Chapter 5 Elasticity PDF

Chapter 5: Elasticity So far, we have simply looked at the direction of a change. We defined the Law of Demand and the Law of Supply. We also looked at a couple events that are likely to shift the demand or the supply curve – resulting in a new equilibrium. Often what we are interested in is respon...

Chapter 5: Elasticity So far, we have simply looked at the direction of a change. We defined the Law of Demand and the Law of Supply. We also looked at a couple events that are likely to shift the demand or the supply curve – resulting in a new equilibrium. Often what we are interested in is responsiveness. For example, say that you are in a band and you get to keep any money collected at the door (the cover charge). Assuming that demand for your band obeys the law of demand you know that if you increase (decrease) the price, fewer (more) people will pay to see you play. Assuming you want to maximize how much you earn it is not exactly straightforward to determine how much you should charge. For example, by increasing the price, you earn more per customer but you have fewer customers. What you need to know is how responsive your customers are to a change in price. We call this Elasticity, it is a measure of responsiveness of Qd or Qs to a change in one of their determinants (price, change in income etc.). The general, and intuitive, answer to the above question is to say that if your customers are not responsive to price then you ought to charge more (and vice versa). In this chapter, we will quantify this intuition with a couple more tools economists use. Price Elasticity of Demand This is the most common elasticity we will discuss and I will denote it as Ed. The Ed measures how much the Qd of a good responds to a change in the price of that good. Here is the general formula: Ed = % change in Qd / % change in P For example, let’s say that we observe a 10% increase in the price of ice cream (10% increase in P) and a subsequent 20% decrease in the amount of ice cream purchased (20% decrease in Qd). We would have: Ed = -20% / +10% = 2 Notice the elasticity does not have any units – the % change units effectively cancel out as you will see in a minute. Also notice that I dropped the negative – the answer here is not -2. Because of the Law of Demand, price and Qd always move in opposite directions so we drop the negative term for convenience. To interpret this number, we would say that for each 1% change in the price of ice cream we expect a 2% change in the Qd of ice cream. Let’s do one more. Say, we observe a 10% increase in the price of gasoline and a subsequent 5% decrease in the amount of gasoline purchased. Ed = -5% / +10% =.5 Now, we say that for each 1% change in the price of gasoline we expect a.5% change in the Qd of gasoline. As one might expect, these numbers tell us that the Qd of ice cream is more sensitive to a change in price than the Qd of gasoline is. Let’s define some determinants of elasticity before we move on to calculations based on demand curves. Defining Elasticities Elasticity is best thought of as a relative concept – we can compare the elasticity (responsiveness) of one good relative to that of another. But for simplicity or convenience we will define some categories. Ed < 1 is considered inelastic – consumers are NOT responsive Ed > 1 is considered elastic – consumers are responsive Ed = 1 is considered unit elastic it draws a line between inelastic and elastic. We also use it in a couple applications below. There are also two special cases which I do not tend to refer to but will never the less pop up from time to time. Ed = 0 is perfectly inelastic. Regardless of the change in price there is absolutely no change in Qd. Ed = infinity is perfectly elastic. Any increase in price will drive Qd down to zero. Across demand curves we can say that steeper demand curves tend to be more inelastic (perfectly inelastic requires a vertical line) and similarly, flatter demand curves tend to be more elastic (perfectly elastic requires a horizontal line). However, elasticity is not slope. Go through the figures below to convince yourself and visualize the relationship between slope and elasticity. Calculating Elasticity To calculate the elasticity from information provided on price and Qd we will use the midpoint method. This is convenient when you are determining elasticity between two points (it will give you the same answer regardless of where you begin). Let’s do a couple examples using the following demand. Point A: P = 100 and Qd = 10 Point B: P = 75 and Qd = 20 Point C: P = 50 and Qd = 30 Point D: P = 25 and Qd = 40 Between any two points ((P1, Qd1) and (P2, Qd2) the midpoint method tells us to determine the Ed as follows: Ed = [(Qd2–Qd1) / ((Qd2+Qd1)/2)] / [(P2–P1) / ((P2+P1)/2)] In words this tells you that for each % change (in Qd and in price) find the difference between the two points and then divide by the average. How about between points A and B? It does not matter what we define as Qd1 or Qd2 so let’s just plug in the numbers. I’ll