# Introduction to Elasticity in Economics

When introducing the concepts of supply and demand, economists often make qualitative statements about how consumers and producers behave. For example, the law of demand states that as the price of a good or service increases, the demand for that good or service decreases. The law of supply states that the quantity of a good produced tends to increase as the market price of that good increases. While these laws are useful, they don't capture everything that economists would like to include in the supply and demand model; as a result, economists have developed quantitative measurements such as elasticity to provide more detail about market behavior.

Elasticity, in short, refers to the relative tendency of certain economic variables to change in response to other variables. In economics, it is important to understand how responsive quantities such as demand and supply are to things like price, income, the prices of related goods, and so on. For example, when the price of gasoline increases by one percent, does the demand for gasoline go down by a little or a lot? Answering these sorts of questions is extremely important to economic and policy decision making, so economists have developed the concept of elasticity to measure the responsiveness of economic quantities.

## Types of Elasticity

Elasticity can take a number of different forms, depending on what cause and effect relationship economists are trying to measure. Price elasticity of demand, for example, measures the responsiveness of demand to changes in price. Price elasticity of supply, in contrast, measures the responsiveness of quantity supplied to changes in price. Income elasticity of demand measures the responsiveness of demand to changes in income, and so on.

## How to Calculate Elasticity

Measures of elasticity all follow the same basic principles, no matter which variables are being measured. In the discussion that follows, we'll use price elasticity of demand as a representative example.

Price elasticity of demand is calculated as the ratio of the relative change in quantity demanded to the relative change in price. Mathematically, the price elasticity of demand is just the percent change in quantity demanded divided by the percent change in price:

Price elasticity of demand = Percent change in demand / Percent change in price

In this way, the price elasticity of demand answers the question "What would be the percent change in quantity demanded in response to a one percent increase in price?" Notice that, because price and quantity demanded to tend to move in opposite directions, the price elasticity of demand usually ends up being a negative number. To make things simpler, economists will often represent price elasticity of demand as an absolute value. (In other words, the price elasticity of demand could just be represented by the positive part of the elasticity number, eg. 3 rather than -3.)

Conceptually, you can think of elasticity as an economic analog to the literal concept of elasticity. In this analogy, the change in price is the force applied to a rubber band, and the change in quantity demanded is how much the rubber band stretches. If the rubber band is very elastic, the rubber band will stretch a lot. If it's very inelastic, it won't stretch very much, and the same can be said for elastic and inelastic demand. In other words, if demand is elastic, it means a change in price will result in a proportional change in demand. If demand is inelastic, it means a change in price will not result in a change in demand.

You may notice that the equation above seems similar, but not identical to, the slope of the mand curve (which also represents price versus quantity demanded). Because the demand curve is drawn with the price on the vertical axis and quantity demanded on the horizontal axis, the slope of the demand curve represents the change in price divided by the change in quantity rather than the change in quantity divided by the change in price. In addition, the slope of the demand curve shows absolute changes in price and quantity whereas price elasticity of demand uses relative (i.e. percent) changes in price and quantity. There are two advantages to calculating elasticity using relative changes. First, percent changes don't have units attached to them, so it doesn't matter what currency is used for the price when calculating elasticity. This means that elasticity comparisons are easy to make across different countries. Second, a one-dollar change in the price of an airplane ticket versus the price of a book, for example, are likely not viewed as the same magnitude of change. Percentage changes are more comparable across different goods and services in many cases, so using percent changes to calculate elasticity makes it easier to compare the elasticities of different items.

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