will increase a lot. 19 Perfectly Inelastic Demand Curve Perfectly inelastic Price demand (elasticity 0) Quantity The quantity demanded is not responsive to any change in price. 20 Elasticity and Total Expenditure Total Expenditure = P x Q Market demand measures the quantity (Q) at each price (P) Total Expenditure = Total Revenue 21 Example 4.10. The Demand Curve for Movie Tickets Price ($/ticket) 12 Price ($/ticket) 10 8 6 Total expenditure ($/day) 12 10 8 6 4 2 0 1000 1600 1800 1600 1000 0 0 4 2 0 1 2 3 4 5 6 Quantity (100s of tickets/day) 22 Total Expenditure as a Function of Price Total revenue is at a maximum at the midpoint on a straight-line demand curve. 12 1,800 1,600 Total expenditure ($/day) Price ($/ticket) 10 8 6 4 2 0 1 2 3 4 5 Quantity (100s of tickets/day) 6 1,000 0 2 4 6 8 10 12 Price ($/ticket) 23 Example 4.11. What happens to total expenditure on shelter when the price is reduced from $12/sq yd to $10/sq yd? Price ($/sq yd) 16 14 12 E 10 8 6 4 F 2 0 Reduction in expenditure from sale at a lower price Increase in expenditure from additional sales 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. G 4 6 8 10 1214 16 Quantity (sq yds/wk) 24 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 =-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. 25 Elasticity and Total Expenditure If demand is... A price increase will... A price reduction will... reduce total expenditure elastic P x Q = increase total expenditure P Q increase total expenditure inelastic Px Q = PQ P x Q = PQ reduce total expenditure Px Q = PQ 26 A demand curve with constant elasticity P Unitary elastic: PxQ=k Q 27 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. 28 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 29 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 30 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 DQ Q Price elasticity of supply DP P P 1 Price elasticity of supply Q slope 31 Example 4.14. A Supply Curve for Which Price Elasticity Declines as Quantity Rises A 8 21 2 2 S B 10 A Observations: 1. Elasticity >0 2. Elasticity >1 for linear supply curve that has a positive Y-intercept. 3. Elasticity decreases as quantity increases. Price 88 4 0 5 B 10 31 2 3 22 3 Quantity 32 Example 4.15. A Supply Curve for Which Price Elasticity is unity A 4 / 1212 / 4 1 S B 5 1515 5 1 B 5 Q Price 4 0 P A 12 The price elasticity of supply will always equal 1 at any point along a straight-line supply curve that passes through the origin. 15 Quantity 33 A challenge Construct an example of supply curve so that price elasticity increases as quantity rises. 34 A Perfectly Inelastic Supply Curve What is the price elasticity of supply of land within Central? Price ($/acre) S Elasticity = 0 at every point along a vertical supply curve 0 Quantity of land in Central (1,000s of acres) 35 Price (cents/cup) A Perfectly Elastic Supply Curve If MC is constant, then the price elasticity of supply at every point along a horizontal supply curve is infinite S 14 0 Quantity of lemonade (cups/day) 36 Determinants of Supply Elasticity 1. 2. 3. 4. Flexibility of inputs Mobility of inputs Ability to produce substitute inputs Time 37 Example 4:16. Why are gasoline prices so much more volatile than car prices? Differences in markets Demand for gasoline is more inelastic Gasoline market has larger and more frequent supply shifts 38 Greater Volatility in Gasoline Prices than in Car Prices S’ Gasoline Price ($/gallon) S 1.69 1.02 D 0 6 7.2 Quantity (millions of gallons/day) 39 Greater Volatility in Gasoline Prices than in Car Prices Cars Price ($1,000s/car) S’ S 17 16.4 D 11 12 Quantity (1,000s of cars/day) Cars 40 Example 4.17. Earnings of YAO Ming Why does YAO Ming earn an annual basketball salary of some US$4.5 million? YAO Ming is a unique and essential inputs, an example of ultimate supply bottleneck. 41 Other examples of unique and essential inputs Dr. Joseph YAM? Mr Mirko Saccani? “The fee was agreed to be $120 million for eight years' of unlimited [Latini]dance lessons and competitions, and Mr Saccani would be her dancing partner and instructor by such agreements.” (SCMP 2006-06-14, CITY3) Who was she, the plaintiff? Mimi Monica Wong, head of HSBC's private banking in Asia. 42 Example 4.18. So why are the fares so different? If you start in Kansas City and you fly to Honolulu round-trip, the fare is a lot lower than if you start the same trip in Honolulu and fly to Kansas City round-trip. Passengers travel on same planes, consuming the same fuel, the same in-flight amenities, and so on. So why are the fares so different? By Karen Hittle, a student of Robert Frank. 43 Example 4.18. So why are the fares so different? If you are starting in Kansas City and going to Honolulu, you are probably going on vacation. You could go lots of different places. You could go to Florida, to Barbados, to Cancun. Because vacationers have many destinations to choose from, airlines must compete fiercely for their business. Given economies of scale inherent in larger aircraft, carriers have a strong incentive to fill additional seats by targeting lower prices to the people who are more sensitive to price – vacationers. But if you are starting in Honolulu on a trip to Kansas City, you are probably not a vacationer. More likely, you either have business or family reasons for traveling. So you are probably not shopping for a destination if you are going to Kansas City. That is why the fares are so different. 44 Example 4.19. Other things being equal, the increase in rents that occur after rent control are abolished is smaller when A. the own price elasticity of demand for rental homes is price inelastic. B. the own price elasticity of demand for rental homes is price elastic. C. the own price elasticity of demand for rental homes has unitary price elasticity. D. rented homes and owned homes are substitutes. E. rented homes and owned homes are complements. 45 Example 4.19. Rent control is a form of PRICE CEILING. Price Ceiling is set at a price LOWER than the market equilibrium price. Excess demand (i.e., shortage) results. P D S Trading Loci Pe Price Ceiling Q 46 Example 4.19. And when the Price Ceiling is lifted, the market equilibrium quantity and price should be restored eventually. Price (rent) should increase. P D S Because supply is upward sloping, ↑P → ↑ TR Price Ceiling Q 47 Example 4.19. Relative inelastic P D S Pe Price Ceiling Relative elastic Q Hence, the increase in rents that occur AFTER abolishing rent control is smaller when (B) The own price elasticity of demand is elastic. 48 End 49