4 Elasticity Both the elasticity coefficient and the total revenue test for measuring price elasticity of demand are presented in the chapter. The text attempts to sharpen students’ ability to estimate price elasticity by discussing its major determinants. The chapter reviews a number of applications and presents empirical estimates for a variety of products. Cross- and income elasticities of demand and price elasticity of supply are also addressed. McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

Price Elasticity of Demand Measures buyers’ responsiveness to price changes Elastic demand Sensitive to price changes Large change in quantity Inelastic demand Insensitive to price changes Small change in quantity Law of demand tells us that consumers will respond to a price decrease by buying more of a product (other things remaining constant), but it does not tell us how much more. The degree of responsiveness or sensitivity of consumers to a change in price is measured by the concept of price elasticity of demand. If demand is elastic, there is a large change in quantity demanded even when price changes by a small amount. When demand is inelastic, there is a very small change in quantity demanded even when there is a large change in price. LO1

Price Elasticity of Demand Formula Formula for price elasticity of demand Ed = Percentage Change in Quantity Demanded of Product X Percentage Change in Price of Product X Quantitative measure of elasticity, Ed = percentage change in quantity/ percentage change in price. LO1

Price Elasticity of Demand Formula Use the midpoint formula Ensures consistent results Change in quantity Change in price Sum of quantities/2 Sum of prices/2 Ed = ÷ Using traditional calculations, the measured elasticity over a given range of prices is sensitive to whether one starts at the higher price and goes down, or the lower price and goes up. The midpoint formula calculates the average elasticity over a range of prices to alleviate that problem. LO1

Price Elasticity of Demand Formula Use percentages Unit free measure Compare responsiveness across products Eliminate the minus sign Easier to compare elasticities Absolute changes depend on the choice of units. For example, a change in the price of a $10,000 car by $1 is very different than a change in the price a of $1 can of beer by $1. The auto’s price is rising by a fraction of a percent while the beer’s price is rising 100 percent. Percentages also make it possible to compare elasticities of demand for different products. Because of the inverse relationship between price and quantity demanded, the actual elasticity of demand will be a negative number. However, we ignore the minus sign and use absolute value. This makes it less confusing to interpret the elasticity coefficient. LO1

Interpretation of Elasticity of Demand Ed > 1 demand is elastic Ed = 1 demand is unit elastic Ed < 1 demand is inelastic Extreme cases Perfectly inelastic Perfectly elastic When the elasticity coefficient is greater than 1, it means that the percentage change in quantity demanded is greater than the percentage change in price (based on the formula), indicating that consumers are sensitive to the change in price, so demand is elastic. When the elasticity coefficient is less than 1, the percentage change in quantity demanded is less than the percentage change in price (based on the formula), indicating that consumers are not very sensitive to price changes. When the elasticity coefficient equals 1, this is a special case called unit elasticity. This means that the percentage change in price and the percentage change in quantity are exactly equal. Perfectly inelastic demand means that consumers will buy exactly the same amount no matter how high or low the price. Perfectly elastic demand means that nothing will be purchased if there is any deviation from the current price. LO1

Perfectly inelastic demand Extreme Cases P D1 Perfectly inelastic demand (Ed = 0) This extreme situation is called perfectly inelastic demand and it is very rare. The demand curve would be vertical and graphs as a line parallel to the vertical axis. The elasticity coefficient is 0. An example of a perfectly inelastic demand might be a diabetic’s demand for insulin. Perfectly inelastic demand LO1

Extreme Cases Perfectly elastic demand P D2 Perfectly elastic demand (Ed = ∞) This extreme situation, in which a small price reduction would cause buyers to increase their purchases from zero to all that it is possible to obtain, is perfectly elastic demand, and the demand curve would be horizontal. The elasticity coefficient is infinite. An example of a perfectly elastic demand is a firm’s demand curve in a purely competitive industry who is unable to change the price. Perfectly elastic demand LO1

Total Revenue = Price X Quantity Inelastic demand Elastic demand Total Revenue Test Total Revenue = Price X Quantity Inelastic demand P and TR move in the same direction Elastic demand P and TR move in opposite directions Total-revenue test is the easiest way to judge whether demand is elastic or inelastic. This test can be used in place of the elasticity formula, unless there is a need to determine the elasticity coefficient. The total revenue test is important to understand the relationship between price elasticity and total revenue. Demand is inelastic if a decrease in price results in a fall in total revenue, or an increase in price results in a rise in total revenue. Demand is elastic if a decrease in price results in a rise in total revenue, or if an increase in price results in a decline in total revenue. Demand is unit elastic if total revenue does not change when the price changes. LO2