use P1 = 100, Qd1 = 10, P2 = 75, and Qd2 = 20 Ed = [(20–10) / ((20+10)/2)] / [(75-100) / ((75+100)/2)] = (10/15) / (-25/87.5) =.667/-.286 = 2.33 Recall that with Ed we ignore the sign but this will not be the case with other elasticities. Now let’s look at the Ed between points C and D. Ed = [(40–30) / ((40+30)/2)] / [(25-50) / ((25+50)/2)] = (10/35) / (-25/37.5) =.286/-.667 = 0.429 This tells us that at high prices Ed tends to be elastic and at low prices Ed tends to be inelastic. Now we can think about the question about the Band and the cover charge. We will use the demand curve above and calculate the bands Total Revenue. Total Revenue (TR) is simply price * quantity demanded. Point P Qd TR A 100 10 1000 B 75 20 1500 C 50 30 1500 D 25 40 1000 Between points A and B we determined that Ed was elastic. This implies that the percent change in Qd is larger than the percent change in P. So when we lower price we get a bigger increase in Qd and as a result, the total revenue increases. Alternatively, between points C and D we determined that Ed was inelastic. In this case, we increase price and get a relatively small decrease in Qd so we end up with an increase in TR. Determinants of Ed 1. Availability of Substitutes If there are many substitute goods available consumers are likely to be more responsive (larger Ed). For example, in the ice cream market consumers might just switch to popsicles, Italian ice, or candy. On the other hand, in the market for gasoline what alternative do you have? Perhaps consumers will reduce recreational trips but for most drivers the commute to work does not change with the gas price. 2. Time Horizon This is related to the availability of substitutes. The idea is that over longer periods of time Ed is likely to become more elastic. For example, the Ed for gasoline might be quite low for the first several months but over time consumers will switch to fuel efficient cars, electric cars, or figure out public transportation. When gas was $4/gallon Hybrids were selling great. Now, at $2 a gallon, pickup trucks are back in fashion (much to the benefit of American auto firms who make good margins on larger trucks – partially because they are protected from foreign competition through tariffs we impose on foreign made pickup trucks). 3. Definition or Scope of the Market  This one is about where we draw the lines around particular markets. The more narrowly we consider the market the more elasticity we will see. For example, are consumers likely to be more responsive to a change in the price of Cheerios or a change in the price of all cereal? Again, the availability of substitutes captures much of the intuition here. If only the price of Cheerios increases, I suspect that many consumers will find a fair amount of available substitutes in the cereal aisle. But, if all cereal increases in price consumers effectively have fewer substitutes, they either pay more or they have to alter their breakfast – eggs, toast, etc. 4. Necessity or Luxury Pretty straightforward. Necessities like food or medicine tend to have low elasticity (consumers are not responsive to changes in price) and luxuries like vacations or nicer clothes tend to have high elasticities (consumers are responsive to changes in price). Other Demand Elasticities We will talk about two other elasticities on the demand side. The calculation and interpretation of these elasticities are the same as above but we will want to keep track of the sign (positive or negative). Income Elasticity of Demand measures how the Qd changes relative to a change in consumer income. Income Elasticity = % change in Qd / % change in income When income rises and this leads to an increase in Qd the income elasticity is positive. Note that if a decrease in income leads to a decrease in Qd the income elasticity is also positive. We refer to these as Normal Goods. On the other hand, when an increase (decrease) in income leads to a decrease (increase) in Qd the income elasticity is negative. We refer to these goods as Inferior Goods. We already defined both these terms, Normal and Inferior Goods, last chapter or so. This elasticity simply allows us to quantify this relationship. Within the Normal Good category, it is also common to distinguish between necessity (food/clothing) and luxury goods (jewelry). While the income elasticity is positive for both sets of goods it is likely much larger for luxuries. This means that when your income goes up you will buy a bit more food and clothing but the impact will be small. There will be a larger uptick in your consumption of goods that you consider luxuries. Cross Price Elasticity measures the change in Qd of one good (X) relative to the change in the price of another related good (Y). Cross Price Elasticity = % change Qd_X / % change P_Y Again, we have already introduced this concept. When the price of peanut butter increases (decreases), we expect that the Qd of jelly decreases (increases). We refer to these products as Complements – you consume them together – and their cross price