We know that:
MR = P + ((dP / dQ) * Q)
MR = marginal revenue
P = price
(dP / dQ) = the derivative of price with respect to quantity
Q = quantity
Since we know that a profit maximizer, sets quantity at the point that marginal revenue is equal to marginal cost (MR = MC), the formula can be written as:
MC = P + ((dP / dQ) * Q)
Dividing by P and rearranging yields:
MC / P = 1 +((dP / dQ) * (Q * P))
And since (P / MC) is a form of markup, we can calculate the appropriate markup for any given market elasticity by:
(P / MC) = (1 / (1 - (1/E)))
(P / MC) = markup on marginal costs
E = price elasticity of demand
In the extreme case where elasticity is infinite:
(P / MC) = (1 / (1 - (1/999999999999999)))
(P / MC) = (1 / 1)
Price is equal to marginal cost. There is no markup.
At the other extreme, where elasticity is equal to unity:
(P /MC) = (1 / (1 - (1/1)))
(P / MC) = (1 / 0)
The markup is infinite.
Most business people do not do marginal cost calculations, but one can arrive at the same conclusion using average variable costs (AVC):
(P / AVC) = (1 / (1 - (1/E)))
Technically, AVC is a valid substitute for MC only in situations of constant returns to scale (LVC = LAC = LMC).
When business people choose the markup that they apply to costs when doing cost-plus pricing, they should be, and often are, considering the price elasticity of demand, whether consciously or not.