We know that:

MR = P + ((dP / dQ) * Q)

where:

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)))

where:

(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.

*See also : pricing, cost-plus pricing, price elasticity of demand, markup, production, costs, and pricing, marketing, microeconomics*