The concept of elasticity is used extensively in economics. It is not a difficult concept to master once you understand what elasticity tells the economist about the demand for a good. The word elasticity basically means responsiveness or sensitivity in everyday language. In fact, when the economist want to know how "price elastic" the demand for apples is, all he really wants to know is how the demand for applies "responds" to a change in the price of apples.

Mathematically, any function (a relationship between a dependent variable and an independent variable) has an elasticity of the dependent variable with respect to the independent variable. Let’s take an example:

The demand function can be written as Q_x^D = f (P_x). This simply means that the demand for good X (Q_x^D) will depend upon the price of good X (P_x). The price elasticity of demand, therefore, simply tells us just "how much" the demand for good X depends upon the price of good X.

Algebraically:

E_D = % D Q_x^D   =   DQ_x^D/Q_x^D
          % D P_x              D P_x/ P_x

Where D (Delta) means "change in." The larger the elasticity, the more responsive or sensitive the demand for good X is to a change in its price.

Let’s answer the following question: Suppose Antonio’s raises the price of pizzas by ten percent and finds that the purchase of pizzas by customers falls by five percent. What is the elasticity of demand for pizzas with respect to their price at Antonio's?

The calculation is simple: Use the second term in the above equation and simply plug in the amounts:

E_D = % D Q_x^D   = -5 = -1
         % D P_x         10     2

This means that each one percent rise in the price of pizzas results in a one-half of one percent decline in the consumption of pizzas.

BUT WAIT!! We have to note that there is a minus sign in front of the 5%. This is because the consumption of pizza decreased when the price was increased. In other words, there is a negative relationship between price and quantity demanded (the law of demand). However, this is where we come to a slight perversion in economics: since the price elasticity of demand is consistently negative, economists forget about the negative sign and pretend that it is consistently positive. Therefore, we can conclude that the price elasticity of demand for Antonio’s pizzas in the above example is equal to ½.

Now that we understand what the demand elasticity is, here are some things we should always remember about it:

Number One (1):

Demand curves are generally composed of points which are elastic, unitary elastic, and inelastic. Points in the upper portion of the curve are elastic. Points in the lower portion of the curve are inelastic. The elastic and inelastic sections of the demand curve are separated by a point (or set of points) of unitary elasticity.

So what does all this mean? Well, basically it means that:

if E_{D >}1, then demand is elastic

if E_D = 1, then demand is unitary elastic

if E_D < 1, then demand is inelastic

If demand is relatively responsive—in percentage terms—to changes in price, it is "elastic" (E_D is greater than one). If E_D is less than one, the amount demanded is relatively unresponsive—in percentage terms—to changes in price. In this case, demand is said to be "inelastic." When E_D is equal to one at a point (or between points) demand is said to be "unitary elastic" at that point (or between those points).

Graphically this can be shown as:
 
 
 
 
 
 
 
 
 
 

Number Two (2):

An important relationship to understand is the one between elasticity and total revenue.
(total revenue = P X Q):

If total revenue rises when P_x falls, the demand is elastic.

If total revenue falls when P_x rises, the demand is elastic.

If total revenue remains constant when P_x falls, the demand is unitary elastic.

If total revenue remains constant when P_x rises, the demand is unitary elastic.

If total revenue falls when P_x falls, the demand is inelastic.

If total revenue rises when P_x rises, the demand is inelastic.

When you think about it, all of this makes sense. If the demand for pizzas is responsive to changes in price, when the price falls, people will increase the number of pizza they demand. Therefore, although each pizza costs less, total revenue increases because people are buying so many more pizzas. On the other hand, if the demand for pizzas is not responsive to changes in price, a fall in the price of pizzas will also mean a fall in total revenue. This is because the same number of pizzas are demanded, but each one costs less.

Number Three (3):

It must be noted that economists, in addition to determining whether certain points on a demand curve are elastic, unitary elastic, or inelastic, also refer to an entire curve as being relatively elastic, unitary elastic, or relatively inelastic.   Graphs:
 
 
 
 
 
 
 
 
 
 

What we really mean to say is that the curve is elastic or inelastic over the relevant range of prices and quantities.

For example, when we observe consumers in a certain market, they usually only consume "so many" of some good per week (for example) and the prices are usually within a certain range. We refer to a range of prices and quantities which are relevant (the curve) as elastic or inelastic.

In addition to the price elasticity of demand, there are other elasticities of interest to economists. These include:

The income elasticity of demand:

E_I = % D Q_x^D
        % D Income

(Note: The sign here will tell us something about what "kind" of good X is—normal or inferior).

The cross price elasticity of demand:

E_xy = % D Q_D
          % D P_Y

(Note: The sign here will tell us something about the relationship between X and Y – substitutes or complements).

The price elasticity of supply:

E_s = % D Q_x^S
        % D P_x

(Note: Usually, the longer the period of time, the more elastic the supply).