Lower price and elastic demand Blue gain exceeds orange loss Total Revenue Test Lower price and elastic demand Blue gain exceeds orange loss $3 2 1 0 10 20 30 40 Q P a b A lower price and elastic demand means that total revenue will rise. Blue gain (extra total revenue from extra sales) exceeds orange loss (the loss in total revenue from the higher price). D1 LO2

Lower price and inelastic demand Orange loss exceeds blue gain Total Revenue Test Lower price and inelastic demand Orange loss exceeds blue gain $4 3 2 1 0 10 20 Q P c A lower price and inelastic demand means that total revenue will fall. Blue gain (extra total revenue from extra sales) is less than the orange loss (the loss in total revenue from the higher price). d D2 LO2

Lower price and unit elastic demand Blue gain equals orange loss Total Revenue Test Lower price and unit elastic demand Blue gain equals orange loss $3 2 1 0 10 20 30 Q P e f A lower price and unit-elastic demand, means that total revenue is unchanged. Blue gain (extra total revenue from extra sales) is exactly equal to the orange loss (the loss in total revenue from the higher price). D3 LO2

Total Revenue Test Price Elasticity of Demand for Movie Tickets as Measured by the Elasticity Coefficient and the Total-Revenue Test (1) Total Quantity of Tickets Demanded per Week, Thousands (2) Price per Ticket (3) Elasticity Coefficient (Ed) (4) Total Revenue (1) X (2) (5) Total Revenue Test 1 $8 $8,000 2 7 5.00 14,000 Elastic 3 6 2.60 18,000 4 5 1.57 20,000 1.00 Unit Elastic 0.64 Inelastic 0.38 8 0.20 8,000 Notice that in the high price region, demand for movie tickets is elastic and revenues increase as price falls. Midway demand for movie tickets is unit elastic and revenues stay the same as price falls. In the low price region, elasticities of demand are inelastic and revenues fall as the price falls. LO2

Elasticity and Total Revenue $8 7 6 5 4 3 2 1 a b c d e f g h Elastic Ed > 1 Unit Elastic Ed = 1 Price Inelastic Ed < 1 D 1 2 3 4 5 6 7 8 Quantity Demanded $20 18 16 14 12 10 8 6 4 2 This graph shows the relationship between price elasticity of demand for movie tickets and total revenue. Demand curve D in (a) is based on Table 4.1 and is marked to show that the hypothetical weekly demand for movie tickets is elastic at higher price ranges and inelastic at lower price ranges. The total-revenue curve, TR, in (b) is derived from demand curve D. When price falls and TR increases, demand is elastic; when price falls and TR is unchanged, demand is unit elastic; and when price falls and TR declines, demand is inelastic. You can see from the graph that elasticity changes along a demand curve. Demand tends to be more elastic in the upper-left portion of demand and more inelastic in the lower-right portion of demand. (Thousands of Dollars) Total Revenue TR 1 2 3 4 5 6 7 8 Quantity Demanded LO2

Summary of Price Elasticity of Demand Price Elasticity of Demand: A Summary Absolute Value of Elasticity Coefficient Demand Is: Description Impact on Total Revenue of a: Price Increase Price Decrease Greater than 1 (Ed > 1) Elastic or relatively elastic Qd changes by a larger percentage than does price Total Revenue decreases Total Revenue increases Equal to 1 (Ed = 1) Unit or unitary elastic Qd changes by the same percentage as does price Total revenue is unchanged Total revenue is unchanged Less than 1 (Ed < 1) Inelastic or relatively inelastic Qd changes by a smaller percentage than does price Total revenue increases Total revenue decreases This is a summary of the rules and concepts related to the elasticity of demand. This is an excellent table to study and help you prepare for the test. It’s a great summary of all of the different pieces to consider with elasticity and get an idea of how they fit together and change. LO2

