Elasticity Review for AP Economics (page 3)
Review questions for this study guide can be found at:
Main Topics: Price Elasticity of Demand, Determinants of Elasticity, Total Revenue, Income Elasticity, Cross-Price Elasticity of Demand, Elasticity of Supply
Studying the economic concept of elasticity is much like a corporate executive workshop, the topic of which is "Sensitivity Training." When we observe a consumer's purchase decision, say for good X, change in response to a change in some external variable (the price of good X or her income), elasticity helps us measure the sensitivity of her consumption to that external change. We also examine the sensitivity of suppliers of good X to a change in the price of good X. We use basic mathematical relationships to measure elasticity, but it is useful to remember that all elasticity formulas measure sensitivity to a change.
Price Elasticity of Demand
The Law of Demand tells us that: "all else equal, when the price of a particular good falls, the quantity demanded for that good rises." But what it fails to answer for us is: "by how much"? Will it be a relatively large increase in quantity demanded or will it be almost negligible? In other words, we would like to measure how sensitive consumers are to a change in the price of this good.
Price Elasticity of Demand Formula
- Ed = (%Δ in quantity demanded of good X)/(%Δ in the price of good X)
Note: The Law of Demand insures that Ed is negative, but, for ease of interpretation, economists usually ignore the fact that price elasticity of demand is negative and simply use the absolute value. The greater this ratio, the more sensitive, or responsive, consumers are to a change in the price of good X.
Range of Price Elasticity
Economists like to classify things. It's a sickness, but it is usually done for a reason. (You do need to know these for the exam.) For example, we classify elasticities based upon how sizeable the reaction of consumers is to a change in the price. Rather than describing consumers as "really responsive" or "really, really responsive" or "super duper responsive," we classify consumer responses as elastic or inelastic. The examples below should clarify things.
The price of a laptop computer increases by 10 percent and we observe a 20 percent decrease in quantity demanded. Using the above formula:
Ed = (–20%)/(+10%) = –2 or simply Ed = 2
- If Ed > 1, demand is said to be "price elastic" for good X. The responsiveness of the consumer exceeded, in percentage terms, the initial change in the price.
The price of a package of chewing gum increases by 10 percent and we observe a 5 percent decrease in quantity demanded. Using the above formula:
Ed = (5%)/(10%) = ½
- If Ed < 1, demand is said to be "price inelastic" for good X. The initial change in the price exceeded, in percentage terms, the responsiveness of the consumer.
The price of oranges increases by 5 percent and the quantity demanded decreases by 5 percent. Using our elasticity formula:
Ed = (5%)/(5%) = 1
- If Ed = 1, demand is said to be "unit elastic" for good X. The initial change in the price is exactly equal to, in percentage terms, the responsiveness of the consumer.
Elasticity on the Demand Curve
Take a very simple demand curve for cheeseburgers: P = 6 – Qd, and plot this demand curve below (Figure 7.1).
Table 7.1 summarizes changes in price, quantity demanded and price elasticity at each point on the demand curve.1
As you can see, in Figure 7.1, the price elasticity of demand is not constant at points A through G on the demand curve. Specifically, as the price rises, Ed rises, telling us that consumers are more price sensitive at higher prices than they are at lower prices. This makes good intuitive sense. When the price is relatively low (e.g., point B) a 50 percent increase in price might be almost negligible to consumers. But if the original price is quite high (point F) then a 50 percent increase in the price is pretty drastic. In fact, if we divide the demand curve in half, you can see that above the midpoint (point D), demand is price elastic and below the midpoint, demand is price inelastic. At the midpoint, demand is unit elastic.
If it is true that any increase in the price results in no decrease in the quantity demanded, then we are describing the special case where demand for the good is perfectly inelastic: Figure 7.2 shows the demand for a life-saving pharmaceutical, for which there is no substitute, and without which the patient dies. A vertical demand curve (D0) tells us that no matter what percentage increase, or decrease, in price, the quantity demanded remains the same. Mathematically speaking, Ed = 0.
In the case where a decrease in the price causes the quantity demanded to increase without limits, then we have the special case where demand is perfectly elastic for that good. Figure 7.2 shows demand for a good (D1), maybe one farmer's grain, which has many substitutes. A horizontal demand curve tells us that even the smallest percentage change in price causes an infinite change in quantity demanded. Mathematically speaking, Ed = ∞.
