Question

the relationship between elasticity of demand (e) average revenue (AR) and marginal revenue(MR) is shown by which of the following formula?
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Answer 1

MR = AR (1 – 1/e)

TR =Price ×Quantity

AR = TR/Q → P×Q/Q

AR = P

MR = ∆TR/∆Q

MR = d(TR)/dQ

MR = d(P×Q)/dQ

Differentiate

MR = P dQ/dQ + Q dp/dQ

MR = P + Q dp/dQ

Taking P common from both , then we have to divide second sum with p

MR = P ( 1 + Q/P dp/dQ )

Replace P by AR because both are same as proven above.

MR = AR ( 1+ Q/P dp/dQ )

- P/Q × ∆ Q/ ∆ P = elasticity [ dp/dQ = ∆p/∆Q]

MR = AR ( 1 - 1/e )