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 wants to know how "price elastic" the demand for apples is, all he really wants to know is how the demand for apples "responds" to a change in the price of apples.

The Price Elasticity of Demand:

Concept:

The demand function can be written as Q_x^D = f (P_x). This simply means that the quantity demanded of 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 = % Q_x^D   
      % P_x             

Where (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.

BUT WAIT!! Because of the law of demand, the price elasticity of demand coefficient will always be negative.  When the price goes up, quantity demanded goes down and vice versa.  However, it is always read as the absolute value -- as positive.  Don't forget this.  Always drop the negative sign when reading the elasticity coefficient.

Economists define the elasticity coefficient such that:

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

if E_D = 1, then demand is unit 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).

Example:  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 = % Q_x^D   = -5 = -.5
      % P_x        10   

So what exactly does the elasticity coefficient tell us? 

**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.

What About How the Demand Curve Looks?

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 a range of prices along an individual's curve as being relatively elastic, unitary elastic, or relatively inelastic -- or sometimes perfectly inelastic or perfectly elastic.   Graphs:
 
 
 
 
 
 
 
 
 
 

What we really mean to say is that the curve is elastic or inelastic over the relevant range of prices and quantities.  Market demand curves are not completely inelastic (or elastic, of course) over the entire price range.

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.

Influences on the Price Elasticity of Demand:

    1.  Time.

    2.  The proportion of one's budget spent on the good.

    *3.  Availability and closeness of known substitutes.

An Important Application:  Pricing Your Good

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

Total Revenue = Price x Quantity

Total Revenue - Total Costs = Profit

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 (or close to the same) number of pizzas are demanded, but each one is sold for a lower price.

 Note:  Short-run is less than a year.  Long-run is more than a year.

Source:  http://www.mackinac.org/article.aspx?ID=1247

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

The Income Elasticity of Demand:

Concept:

E_I = % Q_x^D
     % Income

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

Otherwise the elasticity is read the same as always - it is always positive.

Economists have estimated the following income elasticities:

The Cross Price Elasticity of Demand:

Concept:

E_xy =  % Q_x^D
        % P_Y

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

Otherwise the elasticity is read the same as always - it is always positive.

Economists have estimated the following cross-price elasticities.  Note that the same cross-price elasticity does not come about with the same two goods  - it depends upon how it is calculated.  Does this make sense?