The Many Definitions of Shadow Price

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The Use of Shadow Price in Economics

In the strictest sense, a shadow price is any price that is not a market price. A price that is not based on actual market exchanges must then be calculated or mathematically derived from otherwise indirect data. Shadow prices can be derived for anything from a resource to a good or service. But this is just the tip of the iceberg. While economists tend to be committed to markets as a means of valuation, the lack of a market price is not necessarily a limitation to their research.

In fact, economists recognize “goods” that carry societal value for which there are no markets to set a market price. Such goods might include the intangible like clean air. Conversely, economists also recognize that there exist goods that do have a market-traded value that is simply not a good representation of the good’s true societal value. For example, electricity produced from coal carries a market price that does not consider the impact or “social cost” of coal burning on the environment. It is in these scenarios that economists find it difficult to work, which is why the discipline relies on the calculation of shadow prices to give a “price-like” value to otherwise unpriced resources.

The Many Definitions of Shadow Price

While the most basic understanding of the term shadow price relates simply to the lack of a market price for some resource, good, or service, the meanings of the term as derived from its real world uses relay a more complicated story.

 

In the world of investments, shadow price can refer to the actual market values of a money market fund, which essentially refers to securities that are accounted for based on amortized cost rather than a value assigned by the market. This definition carries less weight in the world of economics.

More relevant to the study of economics, another definition of shadow price denotes it as a proxy value of a good or intangible asset that is most often defined by what must be given up to gain an extra unit of the good or asset.

Last, but not least, shadow prices can also be utilized to derive an inclusive value of the impact of a project, whether it be a benefit or costs, using stated preferences, making the process an extremely subjective one.

In the study of economics, shadow prices are most often used in cost-benefit analyses in which some elements or variables cannot be otherwise quantified by a market price. In order to fully analyze the situation, each variable must be assigned a value, but it is important to note that the calculation of shadow prices in this context is an inexact science.

Technical Explanations of Shadow Price in Economics

In the context of a maximization problem with a constraint (or constrained optimization), the shadow price on the constraint is the amount that the objective function of the maximization would increase by if the constraint were relaxed by one unit. In other words, the shadow price is the marginal utility of relaxing the constant or conversely, the marginal cost of strengthening the constraint. In its most formal mathematical optimization setting, the shadow price is the value of a Lagrange multiplier at the optimal solution.