1 Elasticity and Its Applications PRINCIPLES OF ECONOMICS (ECON 210) BEN VAN KAMMEN, PHD
2 Introduction This is the first of 4 chapters that comprise the middle of this course. These chapters are extensions to the Supply and Demand model. Elasticity: quantifying how sensitive quantity demanded and quantity supplied are. To price. To incomes. To prices of related goods. The Laws of Supply and Demand only say the direction of the relationship between Q and P. Nothing about the magnitude. Elasticity is about measuring this. How sensitive are they?
3 Elasticity defined Elasticity: a numerical measure of how responsive QQ DD or QQ SS is to one of the factors that determine it. Examples, 1. Price Elasticity of Demand 2. Price Elasticity of Supply 3. Income Elasticity of Demand 4. Cross Price Elasticity of Demand
4 Symbolic definitions of elasticity 1. Price Elasticity of Demand (good x) 2. Price Elasticity of Supply 3. Income Elasticity of Demand 4. Cross Price Elasticity of Demand EE PPyy,QQ DD = EE PPxx,QQ DD = % QQ DD % PP xx EE PPxx,QQ SS = % QQ SS % PP xx EE II,QQDD = % QQ DD % II % QQ DD % PPPPPPPPPP oooo ooooooooo gggggggg
5 Illustration Initially the price is $40/unit. The quantity demanded is 100. How does quantity demanded change in each case when the price rises to $50/unit? In both cases, we are raising price by the same amount.
6 Go to Hotseat, buddy.
7 Which curve is more sensitive? Both elasticity calculations have the same % change in price % PP = 100 = 25% 40 The flatter curve decreases quantity demanded by: = 80 pppppppppppppp. 100 The steeper curve decreases quantity demanded by: = 5 pppppppppppppp. 100 The two elasticity calculations are: 80 5 = 3.2 and = 0.2, which reveals that the flatter curve is more elastic. The larger negative effect means it is more sensitive.
8 Really cool mathematical note The terms in the Elasticity definition can be cleverly re-written, EE PPxx,QQ DD = QQ 1 QQ 0 PP 0. PP 1 PP 0 QQ 0 As the price change becomes infinitely small, so does the quantity response. But the ratio of the two changes approaches the (inverse of the) slope of the demand curve: QQ PP. So you can write elasticity: EE PPxx,QQ DD = QQ PP PP 0 QQ 0, where QQ PP is the inverse of the slope of the demand curve at the point, (QQ 0, PP 0 ).
9 The midpoint method for calculating elasticity Maybe you didn t think that mathematical note was as cool as I did. But here s why it s useful. Calculating elasticity at one point is less confusing that calculating it based on two endpoints. Even when you are given two endpoints, you can calculate the elasticity based on the midpoint between them. It s less confusing because you don t have to choose which endpoint to use as the base when you re calculating % change. According to the midpoint method, the effect of changing the price (on a linear demand curve) could be calculated as: EE PPxx,QQ DD = PP mmmmmmmmmmmmmmmm QQ mmmmmmmmmmmmmmmm 1 ssssssssss oooo dddddddddddd cccccccccc.
10 The midpoint method (continued) Using the midpoint eliminates the following confusion. Say you have a linear demand curve that goes through the points: Price $7, Quantity 3 and Price $8 and Quantity 2. Elasticity would be sensitive to the base and would depend on which end point was the starting point. 3 2 EE PPxx,QQ DD = 3 = or EE PP xx,qq DD = 2 = 4? Using the midpoint is independent of the starting point, though. EE PPxx,QQ DD = = 3.
11 Sensitivity to price To illustrate sensitivity to price, consider two extreme examples. This example uses supply, but the concepts of perfectly elastic and perfectly inelastic apply equally to demand. Perfectly inelastic means not at all sensitive. EE PPxx,QQ SS = PP mmmmmmmmmmmmmmmm QQ mmmmmmmmmmmmmmmm 1 = 0 Perfectly elastic means infinitely sensitive. EE PPxx,QQ SS = PP mmmmmmmmmmmmmmmm QQ mmmmmmmmmmmmmmmm 1 0 =
12 Perfect elasticity and perfect inelasticity When supply or demand is perfectly elastic, quantity is so sensitive to price that even a small change would make the quantity response infinitely large. When it is perfectly inelastic, quantity is completely insensitive to price changes and doesn t respond at all. These are the two extreme ends of the elasticity spectrum. What determines where a particular demand (supply) curve will fall on this spectrum?
