Elasticity and its Applications Copyright 2012 Worth Publishers

A hard question: Does slave redemption create more slavery? How will slave traders respond to an increase in demand for slaves? Harvard Sophomore Jay Williams redeems slaves in the Sudan

The Elasticity of Demand The Elasticity of Supply Using Elasticities for Quick Predictions (Optional) Appendix 1: Using Excel to Calculate Elasticities (see book) Appendix 2: Other Types of Elasticities For applications, click here To Try it! questions To Video

But how much does quantity demanded change when price changes? Elasticity of Demand We know there is an inverse relationship between price and quantity demanded. But how much does quantity demanded change when price changes? Instructor Notes:

Elasticity of Demand A demand curve is elastic when an increase in price reduces the quantity demanded a lot (and vice versa). When the same increase in price reduces quantity demanded just a little, then the demand curve is inelastic.

Elasticity of Demand Price Inelastic Demand … Causes a Small Decrease in Quantity Demanded if Demand is Inelastic $50 The Same Price Increase 75 Elastic Demand … Causes a Big Decrease in Quantity Demanded if Demand is Elastic 20 $40 80 Instructor Notes: Figure 4.1: The Same Price Increase Causes a Big Decrease in Quantity Demanded if Demand is Elastic, and a Small Decrease in Quantity Demanded if the Demand Curve is Inelastic Students should note that elastic demand curves are relatively flat while inelastic demand curves are relatively steep. However, it is important that students do not confuse elasticity and slope. They are not the same! Footnote 3 in the text has a nice mathematical presentation of this point. Quantity The More Responsive Quantity Demanded is to a Change in Price, the More Elastic is the Demand Curve

Elasticity Rule Elasticity slope BUT: If two linear demand (or supply) curves run through a common point, then at any given quantity the curve that is FLATTER is MORE ELASTIC

Determinants of the Elasticity of Demand: a preview Availability of Substitutes *** Time Horizon Category of product (specific or broad) Necessities vs. Luxuries Purchase Size *** this is the fundamental determinant

Determinants of the Elasticity of Demand The availability of substitutes is very important. fewer substitutes makes it harder for consumers to adjust Q when P changes… so demand is inelastic. many substitutes? Switching brands when prices change is EASY, so demand is elastic. Instructor Notes: The remaining determinants ultimately relate to this point, so it may be helpful to point this out.

When the patent expires on a brand-name drug and 5 generic drugs come on the market, what happens to elasticity of demand? It rises It falls To next Try it!

Determinants of Elasticity of Demand The time horizon matters. Less time to adjust means lower elasticity Over time consumers can adjust their behavior by finding substitutes (making demand more elastic). Instructor Notes:

Determinants of Elasticity of Demand The classification of the good matters. The less specific the classification, the fewer substitutes there are (making demand inelastic). And vice versa… E.g. the elasticity of demand is higher for “lettuce” than for “food.” Instructor Notes: vs.

Determinants of Elasticity of Demand The nature of the good to the consumer can also affect the elasticity of demand. For necessities, we do not change Q much when P changes For luxuries, we are more sensitive to P changes Instructor Notes: vs.

Determinants of Elasticity of Demand The size of the purchase (relative to our budget) matters. We are less sensitive to price changes when the good feels cheap We are more sensitive to price changes when the good feels expensive Instructor Notes:

Mathematics of Demand Elasticity Elasticity of demand = the percentage change in quantity demanded divided by the percentage change in price. Ed = the percentage change in quantity demanded percentage change in price Or, Where D is the mathematical symbol for “change in” Instructor Notes: Students may need to be reminded how to correctly calculate the Percentage Change in Quantity Demand and Price. Percentage Change in Quantity Demanded: (Qnew – Qold)/Qold Percentage Change in Price: (Pnew – Pold)/Pold

Determinants of Elasticity of Demand Summary of Determinants of Elasticity of Demand Less Elastic More Elastic Fewer Substitutes More Substitutes Short Run (less time) Long Run (more time) Necessities Luxuries Small Part of Budget Large Part of Budget Instructor Notes: Table 4.1: Some Factors Determining the Elasticity of Demand

