Cost-plus Pricing - Cost-plus Pricing and Economic Theory

Cost-plus Pricing and Economic Theory

Cost-plus pricing might appear to be inconsistent with the economic theory of profit maximization. Analysis based on marginal cost equals marginal revenue decision rule may appear to have become irrelevant due to the wide use of cost-plus pricing.However, this conflict is more apparent than real. A comparison of the two approaches to pricing starts with a consideration of costs. Cost-plus pricing is based on average costs and not marginal costs.However, in economic theory long-run marginal and average costs are not very different. Thus, it can be said safely that usage of average costs for pricing may be considered a reasonable approximation of marginal cost decision making.

Second step in comparison involves the target rate of return and the resulting markup. Determination of the target rate of return depends on certain factors. Basically, the decision involves management's perception of demand elasticity and competitive conditions. This can be explained with an example,consider grocery stores.Profits are held down to the intense competition that exists among these firms. Due to this intense competition the markup for most food items is only about 12 percent over cost. If the markup over cost is based on demand conditions,cost-plus pricing may not be inconsistent with profit maximization. This can be shown mathematically.

Marginal revenue is the derivative of total revenue with respect to quantity. Thus

MR = d (TR)/ dQ = d (PQ)/ dQ = P + dP*Q /dQ

(P + dP *Q /dQ) can also be written as P (1 + dPQ /dQP) .Here, (dP /dQ) (Q /P) is 1/E_P, where E_P is price elasticity of demand. Thus

MR = P (1 + 1/E_P ) (equation 1)

In order to maximize profit MR should be equal to MC.To simplify the assumption let MC=AC. Thus the profit maximizing price is the solution to

P (1 + 1/E_P) = AC

which can be written as

P (E_P + 1 /E_P) = AC

Solving for P yields

P = AC (E_P /E_P + 1) (equation 2)

Equation 2 can be interpreted as a cost-plus pricing or markup pricing scheme.That is the price of the product is based on markup over average costs. (E_P + 1 /E_P) which is the markup is a function of the price elasticity of demand. From the equation we can see that the markup and the price elasticity of demand are inversely related, as the demand becomes more elastic the markup becomes smaller.