13 Determinants of elasticity Demand is more elastic under the following circumstances. Availability of close substitutes. When the good is defined specifically rather than broadly. When the good is a luxury rather than a necessity. In the long run rather than the short run. Supply is more elastic under the following circumstances. When producers are able to adjust their output easily. In the long run rather than the short run. Producers can change the scale of their production.
14 What the other elasticity measures tell you about demand Income elasticity can tell you whether a good is: Normal, A luxury, Inferior. Cross price elasticity can tell you whether two goods are substitutes or complements.
15 Normal, luxury, inferior A 1% increase in consumers incomes can generate one of the following changes in QQ DD. An increase of 0-1% An increase of >1% A decrease in QQ DD The first is a case of a normal good; when consumers incomes rise they spend more money on the good in question and the quantity demanded increases. The increase is roughly that good s share in the consumers budget, so 0 EE PPxx,QQ DD 1. The second is a case of a luxury good; consumers make proportionally larger demands than the size of the income increase. The share of this good in the budget increases as well as the budget, itself. Last is an inferior good; when consumers get more income, they substitute away from it and demand less.
16 Substitutes and complements When the price of another good changes and the demand for the good in question changes, the goods are related. Quantity demanded increases when: The price of a complement decreases, or the price of a substitute increases. Quantity demand decreases when: The price of a complement increases, or the price of a substitute decreases. So what is the sign on cross price elasticity?
17 Substitutes and complements (continued) Cross price elasticity for a complement? % QQ DD EE PPyy,QQ DD = % PPPPPPPPPP oooo ooooooooo gggggggg = + < 0 The price of the other good goes up and you demand less of both (because they go together). Cross price elasticity for a substitute? % QQ DD EE PPyy,QQ DD = % PPPPPPPPPP oooo ooooooooo gggggggg = + + > 0 The price of the other good goes up and you demand less of it (and more of this).
18 Substitutes and complements (concluded) Complements are goods that are consumed together, so prices of complements are inversely related to demand. A negative cross price elasticity indicates complementary goods. Substitutes are goods that are perceived as alternatives to each other. The prices of substitutes are positively related to demand. A positive cross price elasticity indicates that the two goods are substitutes.
19 Applications of Elasticity ECON 210: PRINCIPLES OF ECONOMICS
20 Pricing a good to maximize revenue Imagine you are managing a firm that produces some good that has very low marginal cost. Scalable products like software downloads, subscriptions to periodicals, or streaming media services are good examples. You are tasked with finding the price that will make your company the most revenue. And with near zero variable costs, the most profit, too! Revenue can be shown with ease on a graph of a demand curve. Revenue is just the price multiplied by the quantity demanded.
21 Pricing a good to maximize revenue (continued) As it turns out, the price shown on the previous slide is the revenue-maximizing one. You can confirm this with trial and error by trying other prices. If your current price is $80/unit, you could raise revenue by decreasing price. If your current price is $10/unit, you could raise revenue by increasing price.
22 Revenue and elasticity Revenue changes as the price changes. Because of two opposing forces. Cutting (raising) the price tends to decrease (increase) revenue. But cutting price increases sales (quantity), and the quantity change goes in the opposite direction because of the Law of Demand. The effect on revenue depends simply on which force is bigger. % Revenue = % PP xx + % QQ DD, and demand elasticity is EE PPxx,QQ DD = % QQ DD EE % PP PPxx,QQ DD % PP xx = % QQ DD. xx So, combining these two yields: % Revenue = % PP xx 1 + EE PPxx,QQ DD. The effect of a price change depends crucially on the demand elasticity.
23 An elasticity-based pricing strategy To be concrete, consider 10% price changes. We know that when the price is too high, e.g., above $60/unit, a -10% price change increases revenue. So, 0 < % Revenue. % Revenue = EE PPxx,QQ DD. For this to hold, the parentheses must be negative. This is true only if the elasticity is greater then 1 in absolute value. I.e., if demand is elastic, a price cut increases revenue.
24 An elasticity-based pricing strategy Conversely when price is too low (below $60/unit), a +10% price change increases revenue. 0 < % Revenue. % Revenue = EE PPxx,QQ DD. Now the number in parentheses must be positive, which holds when elasticity is less than 1 in absolute value. If demand is inelastic, a price increase increases revenue.
