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

1) In situation 1 in the above table shows that when own price of the commodity is Rs.2, total expenditure is Rs.8.

When the price falls to Rs.1, the total expenditure does not change.
This is Unitary Elastic demand.
As shown in the graph below :

unitary elastic

The demand curve D₃D₃ is a rectangular hyperbola with rectangles OA and OB being equal in areas, showing that a change in price of the commodity does not bring about a change in total expenditure.

2) In situation 2 in the above table shows that when own price of the commodity is Rs.2, total expenditure is Rs.8.
When the price falls to Rs.1, the total expenditure rises to Rs.10.This is Elastic demand.
As shown in the graph below :

elastic demand

The demand curve D₁D₁ is drawn according to the above table. As price falls, total expenditure rises, area of rectangle OB is greater than the area of rectangle OA.

Thus, demand curve is elastic between A and B.

3) In situation 3 in the above table shows that when own price of the commodity is Rs.2, total expenditure is Rs.6.
When the price falls to Rs.1, the total expenditure falls to Rs.4.This is inelastic demand.
As shown in the graph below :

inelastic demand

The demand curve D₂D₂ is inelastic between points A and B as the area of rectangle OB is smaller than the area of rectangle OA.

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

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

It should be noted that total expenditure method of computing elasticity of demand enables us to know only whether price elasticity of demand is equal to one, greater than one, or less than one.
But we cannot get the exact values of the price elasticity.
Thus, total expenditure method gives only a general measure rather than precise and exact measure of price elasticity of demand.