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# 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:
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.