Determinants of Elasticity of Demand Substitutability More substitutes, demand is more elastic Proportion of Income Higher proportion of income, demand is more elastic Luxuries vs. Necessities Luxury goods, demand is more elastic Time More time available, demand is more elastic With more substitutes available, consumers have more alternative options, so when there is a change in price, there is a greater percentage change in quantity demanded, making the demand more elastic. The broader the definition of the market, the more elastic the demand. With a more narrow definition of the market, demand is more inelastic. The greater the proportion of income needed to buy the good the more elastic the demand. Consumers will be more sensitive to changes in prices because the price change can result in thousands of dollars difference. Since luxuries are goods that consumers can go without, they will change the amount they purchase by a greater amount even if the price changes by a small amount. It takes time to alter the amount being purchased, so the more time available, the more elastic the demand. A person doing their Christmas shopping on Christmas Eve has a very inelastic demand because he/she doesn’t have the time to look around for alternative purchases. LO1

Price Elasticity of Demand Selected Price Elasticities of Demand Product or Service Price Elasticity of Demand (Ed) Newspapers .10 Milk .63 Electricity (household) .13 Household appliances Bread .15 Liquor .70 MLB Tickets .23 Movies .87 Telephone Service .26 Beer .90 Cigarettes .25 Shoes .91 Sugar .30 Motor vehicles 1.14 Medical Care .31 Beef 1.27 Eggs .32 China, glassware 1.54 Legal Services .37 Residential land 1.60 Automobile repair .40 Restaurant meals 2.27 Clothing .49 Lamb and mutton 2.65 Gasoline .60 Fresh peas 2.83 Some of the elasticities of the goods in this table are surprising. Use the determinants of demand to discuss why major league baseball tickets are not only inelastic, but they are more inelastic than gasoline. What makes newspapers, movies, and beer inelastic? LO1

Decriminalization of Illegal Drugs Applications of Ed Large Crop Yields Inelastic demand, lower total revenue Excise Taxes Inelastic demand, more total revenue Decriminalization of Illegal Drugs Large crop yields mean that the supply of crops increases and shifts to the right. When this occurs the equilibrium price falls. Since demand is inelastic, the lower price actually leads to lower revenue for farmers. Farmers are worse off when there is a large crop yield. When government wants to impose taxes on goods, it is important for them to understand the elasticity of demand for the good. If they place a tax on a good with an inelastic demand, the higher price won’t decrease the quantity purchased by much, thereby increasing the amount of tax revenue that government collects. LO1

Price Elasticity of Supply Measures sellers’ responsiveness to price changes Elastic supply, producers are responsive to price changes Inelastic supply, producers are not responsive to price changes We know that at higher prices firms are willing and able to produce more, whereas at lower prices firms are willing and able to produce less. Price elasticity of supply measures how sensitive firms are to price changes. This means that even for small changes in price, firms will greatly alter the quantity being produced. On the other hand, when supply is inelastic, this means that the firm is unresponsive to price changes and therefore will not change the amount being produced by much, even when the change in price is large. LO3

Price Elasticity of Supply Formula to compute elasticity Es > 1 supply is elastic Es < 1 supply is inelastic Percentage Change in Quantity Supplied of Product X Percentage Change in Price of Product X Es = We use percentages so it doesn’t matter which unit of measure we are using. The concept of price elasticity also applies to supply. The elasticity formula is the same as that for demand, but we must substitute the word “supplied” for the word “demanded” everywhere in the formula. Just like with price elasticity of demand, we will compute the price elasticity of supply using the midpoint formula. LO3

Price Elasticity of Supply Time is primary determinant of elasticity of supply Time periods considered Market period Short Run Long Run The ease of shifting resources between alternative uses is very important in price elasticity of supply because it will determine how much flexibility a producer has to adjust his/her output to a change in the price. The degree of flexibility, and therefore the time period, will be different in different industries. The market period means that there is no time to adjust output in response to a price change. Some industries may not have a market period. The short run means that there is enough time to adjust output by increasing or decreasing the variable inputs but not the fixed inputs. The long run means that there is enough time to adjust output by increasing or decreasing all inputs. LO3

Elasticity of Supply: The Market Period Perfectly inelastic supply P Q Sm Pm There is no time to adjust to a price change, making the supply perfectly inelastic. With a perfectly inelastic supply, the increase in demand does not change the quantity at all. If we look at the case of the tomato farmer, we can see that on market day he or she loads the truck and goes to the market where upon arriving discovers the price is much higher (lower) than anticipated. The farmer cannot increase (decrease) the amount supplied, this is the market period. P0 D2 D1 Q0 LO3