elasticity will be negative. Conversely, when the price of Coke increase (decrease) we expect the Qd of Pepsi to increase (decrease). We refer to these products as Substitutes – you consume Coke or Pepsi – and their cross price elasticity will be positive. Elasticity of Supply As you might expect this elasticity measures the responsive of producers to a change in the price of their product. The law of supply implies that price and Qs are positively related – if market price rises, firms will want to sell you more. This measures how quickly they can respond or ramp up production. Again, the calculation and interpretation is the same as Ed. Elasticity of Supply (Es) = % change in Qs / % change in P We don’t tend to think of Es as having elastic/inelastic categories but there is no reason why we couldn’t. In general, Es will be larger in industries without specialized inputs and over longer time periods. Applications of Elasticity 1. Elasticity of Demand and Total Revenue We already saw above that when Ed is elastic then reducing price will increase total revenue and that when Ed is inelastic then increasing price will increase total revenue. This implies that total revenue will be maximized when Ed = 1. Keep in mind that this is total revenue not total profit. Also note that consumer expenditure is the same as total revenue. 2. Elasticity and Trade Let’s say that the US and Europe were in a trade war, or at least, that the US wanted to set a retaliatory tax on European imports. Do you think that the US should target the European beer industry or the olive oil industry? I should say that I have not looked into these industries for a while but this is the idea. We want to think about the firm’s ability to push the tax onto consumers. That capacity depends on the alternatives that consumer have. There are not many alternatives for olive oil – Europe is responsible for most of the world’s output. You could switch to vegetable or canola oil but if you want to use olive oil you are more or less stuck with European brands. This implies that US consumers are relatively inelastic with respect to olive oil and so olive oil firms would be in a good position to push the tax onto US consumers. Contrast this with a tax on European beers. There are many tasty domestic beer brands. If the European brands attempted to push the tax onto US consumers, we could rather easily find a substitute beer. In economic terms, this means the US consumers are elastic. Since they are unable (or at least less able) to push the tax onto consumers they have to absorb the expense (profits down). If we wanted to get Europe’s attention, we will have better luck hitting the beer market. 3. Coupons We will re-visit this when we get to price discrimination but the idea of coupons is to segment your market into elastic and inelastic consumers. They are able to sell the product at the lower price (the price offered to the price sensitive – elastic segment). But they don’t want to sell the product at a discount to those who are willing to pay the higher price (the inelastic segment). 4. The new seed farming example from text is also interesting. If demand is relatively inelastic for agricultural products (corn wheat etc.) then an increase in supply (lower price) will only lead to a small increase in Qd and thus a reduction in farmer revenue. What seems unambiguously good (more productive farms) may not be (from perspective of individual farmer they are worse off). 5. Following a similar logic think about the war on drugs which primarily focuses on decreasing supply. A reduction in supply will lead to an increase in price. If demand for drugs is inelastic then this could lead to an increase in revenue for sellers and thus more incentive to deal. 6. 1991 Luxury Tax So, back in 1991 the government imposed a luxury tax. This was an extra 10% charge on luxury goods (cars greater than $30,000 and boats greater than $100,000). How well did this tax work? The fact that it was phased out starting 2 years later gives a good clue. Think about the elasticity for these goods – we expect luxuries to be particularly elastic. The people in the market for these goods have many options for how to spend their money. The tax revenue was much lower than projected. Further, yacht retailers reported a 77% drop in sales and estimated 25,000 layoffs. I got these numbers out of Wall Street Journal (Good Riddance to the Luxury Tax – Jan. 6, 2003). We would explain by saying that yacht producers were ultimately unable to push this tax onto their consumers and as a result, the workers paid the price. To maintain sales, they absorbed the tax as best they could by reducing costs (wages down and layoffs). Presumably, this was not the intent of the law. The point of the above examples, some of which we will re-visit, is to point out that one’s initial intuition may not always be correct. We use economic models and concepts to make our intuition better. By thinking about supply, demand and elasticities you can start thinking about policy more carefully.