Geometric Method for calculating Price Elasticity

(Linear Demand Curve)

Geometric method measures price elasticity of demand at different points on the demand curve.
It is also called ‘point method’ of measuring elasticity of demand.
We would be using linear demand curve, which is a straight line demand curve.
As shown in the below graph :

linear demand curve

MN is a straight line demand curve sloping downwards.

P is a mid point on the demand curve.
It divides the demand curve into two equal segments,
lower segment (PN) and upper segment (PM)
PN = Line segment below the point on  the demand curve

PM =  Line segment above the point on the demand curve

e_p(at P)  = PN / PM

Total expenditure method for calculating Price Elasticity

Prof. Marshall works out a relationship between price elasticity of demand and total expenditure.

He estimates the degree of price elasticity of demand depending on the change in total expenditure following a change in own price of the commodity.

He observes three different situations :
1) If the rise or fall in own price of a commodity causes no change in total expenditure on the commodity,

then elasticity of demand is unitary i.e. unitary elastic demand.

2) If  a fall in own price of the commodity causes a rise in total expenditure and a rise in price causes a fall in total expenditure on the commodity,
then elasticity of demand is greater than unitary i.e. elastic demand.

3) If  a fall in own price of the commodity causes a fall in total expenditure and a rise in price causes a rise in total expenditure on the commodity,
then elasticity of demand is less than unitary i.e. inelastic demand.

Relationship between price elasticity of demand and Total expenditure -
When price of the commodity falls

situation	Price (Rs.) (falls)	Quantity (kg)	Total expenditure (Rs)	Change in Total expenditure	Elasticity Of demand
1	2 1	4 8	8 8	Constant	ep = 1, unitary elastic
2	2 1	4 10	8 10	Increases	ep > 1, elastic
3	2 1	3 4	6 4	decreases	ep < 1, inelastic

Factors affecting Price Elasticity of Demand

It is important to know that demand for some goods is more elastic (e_p>1, percentage change in quantity demanded is more than percentage change in price) while for others it is less elastic (e_p<1, percentage change in quantity demanded is less than percentage change in price), depending on many factors.

Some of the important determinants of price elasticity of demand are:

1) Nature of commodity :

Nature of commodity refers to whether the commodity is ‘necessary’, ‘luxury’ or ‘comfort’ in nature.

‘Necessary’ commodities, such as food items are essential for existence, these goods have to be purchased in fixed quantities, whether the price is high or low.

A change in the price of the necessities may have a small impact on the demand i.e. have inelastic demand (e_p<1).

‘luxury’ or ‘comfort’ commodities, such as television, a.c, furniture etc are not necessary for existence and their consumption can be postponed. Thus their demand changes by larger amount due to a small change in price i.e. have elastic demand (e_p>1).

The demand for necessities is inelastic and the demand for luxuries and comforts is elastic.

Price Elasticity of Demand

By studying Law of demand, we know that demand of a commodity is greatly influenced by the its price.
We learnt that increase in the price of the commodity causes contraction in demand, while decrease in price causes extension in demand.

Thus, law of demand makes a qualitative statement only. It does not tell us about the magnitute/degree of change in quantity demanded in response to change in the price.
It only tells about the direction of change.

Degree of change in quantity demanded in response to change in the price is the subject matter of Elasticity of Demand. 
It makes a Quantitative statement.It tells us about the extent to which the demand responds to change in price.

While measuring the degree of change in demand we always consider percentage values, not the absolute values.

Price elasticity of demand is defined as a measurement of percentage in quantity demanded in response to a given change in own price of the commodity.

e_p = Percentage change in quantity demanded

        Percentage change in price

(Where e_p refers to price elasticity of demand)

Kinds of Price Elasticity of Demand :

There are five different kinds of price elasticity of Demand:

1) Perfectly Elastic Demand : 

A Perfectly Elastic Demand refers to a situation when demand is infinite at the prevailing price.
It is a situation where the slightest rise in the price causes the quantity demanded  of the commodity to fall to zero.

As shown in the figure below. DD is the perfectly elastic demand curve, parallel to X axis.

elastic demand

It shows that at Price Rs.4, quantity demanded may be 10,20, 30 or more units i.e. demand for the commodity is infinite. But if the price increased from Rs.4, the demand falls to zero.And at price lower than Rs.4 an infinitely large quantity is demanded.Cases of perfectly elastic demand curve is very rare.

  e_p = ∞

2) Perfectly Inelastic Demand : 

A Perfectly Inelastic Demand refers to a situation when change in price causes no change in the quantity demanded.The elasticity of demand is zero.

As shown in the figure below. DD is the perfectly inelastic demand curve, parallel to Y axis.

inelastic demand

When price is Rs.2, demand is for 4 units. When the price rises to Rs. 4 or Rs.6 quantity demanded remains constant at 4 units.Hence, elasticity of demand is zero. Cases of perfectly elastic demand curve are also rare.

e_p = 0