25 Pricing a good to maximize revenue (concluded) To sum up: if demand for your product is elastic, you could raise revenue by decreasing price. If demand is inelastic, you could raise revenue by increasing price.
26 Technological progress when demand is inelastic Demand elasticity also determines how producers fare when technology shifts supply outward. If demand is elastic, the total revenue in that industry increases. Price goes down, but quantity goes way up. If demand is inelastic, revenue decreases with technological progress. Price goes down, and quantity only goes up a little.
27 Technological progress and revenues
28 Raising transaction costs when demand is inelastic Society wants some markets to produce less (none?) of their output. Drugs. Prostitution. Inputs that pollute, e.g., coal. On paper it could do this by decreasing supply. The War on Drugs is one strategy to decrease the supply of drugs. By adding additional costs of avoiding law enforcement to the costs of producing and selling drugs. The equilibrium moves up the demand curve: higher prices of drugs mean less quantity. But how elastic is the demand for drugs? How much less drugs do we have?
29 Research suggests: not very elastic When demand is inelastic and you increase the price, revenue goes up. Yes, the revenue of drug dealers. Probably not the objective of the policy. Makes the War exceedingly difficult to win. More money to: bribe enforcement agents, escalate real drug wars, and invent new drugs.
30 Raising transaction costs with a tax The silver lining in this disaster is that the additional revenue spent on drugs does not have to go to drug cartels. Recall that taxing a good also decreases its supply. Something that the states of Washington and Colorado recently remembered. At least with respect to marijuana laws. We will explore the economics of taxation more in a later lecture, but suffice it for now to say that the government could get most of the revenue gains that would otherwise go to sellers in the drugs market. The light green rectangle goes to the government instead of to sellers. Inelastic demand means we still wouldn t discourage much drug use with taxes, but at least we wouldn t be enriching the drug cartels.
31 Cap and trade environmental policies The right to discharge pollution can be viewed as an economic good. In the sense that some production relies on the emission of pollutants. Or at least is made cheaper by polluting. Producers would be willing to pay to emit pollutants if the alternative was shutting down or paying to process pollutants into a clean form. There is a demand curve for the right to pollute.
32 Cap and trade environmental policies (continued) Pollution is a problem if there is no supply curve, i.e., when no one owns the air and can function as seller. Consequently there is no price that firms pay, so they pollute too much. Cap and Trade policies correct this problem by making the right to pollute scarce (the cap ). Then polluters are allowed to trade pollution allowances, allocating them to their most valued uses. This happy outcome is discussed further in chapter 10.3 of the textbook, but I will not elaborate further here.
33 Cap and trade environmental policies (continued) Equilibrium (less pollution)
34 Cap and trade and elasticity This is all very cool, but how does it relate to elasticity? The supply of pollution allowances is perfectly inelastic. If demand increases, the price goes up but quantity does not. Environmentalists can reduce pollution by buying pollution permits and not using ( retiring ) them. This prices some polluters out of the market and reduces pollution even further. And wouldn t be possible without tradable pollution permits.
35 Retiring pollution allowances New equilibrium Remaining pollution Retired permits
36 Put a bounty on snakes, you get more snakes What happens when you do the same thing for a good that has elastic supply? Snake breeding apparently fits this criterion. And it is not very expensive either. We know this because when the governor of Delhi (in India) tried to combat the city s problem with cobras by offering a bounty for the snakes skins, enterprising citizens began farming cobras for the purpose of collecting the bounty.
37 The cobra effect : the bounty creates a market for cobras Equilibrium without bounty: snakes are not valuable enough to pay for Equilibrium with more snakes
38 Put a bounty on snakes, you get more snakes (concluded) Similar incarnations of the cobra effect have been observed in Vietnam (with rats), the U.S. (feral pigs and coyotes). In a non-animal realm, it underlies the failures of gun buy-back programs and the conjecture that public protesters burning of Beatles merchandise (in 1966) actually increased the sales of the band s records. Regarding the cobras, economists generally agree that the best solution would be to let this guy handle the problem.
39 Conclusion Price elasticity tells you how sensitive quantity demanded (or supplied) is to the good s price. Cross price elasticity measures tell you about relationships (substitutes/complements) between goods. Income elasticity measures tell you whether a good is normal or inferior. Elasticity matters a great deal for how firms price their products and for designing policies to increase or decrease the production of goods.
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