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The following are the principal methods of measuring elasticity of demand:- 1. Total Outlay Method 2. Point Method 3. Arc Method. Managerial Economics, Pricing, Functions, Demand, Elasticity of Demand
1. The Total Outlay Method:
Marshall evolved the total outlay, total revenue, or total expenditure method as a measure of elasticity. By comparing the total expenditure of a purchaser both before and after the change in price, it can be known whether his demand for a good is elastic, unity, or less elastic. Total outlay is price multiplied by the quantity of a good purchased –
Total Outlay = Price x Quantity Demanded
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In this method, we compare the total outlay of an individual before and after the changes in price. The price elasticity of demand is generally explained in three ways, viz., equal to unity, greater than unity, and less than unity.
If the elasticity of demand in between two prices is equal to unity, then with a change in price the total expenditure will remain the same. If the elasticity of demand in between two prices is greater than unity, then with a fall in price the total expenditure increases and with a rise in price the total outlay decreases. If the elasticity of demand in between two prices is less than unity, then with a fall in price the total outlay decreases and with a rise in price the total outlay increases.
The above three cases will be explained with the help of an imaginary demand schedule.
If the elasticity of demand in between two prices is equal to unity, then with a change in price, i.e., from Rs.1.50 to Rs.1.00, the total expenditure Rs.3.00 will remain the same. If the elasticity of demand in between two prices is greater than unity, then with a fall in price, the total expenditure rises from Rs.3.20 to Rs.3.50 and with a rise in price the total outlay decreases from Rs.3.50 to Rs.3.20.
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If the elasticity of demand in between two prices is less than unity, then with a fall in price the total outlay decreases from Rs.3.00 to Rs.2.80 and with a rise in price the total outlay increases from Rs.2.80 to Rs.3.00.
Based on the total expenditure of an individual on the product, the company should know the elasticity of demand and accordingly establish the price of the product.
2. The Point Method:
Prof. Marshall devised a geometrical method for measuring elasticity at a point on the demand curve. When the price elasticity of demand is measured at a single point on the same demand curve, it is known as point elasticity of demand. We assume that the demand curve or line is to be intercepted by both the axes and measure the price elasticity of demand at a single point on the demand curve.
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The formula for calculating the price elasticity of demand under this method is as follows –
Let us substitute all the values in the following equation —
With the help of the above formula, we find out various elasticities of demand at various points on the same demand curve or line. The following Fig. 2.7 shows various elasticities of demand at various points on the same demand curve.
Figure 2.7 shows the different elasticities of demand on AB demand curve/line. Suppose the length of the AB demand line is 2 m in length. The point M on the demand curve happens to be the centre point. Then —
It is understood that at a higher point, the elasticity of demand is greater than 1 and at a lower point, the elasticity of demand is less than 1 and at the centre point it is equal to 1.
Even if the demand curve is not a straight line, the same formula will apply to calculate the elasticity of demand.
In Fig. 2.8, DD is the demand curve, and it is not the straight line. There are two points on the demand curve, viz., P and P1. Let us draw a tangent AB through the point P and another tangent A1 B1 through the point P1. At a higher point P, the elasticity of demand is greater than 1 and at a lower point, the elasticity of demand is less than 1.
Even though the two demand lines are having different slopes, they have the same elasticity of demand at a single price.
There are two demand lines AB and AS in Fig. 2.9. Let us draw a horizontal straight line cutting AB line at point K and AS at point T. In the triangle AOB, the price elasticity of demand is –
Even though the two demand lines are having different slopes, the price elasticity will be the same at OP price.
3. The Arc Method:
We have studied the measurement of elasticity at a point on a demand curve, but when elasticity is measured between two points on the same demand curve, it is known as arc elasticity. In the words of Baumol, “Arc elasticity is a measure of the average responsiveness to price change exhibited by a demand curve over some finite stretch of the curve.”
Suppose in Fig. 2.10, the points P and P1 are lying on the DD curve. When elasticity of demand is measured in between two points at two price levels on the same demand curve or line, it is known as arc elasticity. The formula for calculating elasticity of demand under this method is as follows –
Where Q1 and P1 are initial price and quantity, Q2 and P2 are price and quantity after change.
The closer the points P and P1 are, the more accurate is the measure of elasticity on the basis of the above formula. The arc elasticity, in the fact, is the elasticity of the mid-point between P and P1 on the demand curve DD. If there is no difference between the two points and they merge into each other, arc “elasticity” becomes point elasticity.
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