Mathematics of Demand Elasticity Example: If the price of oil increases by 10% and over a period of several years, the quantity demanded falls by 5%, then the long run elasticity of demand for oil is: Instructor Notes:

cigarette tax increase. A Kentucky governor proposed a 70 cent/pack cigarette tax increase. Estimated effects: Average cost of a pack would go from $3.67 to $4.55. Youth smoking would be cut by an estimated 16.6 percent. Adult smoking would decrease by an estimated 4 percent. Instructor Notes: Classroom questions: Is the demand for cigarettes elastic or inelastic? Inelastic Why? Smokers probably view cigarettes as necessities. Why is the elasticity of demand different for youth and adult smokers? Share of budget larger for youth than adult smokers. Could also argue that cigarettes are more of a necessity for adult smokers who have probably been smoking longer and are more addicted.

Using the Midpoint Formula for Elasticity To erase the natural bias associated with choice of base point, we calculate the elasticity of demand using the Midpoint Formula given by: Instructor Notes:

Mathematics of Demand Elasticity Elasticity of demand is always negative, so we typically drop the negative sign and use absolute value instead. If the |Ed| < 1, the demand curve is inelastic. If the |Ed| > 1, the demand curve is elastic. If the |Ed| = 1, the demand curve is unit elastic. Instructor Notes: Students should note some extreme cases that are not explicitly defined in the text but are often used for simplification: Perfectly Elastic Demand Elasticity of demand is infinite A very small change in price will lead to an infinitely large change in quantity demanded Horizontal demand curve Perfectly Inelastic Demand Elasticity of demand is zero A change in price will cause no change in quantity demanded. Vertical demand curve

Mathematics of Demand Elasticity Example: At the initial price of $10, the quantity demanded is 100. When the price rises to $20, the quantity demanded is 90. Instructor Notes:

What is the elasticity of demand for Google searches? The summary: Google ran an experiment and observed the following: Using “time waiting” as the price, calculate Elasticity of Demand for Google searches. Answer: -20% / ((0.5/0.65)x100) = -0.26 The page with 10 results took .4 seconds to generate. The page with 30 results took .9 seconds. Half a second delay caused a 20% drop in traffic. Half a second delay killed user satisfaction. The full text of the post: In an experiment earlier this year, Google discovered how much people care about how long it takes to perform a search. The company varied the number of search results generated per page from 10 to 30. The page with 10 results took .4 seconds to generate. The page with 30 results took .9 seconds. Half a second delay caused a 20% drop in traffic. Half a second delay killed user satisfaction. What’s interesting about this study is that it gives students an opportunity to calculate the price elasticity of demand for Google searches, using “time waiting” as the price of the search: -20% / ((0.5/0.65)*100) = -0.26 Astute students would note that the actual elasticity is higher than what we calculated since all things are not equal. Getting 30 results per page is more valuable than getting 10.

Elasticity of Demand and Total Revenue A firm’s revenues are equal to price per unit times quantity sold. Revenue = Price x Quantity The elasticity of demand directly influences revenues when the price of the good changes. Instructor Notes:

Elasticity of Demand and Total Revenue Revenues Rise as Price Rises if Demand is Inelastic Q P D $10 100 R=$10x100 =$1,000 $20 90 R=$20x90 =$1,800 R=$10x100 =$1,000 Instructor Notes: Figure 4.2: Elasticity and Revenue Panel A Inelastic Demand Revenues rise because the decrease in quantity demanded is less than the increase in price.

Elasticity of Demand and Total Revenue Revenues Fall as Price Rises with Elastic Demand Curves Q P D $10 250 R=$10x250 =$2,500 $20 50 R=$20x50 =$1,000 R=$10x250 =$2,500 Instructor Notes: Figure 4.2: Elasticity and Revenue Panel B Elastic Demand Revenues fall because the decrease in quantity demanded is less than the increase in price.