Comparing the vertical (perfectly inelastic) demand curve to the horizontal (perfectly elastic) demand curve allows us to draw an important generalization. As a demand curve becomes more vertical, the price elasticity falls and consumers become more price inelastic. The opposite generalization can be made as the demand curve becomes more horizontal. Figure 7.3 illustrates some general points about slope and elasticity.
- In general, the more vertical a good's demand curve (D0), the more inelastic the demand for that good.
- The more horizontal a good's demand curve (D1), the more elastic the demand for that good.
- Despite this generalization, be careful, elasticity and slope are not equivalent measures.
Determinants of Elasticity
Perfectly elastic and perfectly inelastic demand curves are usually reserved for the hypothetical example, but they illustrate that Ed differs across consumer goods. Your intuition is that consumers respond to a price change in different ways. A 10 percent increase in the price of a car might have a drastically different consumer response from what we observe from a 10 percent increase in the price of a college education, a package of mechanical pencils or a hotel stay in Fort Lauderdale. Let's look at some general explanations for why elasticity differs.
- Number of Good Substitutes
- Proportion of Income
If the price of good X increases, and many substitutes exist, the decrease in quantity demanded can be quite elastic. For this reason we expect Ed of orange juice to be high since there are many substitutes available to drinkers of fruit juice.
Corollary: Often times you hear of a good that is a "necessity" or a "frivolity." These adjectives are reiterating a relative lack of or a relative wealth of good substitutes.
The more narrowly the product is defined, the more elastic it becomes. If we narrow our focus from orange juice down to one brand of orange juice (i.e., Minutemaid), the number of substitutes grows and we predict that so too does the price elasticity of demand for Minutemaid brand orange juice. Likewise, the demand for blue Chevrolet SUVs is more elastic than the demand for Chevrolet SUVs which, in turn, is more elastic than the demand for all SUVs.
If the price of a good increases, the consumer loses purchasing power. If that good takes up a large proportion of the consumer's income, he greatly feels the pinch of the income effect, and his responsiveness might be significant. If the price of toothpicks increased by 10 percent, the typical household probably would not feel the lost purchasing power and Ed would be low. The opposite would be true if the price of food items increased by 10 percent.
A young full-time college student is purchasing her education by the credit-hour and supporting herself with a part-time job on the weekends and evenings. Since the student is living on a relatively small monthly income, if the price of a credit-hour increases, the response might be very elastic. The student might drop down to part-time status or drop out of college altogether so that she can save enough money to return next quarter.
Consumers faced by a rising price are usually fairly resourceful in their ability to find a way of decreasing the quantity demanded of a good. The difficulty faced by consumers is that they might not have time, at least not initially, to find a substitute for the more expensive good. We expect price elasticity to increase as more time passes after the initial increase in the price.
If the price of gasoline rises, consumers driving large SUVs do not immediately switch to small cars and Ed is low. But given enough time, if the gas price remains high, the Ed for gasoline increases.
Total Revenue and Elasticity
Discussing price elasticity and making simple calculations is not just a delightful academic exercise for students. Knowing how sensitive consumers are to changes in price is important to those who benefit from selling goods to those consumers—the sellers. Sellers compute total revenues collected from selling goods.
- Total Revenue = Price * Quantity demanded
A seller might think, "If I continue to raise the price, my total revenues must continue to rise." A student of microeconomics knows that this is flawed logic, because quantity demanded falls when the price rises, making the impact on total revenue uncertain.
- Here's what's happening: (Price↑) * (Quantity demanded↓) = Total Revenue
With price going up and quantity demanded going down, it's like a tug-of-war between two teams, with total revenue being pulled in the direction of the strongest team.
Whether or not the total revenue increases with a price increase depends upon whether or not the gain from the higher price offsets the loss from lower quantity demanded. Price elasticity is an excellent way to predict how total revenue changes with a price change. This is sometimes called the total revenue test. Table 7.2 extends our earlier table by adding a column for total revenue at points A through G.
As you can see, if the price rises in the inelastic range of the demand curve, total revenues rise. However, if the price continues to rise into the elastic range, total revenues begin to fall. Why? Maybe a reminder of what it means for demand to be elastic helps to predict which team wins the tug-of-war.
