PED means Price Elasticity of Demand

  Elastic versus Inelastic    How is Elasticity calculated?    Earth-Shattering Statement

The Law of Demand states that, for normal goods,

"As the price goes up the quantity demanded will tend to fall, and vice versa."

We are going to learn how to find out exactly by how much quantity demanded will fall if there is an increase in the price of the good, and therefore by how much the quantity demanded will rise if there is a reduction in the price of the good.

Definition

Elasticity of Demand measures the proportionate change in quantity demanded in respect of a proportionate change in price.

Elastic versus Inelastic

It is not enough for a producer to know that if the price is increased the quantity demanded will tend to fall. The producer will need to be able to establish whether, having increased the price, more revenue, less revenue or the same amount of revenue will be received. Elasticity measures this.

• Elasticity shows how responsive the total quantity demanded is in respect of a change in price.

A rubber band is elastic. If you apply pressure to it, it will stretch until a point is reached where the tension causes the rubber band to break. The rubber band can, therefore, be said to be responsive, or sensitive, to pressure. On the other hand, a shoe lace, when extended to its full length, will not yield to pressure - it is the length it is, and that is all. The shoe lace can be said to be non-responsive, or insensitive, to pressure. In economic terms we would say that the shoe lace is inelastic.

 We can now apply this rubber band / string analogy to the laws of demand.

• Inelastic: A good is said to be inelastic in demand if a 1% change in price results in a change in quantity demanded of less than 1%.
  Elastic: Likewise a good is described as being elastic in demand if a 1% change in price causes a change in quantity of more than 1%.
  Unitary: If a 1% change in price brings about a 1% change in quantity demanded, we say that we have Unitary elasticity.

  Examination tip

  A small point to note at this stage: it is the demand (or later on we will be talking about the supply) of a good which is either elastic or inelastic - it is not the good itself. Do not, for example, describe petrol as being inelastic or chocolates as being elastic. It is the demand for these goods which may be inelastic or elastic.

Time to try a little puzzle     Top of Page

How is Elasticity calculated?

Elasticity can be calculated by dividing the proportionate change in quantity demanded by the proportionate change in price. For example:

If we assume that the price has risen from 8p to 10p, the quantity demanded has fallen from 150 to 100.

Therefore a 25% increase in price has caused a 33.33% (50 � 150) decrease in demand.

• This would give us an elasticity figure of 1.33 in absolute terms. [33.33 � 25]

But, if we assume that the price has fallen from 10p to 8p (a 20% reduction), there is a 50% (50 �100) increase in total demand.

• This gives an elasticity figure of 2.5 in absolute terms. [50 � 20].

  • The phrase "Absolute Terms" means that you ignore the sign in the number, and treat the absolute value of the number

So we have two potential right answers, depending on whether the price is increasing or decreasing.

This is clearly a nonsense.

We want one correct answer on which we can rely. The supplier of goods wants to know what the demand elasticity is for his product within specified price ranges. The Minister for Finance also is keen to know what the elasticity of goods is. Both the supplier and the Minister wish to maximise revenue - the amount of money they receive.

To resolve the problem of two potential correct answers, the following formula has been devised. It calculates Arc Elasticity of Demand. An arc is a segment of the demand curve, represented by the quantities demanded at the prices P1 and P2.

where P1 is the first price, P2 is the second price, Q1 is the first quantity demanded, and Q2 is the second quantity demanded. The symbol is pronounced "delta" (Greek) and it means "change in".

Top of Page

All Numbers are Greater than, Equal to, or Less than One

This is hardly an earth-shattering statement, and is also true of any other number, of course. However, your understanding of elasticity hinges on your clinging to this statement at all times.

The arc elasticity formula above is used to calculate elasticity, and the answer to it will determine whether demand is elastic, inelastic or unitary, depending on whether the result is greater than, less than, or equal to 1, in absolute terms. "Absolute terms" just means "ignore the plus or minus sign".

When we work out the arc elasticity formula, an answer

less than 1 in absolute terms means that the demand is inelastic;

greater than 1 in absolute terms means that the demand is elastic;

equal to 1 in absolute terms denotes unitary elasticity.

Applying the Arc formula of elasticity to the example above, we get

•  = 900 � -500 = -1.8 or 1.8 in absolute terms.

This Arc formula resolves the difficulty of deciding whether the price has gone up or come down. 10 + 8 = 8 + 10. In other words, it does not matter which is P1 and which is P2 or which is Q1 and Q2 - the result will be the same.

To explain the significance of the sign. If we assume that the change in quantity is +50, it must be because the price has changed by -2. (Basic law of demand - quantity up = price down, and vice-versa). Therefore a plus by a minus will result in a minus answer.

The answer (the coefficient) is -1.8. Ignoring the sign, we get 1.8.

What does this mean? How is this figure to be interpreted?

An answer of 1.8 means that for every 1% change in price there will be a 1.8% change in demand.

• So, if the supplier increased the price by 5% a fall-off in demand of 9% (5 x 1.8) could be expected. Boxes of matches, according to the above example, would be said to have an elastic demand.
  
  It can be readily seen, therefore, that if the supplier knows that the price elasticity of demand (PED) for his goods is 1.8, total revenue will fall if the price is increased.

The next click you make might just do half your homework for you! (A double-click, however, will not do it all!!)

• Click here for an Arc Elasticity Calculator. Just type in figures for P1, P2, Q1 and Q2 and you will be given the Elasticity Figure and the change in Revenue because of the Price changes.  Enjoy!

Top of Page