Elasticity of Demand and Total Revenue Summary of Relationship between Elasticity of Demand and Revenues Absolute Value of Elasticity Name Price and Revenue Inelastic P and R Move Together Elastic P and R Move Opposite Unit Elastic P Moves but R Stays the Same Instructor Notes:

Applications of Elasticity of Demand How the American Farmer has Worked Himself Out of a Job: Increased agricultural productivity has the supply of food BUT the supply of farmers…. And their revenues because the demand for most agricultural products is inelastic.

Applications of Elasticity of Demand Why the War on Drugs is Hard to Win: Because demand for most illegal drugs is inelastic, drug dealers earn greater revenue and gain more power as the drug war becomes more effective. Instructor Notes:

The elasticity of demand for eggs has been estimated to be 0. 1 The elasticity of demand for eggs has been estimated to be 0.1. If egg producers raised their prices by 10 percent, what will happen to their total revenue? It will increase It will decrease It won’t change Instructor Notes: To next Try it!

They think it’s elastic They think it’s inelastic If a fashionable clothing store raised its prices by 25 percent, what does that tell you about the store’s estimate of the elasticity of demand for its products? They think it’s elastic They think it’s inelastic To next Try it!

But how strong is that relationship? Elasticity of Supply The law of supply indicates a direct relationship between price and quantity supplied. But how strong is that relationship? Instructor Notes:

Elasticity of Supply A supply curve is elastic if a rise in price increases the quantity supplied a lot (and vice versa). it’s inelastic if sellers change quantity just a little.

Elasticity of Supply Quantity Price per Unit Elasticity of Supply Captures the Sensitivity of Quantity Supplied to Changes in Price Inelastic Supply Elastic Supply …Causes a Small Increase in Quantity Supplied if Supply is Inelastic $50 The Same Price Increase 85 …Causes a Big Increase in Quantity Supplied if Supply is Elastic 170 $40 Instructor Notes: Figure 4.5 The Same Price Increase Causes a Small Increase in Quantity Supplied If the Supply Curve is Inelastic and a Big Increase in Quantity Supplied Is Inelastic and a Big Increase In Quantity Supplied If the Supply Curve Is Inelastic 80

Determinants of Elasticity of Supply Change in Per-Unit Costs with Increased Production Time Horizon Share of Market for Inputs Geographic Scope Instructor Notes:

Determinants of Elasticity of Supply How quickly do per-unit costs increase when more is produced? If increased production is very expensive, then the supply curve will be inelastic. If production can increase with little extra cost, then the supply curve will be elastic. Instructor Notes: Ivory: increasing collection costs, inelastic supply

Determinants of Elasticity of Supply The time horizon matters. Immediately following a price increase, producers can expand output only using their current capacity (making supply inelastic). Over time, however, producers can expand their capacity (making supply elastic). Instructor Notes:

Determinants of Elasticity of Supply The share of the market for the inputs used in production matters. Supply is elastic when the industry can be expanded without causing a big increase in the demand (and price) for the industry’s inputs. Supply is inelastic when industry expansion causes a significant increase in the demand/price for inputs. Instructor Notes:

Determinants of Elasticity of Supply The geographic scope of the market matters. The wider the scope of the market of a good, the less elastic its supply. The narrower the scope of the market of a good, the more elastic its supply. Instructor Notes:

Determinants of Elasticity of Supply Summary of Determinants of Elasticity of Supply Less Elastic More Elastic Difficult to Increase Production at Constant Unit Cost Easy to Increase Production at Constant Unit Cost Raw Materials Manufactured Goods Short Run Long Run Large Share of Market for Inputs Small Share of Market for Inputs Global Supply Local Supply Instructor Notes:

Mathematics of Supply Elasticity Elasticity of supply = the percentage change in quantity supplied divided by the percentage change in price (use the midpoint formula here too!) Es = the percentage change in quantity supplied percentage change in price Or, Instructor Notes: Students may need to be reminded how to correctly calculate the Percentage Change in Quantity Demand and Price. Percentage Change in Quantity Demanded: (Qnew – Qold)/Qold Percentage Change in Price: (Pnew – Pold)/Pold

Using the Midpoint Formula for Elasticity Again we use the Midpoint Formula given by: Instructor Notes:

