Cost-plus pricing with elasticity considerations
262444
94539064
2006-12-15T17:25:00Z
Robertvan1
306178
clean up using [[Project:AWB|AWB]]
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 (business)|product]] at the calculated price. To compensate for this, some economists have tried to apply the principles of [[price elasticity of demand|price elasticity]] to cost-plus pricing.
We know that:<blockquote>MR = P + ((dP / dQ) * Q)</blockquote>
where: <blockquote>
MR = marginal revenue<BR>
P = price<br>
(dP / dQ) = the derivative of price with respect to quantity<BR>
Q = quantity</blockquote>
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:<blockquote>MC = P + ((dP / dQ) * Q)</blockquote>
Dividing by P and rearranging yields:<blockquote>MC / P = 1 +((dP / dQ) * (Q / P))</blockquote>
And since (P / MC) is a form of markup, we can calculate the appropriate markup for any given market elasticity by:<blockquote>(P / MC) = (1 / (1 - (1/E)))</blockquote> where:<blockquote>(P / MC) = markup on marginal costs<BR>E = price elasticity of demand</blockquote>
In the extreme case where elasticity is infinite:<blockquote>(P / MC) = (1 / (1 - (1/999999999999999)))<BR> (P / MC) = (1 / 1)</blockquote>Price is equal to marginal cost. There is no markup.
At the other extreme, where elasticity is equal to unity:<blockquote>(P /MC) = (1 / (1 - (1/1)))<BR> (P / MC) = (1 / 0) </blockquote>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):<blockquote> (P / AVC) = (1 / (1 - (1/E)))</blockquote> 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 (business)|markup]], [[production, costs, and pricing]], [[marketing]], [[microeconomics]]''
[[Category:Pricing]]
[[Category:Marketing]]