In Figures 7.4 and 7.5, we can graphically illustrate the connection between the demand curve, elasticity, and total revenue.
Income Elasticity of Demand
In the case of the income elasticity, it is a measure of how sensitive consumption of good X is to a change in a consumer's income.
- EI = (% Δ Qd good X)/(% Δ Income)
Jason's income rises 5 percent and we see his consumption of fast food meals rise 10 percent.
EI = 10%/5% = 2
So what do we make of this? First, because EI is greater than zero, we can determine that fast food meals are a normal good for Jason. Second, at least in this example, the consumption of fast food meals is quite income elastic. A relatively small percentage increase in income causes a large, in fact twofold, percentage increase in fast food meals. Some refer to these goods as luxuries.
Jen's income rises 5 percent and we observe her consumption of bread rise 1 percent.
EI = 1%/5% = .2
Once again, this measure would indicate that bread is a normal good as more income prompts more bread consumption. However, the relatively small increase in consumption compared to the increase in income tells us that bread is relatively income inelastic. This makes sense, after all, how much more bread does one really wish to consume as their income rises? If Jen's income doubled, would she double, or more than double, her consumption of bread? These goods are often referred to as necessities.
Consumer income increases by 5 percent and we observe consumption of packaged bologna decrease by 2 percent.
EI = –2%/5%= –.4
Again, there are two important observations that can be made here. First, because consumption of bologna decreased with an increase in income, we can conclude that bologna, in this example, is an inferior good. Second, there is a relatively inelastic response in bologna consumption to a change in income.
Cross-Price Elasticity of Demand
Consumers also change their consumption of good X when the price of a related good, good Y changes. The sensitivity of consumption of good X to a change in the price of good Y is called the cross-price elasticity of demand.
- Ex,y = (% Δ Qd good X )/(% Δ Price good Y )
The price of eggs increases by 1 percent and the consumption of bacon falls 2 percent. The fact that bacon consumption fell when eggs became more expensive tells us that these goods are complementary goods.
Ex,y = (% Δ Qd bacon)/(% Δ Price eggs) = –2%/1% = –2
The price of Honda cars increases 2 percent and consumption of Ford cars increases 4 percent. Because Ford cars saw increased consumption when Honda cars got more expensive, the two goods are substitutes.
Ex,y = (% Δ Qd Ford)/(% Δ Price Honda) = 2%/1% = +2
Price Elasticity of Supply
Now that we have addressed the sensitivity of consumer consumption of good X, let us discuss elasticity from the supplier's perspective. When the price of good X changes, we expect quantity supplied to change. The Law of Supply predicts that as the price of good X increases, so too does quantity supplied. But what we do not know is, "by how much?" The price elasticity of supply helps to measure this response.
Price Elasticity of Supply Formula
- Es = (% Δ in quantity supplied of good X)/(% Δ in the price of good X)
Note: The Law of Supply insures that Es is positive. The greater this ratio, the more sensitive, or responsive, suppliers are to a change in the price of good X.
The Element of Time
Perhaps the most important determinant of how price elastic suppliers are in a particular industry is the time that it takes suppliers to change the quantity supplied once the price of the good itself has changed. This flexibility of course is different for different types of producers.
A local attorney produces hours of legal service in a small midwestern town from her small office. At the current market price for an hour of legal advice, she works a 40-hour workweek with the help of one clerical employee. If the price of an hour of legal assistance rises by 10 percent in the local market, initially our attorney responds by working a few additional hours each weekday evening and on Saturday, but the constraints of the calendar allow for only an increase of 5 percent in the hours that she supplies.
Short term Es = 5%/10% = .5
If this higher price is maintained for a month or two, the attorney might ask her employee to work additional hours, thus allowing the small office to increase the quantity of hours supplied by 10 percent. And, if the price continues to stay at the higher rate, she might expand the office and employ a junior associate and thus increase the hours supplied by 20 percent.
- Long term Es = 20%/10% = 2
Because suppliers, once the price of the good has changed, usually cannot quickly change the quantity supplied, economists predict that the price elasticity of supply increases as time passes. Figure 7.6 illustrates the short-term (SSR) and long-term (SLR) supply curves for our attorney. In general, the less steep the supply curve, the more elastic suppliers are in response to a change in the price.
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