There are four methods of measuring elasticity of demand. These are:-
- Total outlay or expenditure method;
- Point methods often referred to as the geometrical method;
- Arc method, and
- Mathematical method
- Total Outlay Method: One method of measuring price elasticity of demand, according to Marshall is to consider the change in the price and the consequent change in the demand for the product in relation to the total amount of money spent by the consumers on the product (or the total revenue received by the sellers). If the fall in price and the increase in demand for the product were proportionate, there would be no change in the total expenditure of the consumers. As for example-
Price per Unit | No. of Units Demanded | Total Expenditure
(Total Revenue) |
15 | 2,000 units | 30,000 |
10 | 3,000 units | 30,000 |
In this example, the proportional change in demand and proportionate change in price are equal and, therefore, there is no change in total expenditure. In this case, elasticity of demand is said to be unity or one.
Suppose, the proportionate change in demand and is more than that of the price, total expenditure of the consumers will increase. For instance-
Price per Unit | No. of Units Demanded | Total Expenditure
(Total Revenue) |
15 | 2,000 units | 30,000 |
10 | 4,000 units | 40,000 |
In this example, total expenditure by the consumers has increased because the change in demand is more than the change in price. Here the elasticity of demand is more than one or unity.
Finally, total expenditure of consumer may be less, when the price falls. This may happen when the increase in demand is proportionately less than the fall in price. For example-
Price per Unit | No. of Units Demanded | Total Expenditure
(Total Revenue) |
15 | 2,000 units | 30,000 |
10 | 2,500 units | 25,000 |
When total expenditure is less for a given fall in price, elasticity is said to be less than unity or less than one
2. Point method/geometric method
Point method is used when the demand curve is a straight line. In this method we measure elasticity at a particular point on the demand curve. This method has now become the most common method of measuring elasticity of demand. We draw a demand curve DD and draw line AB tangent to the demand curve as in the Figure. The slope of DD in AB is the same between point P and P_{1′} we find elasticity between two points P and P_{1} which we should assume to be close to each other (so close that they can be taken as one point).
The elasticity of demand can be defined as:
Now the percentage change in the quantity demanded can be presented as:
Similarly, the percentage change in price can be presented as:
The formula can be elaborated as:
After simplification we have
After re-arranging the above equation, we get
Or, ________________________________, in which
Change in quantity demanded
Change in price
P = price
Q = Quantity
3. Arc method
The point method of measuring price elasticity of demand is not very realistic since demand schedules with minute changes in prices and quantities demanded are rarely available. In reality we nay come across demand schedules that have gaps in prices as well as in quantities. The most satisfactory solution is the use of the mid points between the old and the new figures in the case of both price and quantity demanded. This method of measurement is known as arc elasticity as different from point elasticity. Arc signifies a segment or portion of a curve between two points. The formula for measuring the arc elasticity is:
; In Which
Q= Original quantity demanded
Q1= New quantity demanded
P= Original price
P1= New price
Let us take a concrete example to explain the arc method. The demand for a commodity was 2,000 units per week when the price was Rs. 5/- per unit the demand contracted to 2500 units when price was raised from Rs. 5/- to Rs. 10/- per unit.
The formula to calculate elasticity of demand by arc method is:
Substituting the figures in the above equation
-3/5
.6
Elasticity is – =. 6
Negative sign in elasticity coefficient represents the reciprocal relation between price and quantity.
4. Mathematical Method
The point elasticity can also be calculated mathematically. We know that the slope of demand curve at any point is
Expressed by the differential, . But in case in case we take the reciprocal of the
Slope to get, and multiply it by the ratio of original price to original quantity
p/q, we get , which is nothing else but the elasticity of demand
Illustration: If the demand function of a consumer is Q = 500 – 20
Found when p = 10
From Q = 500 – 20 p we find that at p =10. Q=500 –20 × 10 = 300
The elasticity of demand = = –20 ×10/300 =-2/3
= – .67
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