Elasticity of Supply: The Short Run Supply is more elastic than in market period P Q Ss Ps In the short run there is enough time to adjust output by increasing or decreasing the variable inputs but not the fixed inputs. Supply is more elastic than in the market period, thereby resulting in a smaller increase in price but also an increase in quantity. In the short run, the tomato farmer can increase (decrease) the supply somewhat by increasing (decreasing) the variable inputs like labor, fertilizer, irrigation, etc. However, the tomato farmer cannot increase (decrease) the size of the farm in this time period because farm size is fixed. P0 D2 D1 Q0 Qs LO3

Elasticity of Supply: The Long Run Supply is even more elastic than in the short run P Q Sl Pl In the long run there is enough time to adjust output by increasing or decreasing all inputs since all inputs are variable by this time. This means that supply will be even more elastic and with the same increase in demand, there is an even greater increase in the quantity than in the short run, but a smaller increase in price. In the long run all inputs are variable even the farm size. The tomato farmer can expand (reduce) the size of the farm in regards to long run price increases. P0 D2 D1 Q0 Ql LO3

Applications of Elasticity of Supply Antiques Inelastic supply Reproductions More elastic supply Volatile gold prices Antiques and other non-reproducible commodities have an inelastic supply, sometimes the supply is perfectly inelastic. This makes their prices highly susceptible to fluctuations in demand. The more inelastic the supply, the greater the changes in price when demand changes. Reproductions, on the other hand, have a much more elastic supply so the prices tend to remain lower even when there is an increase in demand. Gold prices are volatile because the supply of gold is highly inelastic, and unstable demand from speculation causes prices to fluctuate significantly. LO3

Cross Elasticity of Demand Measures responsiveness of sales to change in the price of another good Substitutes – positive sign Complements – negative sign Independent goods - zero Percentage change in quantity demanded of product X Ex,y = Percentage change in price of product Y We know that if the price of Pepsi increases it not only impacts the quantity of Pepsi that is purchased, but it also impacts the quantity of related goods that are purchased. Cross elasticity of demand refers to the effect of a change in a product’s price on the quantity demanded for another product. If the goods are substitutes, they will have a positive cross elasticity of demand since the change in the price of one good and the change in the demand for its substitute move in the same direction. If the goods are complements, they will have a negative cross elasticity of demand since the change in the price of one good and the demand for its complement move in opposite directions. LO4

Cross Elasticity of Demand Application Change the price? Allow a merger? Companies can use cross-price elasticity to determine whether raising the price of one of their products will affect sales of another of their products. Government can use it to determine whether to allow a proposed merger of two companies or not. If there is a high cross-price elasticity between the two companies’ products the government will likely not allow the merger. LO4

Income Elasticity of Demand Measures responsiveness of buyers to changes in income Normal goods – positive sign Inferior goods – negative sign Percentage change in quantity demanded Ei = Percentage change in income Income elasticity of demand refers to the percentage change in quantity demanded that results from some percentage change in consumer income. A positive income elasticity indicates a normal or superior good. A negative income elasticity indicates an inferior good. Those industries that are income elastic will expand at a higher rate as the economy grows. LO4

Income Elasticity Insights High income elasticities Most affected by a recession Low or negative income Least affected by a recession Income elasticity helps us understand which products and industries will be most affected when household incomes fall during economic downturns. LO4

Ex,y and Ei Cross and Income Elasticities of Demand Value of Coefficient Description Type of Good(s) Cross elasticity: Positive (Ewz > 0) Negative (Exy < 0) Quantity demanded of W changes in same direction as change in price of Z Quantity demanded of X changes in opposite direction from change in price of Y Substitutes Complements Income elasticity: Positive (Ei >0) Negative (Ei<0) Quantity demanded of the product changes in same direction as change in income Quantity demanded of the product changes in opposite direction from change in income Normal or superior Inferior This is an excellent table that summarizes many of the characteristics of cross-price elasticity and income elasticity. It is a great table to study when you are getting ready for the test. LO4

Elasticity and Pricing Power Charge different prices based on price elasticities Examples: Business air travelers Adult vs. child Some firms have “market power” or “pricing power” that allows them to set their product at prices that are in their best interests. For some goods and services, firms may find it advantageous to determine differences in price elasticity of demand and then charge different prices to different buyers. Business air travelers have a more inelastic demand for air travel, so they are charged higher prices since they will stay pay it. Families are sensitive to prices, so firms will charge lower prices for children as a result of the more elastic demand.