Cost-plus Pricing With Elasticity Considerations

**Cost-plus pricing** is a pricing strategy in which the selling price is determined by adding a specific dollar amount markup to a product's unit cost. An alternative pricing method is value-based pricing.^{[1]}

Cost-plus pricing is often used on government contracts (cost-plus contracts), and was criticized for reducing pressure on suppliers to control direct costs, indirect costs and fixed costs whether related to the production and sale of the product or service or not.

Cost breakdowns must be deliberately maintained. This information is necessary to generate accurate cost estimates.

Cost-plus pricing is especially common for utilities and single-buyer products that are manufactured to the buyer's specification such as military procurement.

The two steps in computing the price are to compute the unit cost and to add a markup. The unit cost is the total cost divided by the number of units. The total cost is the sum of fixed and variable costs. Fixed costs do not generally depend on the number of units, while variable costs do. The markup is a percentage that is expected to provide an acceptable rate of return to the manufacturer.^{[1]}

Buyers may perceive that cost-plus pricing is a reasonable approach. In some cases, the markup is mutually agreed upon by buyer and seller.

In product areas that feature relatively similar production costs, cost-plus pricing can offer competitive stability if all firms adopt cost-plus pricing.

Cost-based pricing is a way to induce a seller to accept a contract whose total costs represent a large fraction of the seller's revenues, or in which costs are uncertain at contract signing.

Cost-plus pricing is not common in markets that are (nearly) perfectly competitive, in which prices and output are driven to the point at which marginal cost equals marginal revenue. In the long run, marginal and average costs (as in cost-plus) tend to converge, reducing the difference between the two strategies. It works great when a business is in need of short-term finance.

Although this method of pricing has limited application as mentioned above, it is commonly used for the purpose of ensuring a firm is "breaking even" and not operating at a loss.^{[2]} 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

Q = quantity

P = price

(dP / dQ) = the derivative of price with respect to 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.

- Pricing
- Price elasticity of demand
- Markup (business)
- Outline of industrial organization
- Marketing
- Microeconomics

This article uses material from the Wikipedia page available here. It is released under the Creative Commons Attribution-Share-Alike License 3.0.

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