Measurement of Price Elasticity of Demand:
In order to compare elasticity of demand of different goods it is important to measure elasticity of demand. The measurement of elasticity of demand can be looked at two point of view –
1. Point elasticity
2. Arc elasticity
1. Point Elasticity :
When price elasticity of demand is measured at a particular point on a demand curve, it is called point elasticity.
In the given figure when we want to measure the elasticity of demand at point R on the demand curve, we call it point elasticity. So we can say that, when the price elasticity is measured for a very small changes in price and quantity, it is called point elasticity. The method used for measuring point elasticity is called ‘point Method’.
2. Arc elasticity :
When elasticity of demand is measured over a finite range or arc of a demand curve, it is called arc elasticity of demand.
When changes in price and quantity are significantly large, they show a movement from one point on the demand curve to another point, making an arc. Thus, arc elasticity is a measure of the elasticity between two points on the demand curve.
In the above figure, the measure of elasticity between point R and R1, on the demand curve DD is the measure of arc elasticity.
The arc elasticity can be measured by ‘Percentage Method’ and ‘Total Expenditure Method’.
This way there are three methods of measurement of price elasticity of demand.
1. Percentage or Proportionate Method
2. Total Expenditure Method
3. Point Method or Geometric Method
1. Percentage or Proportionate Method:
Price elasticity of demand is measured by the ratio of percentage change in the quantity demanded to a percentage change in the price of the commodity. Thus,
ep = percentage change in quantity demanded ÷ percentage change in Price
ep = (change in quantity demanded × 100 / initial quantity) ÷ (change in price ×100 / initial price)
= (∆Q ×100 / Q) ÷ (∆P ×100 / P)
= (∆Q / Q) ÷ (∆P / P)
= (∆Q / Q) × (P / ∆P )
ep =( ∆Q / ∆P) × (P / Q)
Where,
ep = Price elasticity of demand
∆Q = change in quantity demanded
∆P = change in Price
Q = initial quantity
P = initial Price
Features of Percentage Method:
When calculating the price elasticity of demand using this formula, it should always be kept in mind that price elasticity of demand is a negative number because of the negative sloping of demand curve. Due to negative or downward sloping of demand curve the price and quantity demanded change in opposite directions from each other. One change will be positive and the other negative.
Hence the computation of elasticity of demand will always result in a negative value. Thus, while calculating price elasticity of demand by percentage method, common practice is to ignore the negative signs i. e. we should take only absolute value not their signs.
Another important feature of the percentage method is that it does not depend on the units of measurement of quantity of demand – whether Kg of rice or litres of petrol – or the measure of price – whether in Indian rupees or in US dollars. It is a unit free measure because it uses the percentage changes in prices and the quantity demanded. Therefore we can compare the price sensitivity of demand for different goods regardless of the units for measuring either of price or quantity.
Advantages of Percentage Method :
1. The percentage method gives more precise and exact measure of elasticity.
2. Larger value for price elasticity of demand indicates that demand is more sensitive to changes in price.
3. Smaller value for price elasticity of demand indicates that demand is less sensitive to price changes.
Limitations of Percentage Method :
A major problem related to the percentage method is that the percentage change depends on the base or starting point. Here the question arise – should we take the initial quantity/ price or the new quantity/ price as the starting point?
2. Total Expenditure Method:
Another method of measuring the price elasticity of demand suggested by Marshall is the ‘Total Expenditure Method’ .
Total expenditure is the expenditure incurred by households on the purchase of a commodity. It is the product of the price (P) of a commodity and the quantity demanded(Q) at that price, i.e. ,
T E = P × Q
Where TE = Total Expenditure
P = price of the commodity
Q = quantity demanded of the commodity
According to the Total expenditure method –
“Elasticity of demand can be measured by considering the change in total expenditure incurred on a commodity as a result of change in price of the commodity”.
In this method, we compare the total expenditure incurred on a commodity before and after the price change and hence we can know the price elasticity of demand.
By using thus method we can categorise three types of elasticities –
1. Elastic Demand
2. Inelastic Demand
3. Unitary Elastic Demand
1. Elastic Demand:
When a fall in the price of the commodity result in increase in total expenditure and a rise in the price leads to decrease in total expenditure, the demand is said to be elastic and elasticity of demand (ep) will be greater than one (ep > 1 ).
When total expenditure moves in the opposite direction to the change in price, the elasticity of demand is greater than one.
In this type of demand the change in quantity demanded is more than the change in price.
Demand schedule for elastic demand:
|
Price (Rs) |
Quantity (Units) |
Total Expenditure |
ep |
|
60 |
10 |
600 |
ep >1 |
|
50 |
13 |
650 |
The demand schedule shows that when price falls from Rs 60 to Rs 50 , total expenditure rise from Rs 600 to Rs 650.
Demand curve for Elastic Demand
In the given figure, the total expenditure corresponding to price Rs 60 is represented by rectangle OA, and total expenditure corresponding to price Rs 50 is represented by rectangle OB.
As the area of rectangle OB is greater than area of rectangle OA
Area of OB > Area of OA
This clearly indicates that the increase in total expenditure with the fall in price. This demand curve D1D1, is elastic between A and B.
2. Inelastic Demand:
When a fall in the price of a commodity reduces total expenditure and a rise in its price increases total expenditure, price elasticity of demand will be less than one (ep), and the demand is said to be inelastic demand.
In this type of demand, total expenditure moves in the same direction as change in price. In this case the change is price is more than the change in quantity therefore, the price elasticity of demand is less than one. This type of demand is illustrated by the given figure.
