There is a crucial relationship between the AR, MR and elasticity of demand, which is used extensively in the theory of pricing. The relationship is expressed in the form of formula,
But, AQ is marginal revenue and SQ is average revenue corresponding to point ‘B’ at OQ level of output. Hence, equation (2.9) can be written as
The above relationship can be utilised to find out the marginal revenue corresponding to the average revenue at any given level of quantity sold, provided the price elasticity of demand is known.
The relation between AR, MR and elasticity of demand (e) can now be written as
With the help of the above formula, it is possible to find MR, given AR (price) and elasticity of demand. For example, for AR = 10 and e = 2,
Thus, for e = I, MR = 0. This is very useful relationship and should be noted carefully. Here, total revenue outlay is not affected by change in price, as discussed under ‘Total Outlay Method’ in Chapter 2 on Elasticity of Demand.
It can also be shown that at every point on the demand curve, where elasticity is greater than unity, MR is positive (but, less than AR). Further, at every point on the demand curve where elasticity is less than unity, MR is negative. This can be verified by substituting the value of elasticity in equation (14.9). An increase in the price will result in an increase and a decrease of the total revenue in these two cases respectively and vice-versa. AR, being price is always positive.
In Fig. 2.24, elasticity at middle point ‘S’ is SB/SB, i.e., 1 and MR is equal to zero. MR curve is shown cutting the X-axis at point ‘Q’. At all the points on the demand curve between ‘S’ and ‘B’ (for a lesser quantity than OQ), the numerator is greater than the denominator.
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Hence, e > 1 and MR is positive. Further, at all the points on the demand curve between ‘S’ and ‘C’ (for a greater quantity than OQ) numerator point is less than the denominator. So, e < 1 and MR is negative.
In extreme case, when the elasticity of demand is zero, AR is equal to zero while MR is equal to minus infinity and so the gap between the two is maximum. When the elasticity of
the elasticity of demand increases, MR and AR curves becomes closer and closer to each other.
The gap between them reduces to zero under perfect competition, when the demand curve is perfectly elastic.
