Question

Given that P is the unit price of a good, Ep is the price elasticity of demand, and MR is the marginal revenue. Show that the relationship that connects MR,P, and Ep is MR=P(1-1/Ep)

Answer 1

Ed = (∂Q/∂P)P/Q,

TR = P(Q)×Q,

$∂TR/∂Q = (∂P/∂Q)×Q + (∂Q/∂Q)×P$

MR = (∂P/∂Q)×Q + P,

divide and multiply by P:

MR = [(∂P/∂Q)Q/P]×P + P,

MR = [1/Ed ]×P + P,

$MR = P×(1 + 1/Ed ).$