Cost-plus pricing with elasticity considerations

One of the most common pricing methods used by firms is cost-plus pricing.
In spite of its ubiquity, economists rightly point out that it has serious
methodological flaws. It takes no account of demand. There is no way of
determining if potential customers will purchase the product at the
calculated price. To compensate for this, some economists have tried to
apply the principles of price elasticity to cost-plus pricing.

We know that:
MR = P + ((dP / dQ) * Q)
where:
تتتتتتMR = marginal revenue
تتتتتتP = price
تتتتتت(dP / dQ) = the derivative of price with respect to quantity
تتتتتتQ = 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:
تتتتتت(P / MC) = markup on marginal costs
تتتتتتE = 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.

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