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Maximization and Optimization at the Margin

Optimizing at the margin can bring about static economic efficiency.

K. K. Fung

Static efficiency1 is maximized when the additional benefit (i.e., marginal benefit) from an action equals its additional cost (i.e., marginal cost) when marginal cost is increasing. Thus, profit is maximized when the marginal revenue from selling one more unit equals the marginal cost of producing it. Similarly, pollution is at an optimal level when the marginal benefit from an additional unit of pollution equals to its marginal damage when marginal damage is increasing.

Inefficiency results when activities are carried short of or beyond the point where marginal benefit (MB) equals to marginal cost (MC). For example, when sellers cannot charge different buyers according to their maximum willingness to pay (i.e., reservation price2), the marginal revenue (MR) to the seller is lower than the marginal benefit to the buyer, the resulting profit-maximizing output where MR = MC is therefore lower than the efficient level where MB = MC. This happens when single pricing3 is practiced in markets for differentiated products4.

Similarly, when entry into an activity cannot be limited, the marginal entrant is only interested in the average benefit and not the marginal benefit of the activity. Even though the marginal benefit may be negative, entry will continue as long as the average benefit is positive and exceeds the marginal cost of entry. The resulting level of activity is therefore much higher than the efficient level where MB = MC. This happens when an activity revolves around a resource owned in common. Excessive entry leads to what is commonly known as “tragedy of the commons”.

Notes:

  1. Efficiency resulting from doing things right rather than doing the right things.
  2. The highest price one is willing to pay rather than doing without.
  3. Charging the same price to all buyers regardless of their reservation prices in one pricing period.
  4. Mature products that are modified to gain a slight edge over similar products to escape the fate of being a commodity.

Topics:

Marginal optimization, Profit maximization

Keywords

average benefit, entry, margin, marginal benefit, marginal cost, marginal revenue, Maximization, MB, MC, MR, optimization, pollution, profit, single pricing, tragedy of the commons