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Meaning and Types of Elasticity of Demand

1- Elasticity of Demand
Elasticity of demand refers to the responsiveness of quantity demanded of a commodity due to a change in any determinant of demand. It is a measure of how much the quantity demanded of a commodity responds to the change in the price of the commodity, the income of the consumer, prices of related goods etc. In other words, the elasticity of demand refers to the ratio of percentage change in quantity demanded of a commodity to the percentage change in any determinant of demand. Hence, the elasticity of demand can be expressed in a symbolical form as below.

ep = % change in Qnt. demanded / % change in any determinant of demand
`%\ΔQ=\frac{(Q2-Q1)}{Q1}×100`
`%\ΔP=\frac{(P2-P1)}{P1}×100`
`\ep=\frac{%ΔQ}{%ΔP}`

Where;
%🛆Q = Percentage change in quantity demanded
%🛆P = Percentage change in price (or any other determinant of demand such as % 🛆Y, %🛆X etc.),
P1 = Initial price of goods,
P2 = New price of good,
Q1 = Initial quantity demanded of goods at the initial price,
Q2 = New quantity demanded of goods at the new price,
%🛆Y = Percentage change in income of consumers,
%🛆X = Percentage change in the price of related goods,

Remember;
Elasticity is a sensitivity or responsiveness of demand to a change in an independent variable and calculated as the percentage change in demand divided by percentage change in an independent variable.

2- Types of Elasticity
The elasticity of demand is generally divided into price elasticity, income elasticity, and cross elasticity of demand. Each of them has been explained separately.

2.1- Price Elasticity of Demand
Price elasticity of demand is a measure of how much the quantity demanded of a commodity responds to a change in the price of that commodity. In other words, it is the ratio of the percentage change in quantity demanded of a commodity to the percentage change in its price, on remaining the other things same.

Price elasticity of demand is expressed symbolically as;
ep = % change in quantity demanded/% change in price 
`%\ΔQ=\frac{(Q2-Q1)}{Q1}×100`
`%\ΔP=\frac{(P2-P1)}{P1}×100`
`\ep=\frac{%ΔQ}{%ΔP}`

Or, `\ep=-\frac{ΔQ}{ΔP}×frac{P}{Q}`
Where;
%🛆Q = Percentage change in quantity demanded
%🛆P = Percentage change in price,
P1 = Initial price of goods,
P2 = New price of good,
Q1 = Initial quantity demanded of goods at the initial price,
Q2 = New quantity demanded of goods at the new price,

Remember;
It is the result of percentage change in quantity divided by percentage change in price, or it is the responsiveness of demand to a change in the price.

Example;
Suppose quantity demanded of sugar was 200 kg. at $10 per kg. when the price goes up $12 per kg. demand for sugar decreases to 180 kg. 

Solution;
Given,    P1=$10,    P2=$12,    Q1=200,    Q2=180
             △P = P2 - P1,              △Q =  Q2 - Q1
             △P = 12 - 1o,               △Q =  180 - 200
             △P = 2,                        △Q =  -20,

As we know that,
`\ep=-\frac{ΔQ}{ΔP}×frac{P}{Q}`
`\=-\frac{−20}{2}×frac{10}{200}`
`\=10×0.05`
`\=0.5`

2.2- Types of Price Elasticity of Demand
There are five types of price elasticity of demand. They are given as below.

2.2.1- Perfectly elastic
2.2.2- Relatively elastic or more than unity
2.2.3- Unitary elastic or equal to unity
2.2.4- Relatively inelastic or less than unity
2.2.5- Perfectly inelastic

All these types of price elasticity of demand have been explained as under.

2.2.1- Perfectly elastic demand (ep = ∞)
Price elasticity of demand is said to be perfectly elastic demand when a micro or unseen change in the price of a commodity brings a greater or even sometimes the greatest change in quantity demanded of the commodity. A very small reduction in the price, can make a buyer to demand for the quantity from zero to all he wants to purchase, and an unseen rise in the price makes him to cut in demand completely.

The elasticity of demand in such a case is hyper-sensitive and elasticity of demand is infinite. Goods that have such a perfectly price elasticity of demand are rarely found in real life and so this type of elasticity has only theoretical importance.
The concept of perfectly elastic demand has also been explained in a diagrammatic form as;
The above diagram shows the nature of a perfectly elastic demand curve. In the diagram, PD is the demand curve which is horizontal to X-axis. It shows that at OP price, the quantity demanded is equal to zero but if there is an unseen fall in the price the, demand may go up to OQ or greater than that one. 

2.2.2- Relatively elastic or more than unity (ep > 1)
Price elasticity of demand is said to be relatively elastic or greater than one when the percentage change in quantity demanded of a commodity is greater than that of the percentage change in its price. For instance, if a fall in price by 50% brings an increase in demand by more than 50%, then the price elasticity of demand will be relatively elastic. The following diagram shows the relative elasticity demand.
In the above diagram, demand for goods is equal to OQ1 at OP2 unit price. With a fall in the price by 50%, there is an expansion in demand by 75%. It is seen that the percentage change in demanded is more than that of a change in the price. So the demand for goods as represented by demand curve DD is more elastic.

2.2.3- Unitary elastic or equal to unity
Price elasticity of demand is said to be unitary or equal to one when the percentage change in quantity demanded equals the percentage change in its price. For instance, if a fall or rise in price by 50% also brings an increase or decrease in demand by 50%, then the price elasticity of demand will be equal to unitary. The following diagram shows unitary elasticity demand.

In the above diagram, demand for goods is equal to OQ1 at OP2 unit price. With a fall in the price by 50%, there is an expansion in demand also by 50%. It is seen that the percentage change in demand is also equal to a change in the price. So the demand for goods as represented by demand curve DD is unitary elastic.

2.2.4- Relatively inelastic or less than unity
Price elasticity of demand is said to be relatively inelastic or less than unity when the percentage change in quantity demanded is less than the percentage change in its price. For instance, if a fall or rise in price by 50% brings about an increase or decrease in demand by less than 50%, then the price elasticity of demand will be relatively inelastic or less than unity. The following diagram shows the relative inelasticity demand.
In the above diagram, demand for goods is equal to OQ1 at OP2 unit price. With a fall in the price by 50%, there is an expansion in demand only by 40%. It is seen that the percentage change in demand is less than the change in the price. So the demand for goods as represented by demand curve DD is relatively inelastic or less than unity.

2.2.5- Perfectly inelastic
Price elasticity of demand is said to be inelastic when the quantity demanded of a commodity remains unchanged or unresponsive even if there is any change in the price. 
For instance, if a fall or rise in price by 50% does not bring any change in demand or the demand remains constant, then the price elasticity of demand will be perfectly inelastic. The nature of perfectly elastic has been shown in the following diagram.

In the above diagram, demand for goods is equal to OQ1 at OP2 unit price. With a fall in the price by 50%, there is no change in quantity demanded or demand is remaining unresponsive. So the demand for goods as represented by demand curve DQ1 is perfectly inelastic.

Table showing elasticity of various types of goods

 Types of elasticity

 Variety of goods

1. Perfectly elastic

No practical importance, rare use,

2. Relatively elastic

Luxurious goods and goods having close substitutes,

3. Unitary elastic

No specific goods,

4. Relatively inelastic

Goods of daily uses, goods having no close substitutes

5. Perfectly inelastic

Most necessary goods and service,



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