Mathematics of Supply Elasticity Example: If the price of cocoa rises by 10% and the quantity supplied increases by 3%, then the elasticity of supply for cocoa is: Instructor Notes:

Mathematics of Supply Elasticity If the Es < 1, the supply curve is inelastic. If the Es > 1, the supply curve is elastic. If the Es = 1, the supply curve is unit elastic. Instructor Notes: Students should note some extreme cases that are not explicitly defined in the text but are often used for simplification: Perfectly Elastic Demand Elasticity of demand is infinite A very small change in price will lead to an infinitely large change in quantity demanded Horizontal demand curve Perfectly Inelastic Demand Elasticity of demand is zero A change in price will cause no change in quantity demanded. Vertical demand curve

Mathematics of Supply Elasticity Example: At the initial price of $10, the quantity supplied is 100. When the price rises to $20, the quantity supplied is 110. Instructor Notes:

Slave Redemption and Elasticity Slave Redemption Works Best When the Supply Curve for Slaves is Perfectly Inelastic If the Supply Curve for Slaves is Elastic, Slave Redemption is less helpful

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Gun Buybacks and Elasticity The supply of guns to a local region is very elastic, so local buybacks don’t affect the number of guns on the street (nor affect their price.)

A computer manufacturer makes an experimental computer chip that critics praise, leading to a huge increase in the demand for the chip. How elastic is supply in the short run? What about the long run? Graph both. Instructor Notes: To next Try it!

Will the same increase in the demand for housing increase prices more in Manhattan or in Des Moines, Iowa? Graph both. To next Try it!

If the price of a sushi roll drops from $8 to $4, and sales rise from 20 to 40 units, what is the (absolute value) of the price elasticity of demand? 0.5 0.66 1 2 To next Try it!

If price falls from $60 to $40, total revenue changes by _______, so demand is _______. $240; inelastic $480; elastic $360; inelastic $120; elastic To next Try it!

Which supply curve is the most elastic? Price Quantity S1 S2 S3 S4 To next Try it!

Elasticity and Quick Predictions Two simple formulas allow for quick predictions of price changes (using elasticities): Instructor Notes:

Cross-Price Elasticity of Demand The Cross-Price Elasticity of Demand measures how sensitive the quantity demanded of good A is to the price of good B. Cross-Price Elasticity of Demand = Instructor Notes: Students may need to be reminded how to correctly calculate the Percentage Change in Quantity Demanded and Price. Percentage Change in Quantity Demanded: (Qnew – Qold)/Qold Percentage Change in Price: (Pnew – Pold)/Pold

Cross-Price Elasticity of Demand For substitutes, Cross-Price Elasticity of Demand is positive. An increase in the price of one brand of milk will increase the demand for other brands. For complements, Cross-Price Elasticity of Demand is negative. An increase in the price of milk causes a decrease in demand for Oreos. Instructor Notes:

Income Elasticity of Demand The Income Elasticity of Demand measures how sensitive the quantity demanded of a good is to changes in income. Income Elasticity of Demand = Instructor Notes: Students may need to be reminded how to correctly calculate the Percentage Change in Quantity Demanded and Income. Percentage Change in Quantity Demanded: (Q – Q)/Q Percentage Change in Income: (I – I)/I

Income Elasticity of Demand The income elasticity of demand can be used to distinguish normal from inferior goods. For normal goods, Income Elasticity is positive. For luxury goods, Income Elasticity is greater than one. For inferior goods, Income Elasticity is negative. Instructor Notes:

Tonya consumes 10 boxes of Ramen Noodles a year when her yearly income is $40,000. After her income falls to $30,000 a year, she consumes 40 boxes of Ramen Noodles a year. Calculate her income elasticity of demand for Ramen Noodles. 4.2 –4.2 –2.25 2.25 To next Try it!

The price of Good B increases by 4%, causing the quantity demanded of Good A to decrease by 6%. The cross-price elasticity of demand is _____, and the goods are ______. 1.5; substitutes –1.5; complements 0.67; complements –2.4; substitutes Back to