Demand Schedule for Inelastic Demand:
|
Price (Rs) |
Quantity(units) |
Total expenditure |
ep |
|
60 |
10 |
600 |
ep < 1 |
|
50 |
11 |
550 |
Demand Curve for Inelastic Demand:
In the given demand schedule the demand is clearly inelastic as the price fall from Rs 60 to Rs 50, the total expenditure also falls from Rs 600 to Rs 550.
Similarly, in the given graph, area of rectangle OA represents the total expenditure corresponding to price Rs 60, while area of rectangle OB represents the total expenditure corresponding to the price Rs 50.
Since the area of rectangle OA is greater than the area of rectangle OB.
Area of rectangle OA > Area of rectangle OB
This shows the fall in total expenditure with the fall in price. This the demand curve D2D2 is inelastic.
3. Unitary elastic demand :
When total expenditure does not change with the change in the price of the commodity, the demand is said to be unitary elastic demand.
In this case the total expenditure remains constant with the rise and fall in the price.
The elasticity of demand will be equal to one. Thus it is unitary elastic demand.
Demand schedule for Unitary Elastic Demand:
|
Price (Rs) |
Quantity(units) |
Total expenditure |
ep |
|
60 |
10 |
600 |
ep=1 |
|
50 |
12 |
600 |
In the given schedule, the demand is unitary elastic as with fall in price from Rs 60 to Rs 50, total expenditure remains unchanged at Rs 600.
Demand Curve for Unitary Elastic Demand:
Similarly, in the given figure, the area of rectangle OA is same as the area of rectangle OB which shows that a change in the price of the commodity does not bring about a change in total expenditure.
Area of rectangle OA = Area of rectangle OB
This shows that the demand curve D3D3 is unitary elastic.
Types of Demand in Total Expenditure Method :
|
SN |
Type of Elasticity of Demand |
Numeric value |
Change in |
|
|
Fall in Price |
Rise in Price |
|||
|
1. |
Elastic |
ep>1 |
Total |
Total |
|
2. |
Inelastic |
ep < 1 |
Total |
Total |
|
3. |
Unitary Elastic |
ep = 1 |
Total |
Total |
3. Point Method (Geometric method) :
Point method is used to measure the elasticity of demand at any particular point on a demand curve.
According to this method, price elasticity of demand at any point on the demand curve can be measured by dividing the line segment below the point on the demand curve by the line segment above the point on the demand curve.
ep = ( line segment below the point on the demand curve)/ ( line segment above the point on demand curve)
1. On a straight line demand curve:
In the given figure demand curve AB is a straight line demand curve and is intercepted by both the axes. If we want to measure the price elasticity of demand at point R, where the lower line segment is RB and upper line segment is RA .
Therefore,
ep at point R = (Lower line segment) / (Upper line segment)
ep = RB / RA
Since, RB > RA thus, ep > 1
Therefore the demand is elastic demand.
Similarly, if we want to measure the elasticity of demand at any other point on the demand curve,K.
ep at K = KB / KA
Since KB < KA
Therefore, ep < 1
Thus, the demand is inelastic in nature.
Measuring Price Elasticity of Demand at different points on a straight line demand curve:
Point method can be used to measure the elasticity of demand at different points on a straight line demand curve AB, which is intercepted by both the axes.
We find, that the price elasticity of demand at different points of demand curve is different.
In the given figure, AB is a straight line demand curve, with point A, as its Y – intercepts, B as its X intercept and D as its mid – point.
1. At point A :
At point A, the demand curve touches the vertical axis (Y).
ep at A = (line segment below A) / (line segment above A)
Since the line segment above A = 0
ep at A = AB / 0
ep at A = infinity
Therefore the demand is perfectly elastic .
2. At any point E above the mid point:
Since point E, is above the mid point
ep at E = (line segment below E) / (line segment above E)
ep at E = BE / AE
Since , BE > AE
Therefore, ep > 1
Demand is said to be elastic demand.
3. At the mid point D :
Since the point D is mid point the line segment above and below D is equal
Or BD = DA
ep = 1
The demand is unitary elastic demand.
4. At any point below the mid point:
If we want to measure the elasticity at any point below the mid point say C, where the lower line segment is smaller than upper line segment
Thus, BC < CA
ep at C = BC / CA
ep < 1
The demand is inelastic.
5. At point B:
At point B where the demand curve touches the horizontal axis (x) the lower line segment is zero.
ep at B = 0 / AB
ep at B = 0
Therefore the demand is perfectly inelastic.
So it can be concluded that, as we travel downward from left to right in a straight line demand curve, the price elasticity of demand varies from infinity at Y – intercept to zero at X – intercept, being greater than unity at any point above the mid point, equal to unitary at mid point and less than unity at any point below the mid point.
So the straight line demand curve is more elastic towards its left hand end and less elastic towards its right hand end.
2. On the non – linear demand Curve:
In addition to the straight line demand curve. Point method can also be used to measure the elasticity at any point on a curved demand curve.
In order to calculate the price elasticity of demand at any point on curved demand curve, we have to draw a tangent to the demand curve through the chosen point and measure the elasticity of the tangent at this point as the ratio of lower line segment to the upper line segment.
In the given figure curve DD, is a curved demand curve. If we want to measure the elasticity at point R on the demand curve DD, we have to draw a line AB, tangent to the demand curve at point R. Since the slope of demand curve at R is equal to the slope of the tangent at that point.
The price elasticity of the demand curve DD at R will be equal to the elasticity of the tangent AB at point R.
Thus,
ep at R = (lower line segment)/ (upper line segment)
ep at R = BR / RA