The most significant uses of the price elasticity of demand, used specifically in business decision-making. It refer to the relationship between price elasticity and the marginal change in the total revenue of the firm planning to change the price of its product. The relationship between marginal revenue (MR) and the price elasticity can be derived as follows.
Let's suppose that a given output, Q, is being sold at a price P, so that total revenue, TR, equals P times Q, which is
TR = P X Q ...................Eq. I
Because P and Q in eq. I are inversely related, a question arises, whether a change in P will decrease or increase or leave the TR unaffected. It depends on whether MR is greater than or less than or equal to zero, i.e., whether
MR > 0, MR < 0, or MR = 0
Marginal revenue, (MR) can be attained by differentiating TR = PQ with respect to P as illustrated below.
MR = δ (PQ) / δQ
= {P + δQ/ δQ} + {Q+ (δP/ δQ)}
=P+ {Q + (δP/ δQ)}
MR = P [1+ (Q/P). δP/ δQ]
Note that Q/P. δP/ δQ is the reciprocal of the elasticity that equals
(-P/Q). (δQ/ δP)
Thus, Q/P. δP/ δQ = -1/e
By substituting -1/e for Q/P. δP/ δQ in eq.1, we get
MR= P+ {1- (1/e)} ....... Eq.2
Equation 2 gives the relationship between price-elasticity (e) and MR.