## Elasticity

(Research Starters)

Presenting some applications and insights to undergraduate students on the topic of elasticity, this essay contains discourse that aims to facilitate their understanding of the concept. The essay addresses several variants of elasticity along with definitions, calculations, and examples. A large portion of this essay covers price, cross, and income elasticities of demand. The author devotes an ample amount of attention to those demand elasticities striving to alleviate learning difficulties. Frequently, students encounter problems associated with line graph characteristics, expenditure and revenue changes, and elasticity determinants. The article also presents price elasticity of supply and its comparative relevance to those who incur the tax burden on some items.

Keywords Demand; Economics; Elasticity; Income; Price; Revenues; Supply; Taxes

### Economics: Elasticity

### Overview

Elasticity is a concept of central importance to business, marketing, and economics. Studies in economics begin by expressing the importance of the ceteris paribus (translation means all else is held constant) assumption and by focusing on relationships between the possible prices of an item and the quantities consumers are willing and able to purchase at each price; likewise, the quantities suppliers are willing and able to produce. On the consumer or demand side, students learn very early in their coursework that an inverse relationship exists between price and quantity in accordance with the Law of Demand. Relatively speaking, smaller amounts are in demand at higher prices and vice versa. On the producer or supply side, they learn that a positive relationship exists according to the Law of Supply. Whether one chooses to focus on demand or on supply, elasticity is a concept that helps us to understand in precise terms exactly how much quantity changes in response to a price change.

Many students who complete and evaluate introductory courses in economics for non-business majors find the elasticity topic easy to comprehend. In addition, they report that the topic makes perfect sense to them and is highly relevant to their everyday exchanges. However, they report having difficulties mastering the varied types (price, income, and cross) of elasticity. To overcome those obstacles they encourage other students to elicit examples from their professors and to practice calculating, interpreting, and applying elasticity.

Some commonly used textbooks in economics (Arnold, 2005; Guell, 2007; McConnell & Brue, 2008; Parkin, 2000) provide basic topical coverage, but unfortunately very few articles found during a recent search of electronic publications present economic elasticity in a straightforward manner, without references and narrow application to a specific context. Furthermore, those contexts usually require readers to have an advanced understanding of economics and other business disciplines. In a demonstration of how the elasticity concept is relevant to marketing, Dickinson (2002) makes the case that text book presentations of elasticity provide a weak foundation for studying price-quantity interactions and for simulating behavioral complexities of consumers in the marketplace. From an economics education perspective, this article represents one effort to facilitate an undergraduate student's understanding of the elasticity concept.

### Applications

### Price Elasticity of Demand

Cigarette smokers, beer drinkers, and motor vehicle drivers are consumers whom are likely to identify most readily with the elasticity concept. Examples pertaining to alcohol and tobacco will follow later, but gasoline prices serve as an excellent example for starters. Motor vehicle drivers these days probably retain their awareness of the daily price for gasoline and its fluctuations during any given period. Furthermore, it is likely that these consumers will purchase greater quantities when the price of gasoline falls and fewer quantities when the price rises. Calculations of the price elasticity of demand for gasoline allow us to determine precisely in percentage terms how sensitive drivers' purchases of fuel are in response to changes in its price. Though most dislike rising gasoline prices and generate some noise about it, the evidence strongly suggests that consumer demand is unresponsive or inelastic as they tend to purchase the same amounts over time irrespective of price. To explore this observation further, students need to understand demand elasticity coefficients, calculate them, and determine whether demand for gasoline is truly inelastic.

Guell (2007, p. 41) summarizes a few studies on the price elasticity of demand for gasoline by informing us that any given 10 percent increase in its price will result in a decrease of less than 3 percent in quantities purchased; coincidentally, the gasoline prices tend to fluctuate by 10 percent or more during any given week. The latter percentage varies depending on how long consumers have to adjust their driving and spending habits; for example, the amount of gasoline in their car's tank and the remoteness of their geographic location jointly influence whether they can afford to shop for cheaper gasoline. Research on price elasticity of demand for gasoline also shows the coefficient is 0.08 in the "short-run" and it is 0.24 in the "long-run."

### Calculating

Note the simplifying omission of the negative sign from the aforementioned coefficients because of the explicit inverse relationship that exists between price and quantity demanded. Calculations of the elasticity coefficient involve division of the percentage change in quantity demanded by the percentage change in price. The coefficient is unit free and its basic formula is:

Percent change in quantity demanded/Percent change in price

Percent change is the observed difference between two points, namely the starting point and the endpoint, divided by the value at the starting point. Readers of textbooks will find variants in the formula that are merely designed to accommodate calculations whether one holds an interest in the observing the elasticity at the starting point, the endpoint, or somewhere near the middle of those two points and when facing different shapes of the line that represents all the price-quantity combinations.

Another justification for omitting the negative sign is to simplify interpretations of a price elasticity of demand coefficient by examining it as an absolute term. In the broadest sense, we can think about and talk about elasticity of a specific item at its extremes along a demand spectrum. The demand for an item is either elastic, inelastic, or unitary elastic when the respective coefficient as an absolute term is greater than one, less than one, or equal to one. The coefficient in the gasoline example is less than one, which informs us that the demand for gasoline is inelastic; in other words, consumers are unresponsive to changes in the price of gasoline. We generally dislike the price hike, but collectively gasoline consumers maintain their purchase levels.

Think of the larger array of items that you purchase on a regular basis. My guess is that readers of this article, like other consumers, are more responsive to changes in price for some items and not so for other items. In absolute terms, price elasticity of demand coefficients range between zero and infinity extending outwardly from unitary elasticity, which is where the coefficient is equal to one. Those extremes carry specific names. At one extreme, your purchases of an item will cease or go to zero quantity when a price increase occurs. Demand is perfectly elastic in this instance. At another extreme, your purchases of an item will remain the same regardless of price. Demand is perfectly inelastic in this instance.

### Demand Line Graphs

The coefficient of elasticity is different than, but...

(The entire section is 3486 words.)