Shadow price

A shadow price is commonly referred to as a monetary value assigned to currently unknowable or difficult-to-calculate costs. It is based on the willingness to pay principle - in the absence of market prices, the most accurate measure of the value of a good or service is what people are willing to give up in order to get it. Shadow pricing is often calculated on certain assumptions and premises. As a result, it is subjective and somewhat imprecise and inaccurate. The origin of these costs is typically due to an externalization of costs or an unwillingness to recalculate a system to account for marginal production. For example, consider a firm that already has a factory full of equipment and staff. They might estimate the shadow price for a few more units of production as simply the cost of the overtime. In this manner, some goods and services have near zero shadow prices, for example information goods. Less formally, a shadow price can be thought of as the cost of decisions made at the margin without consideration for the total cost. A shadow price is commonly referred to as a monetary value assigned to currently unknowable or difficult-to-calculate costs. It is based on the willingness to pay principle - in the absence of market prices, the most accurate measure of the value of a good or service is what people are willing to give up in order to get it. Shadow pricing is often calculated on certain assumptions and premises. As a result, it is subjective and somewhat imprecise and inaccurate. The origin of these costs is typically due to an externalization of costs or an unwillingness to recalculate a system to account for marginal production. For example, consider a firm that already has a factory full of equipment and staff. They might estimate the shadow price for a few more units of production as simply the cost of the overtime. In this manner, some goods and services have near zero shadow prices, for example information goods. Less formally, a shadow price can be thought of as the cost of decisions made at the margin without consideration for the total cost. While shadow pricing may be imprecise and inaccurate, it is still frequently employed as a useful technique and is widely used in cost-benefit analyses. For instance, before taking on a project, businesses and governments may want to weigh the costs and benefits of the project to decide whether the project is worthwhile. While tangible costs and benefits such as the cost of labor are easy to quantify, intangible costs and benefits such as the number of hours saved is much more difficult to quantify. In this case, business owners and policymakers turn to shadow pricing to determine what these intangibles are. There are usually numerous tools that help those to determine what the monetary values of these intangibles are. Some of the most common are: contingent valuation, revealed preferences, and hedonic pricing. In constrained optimization in economics, the shadow price is the change, per infinitesimal unit of the constraint, in the optimal value of the objective function of an optimization problem obtained by relaxing the constraint. If the objective function is utility, it is the marginal utility of relaxing the constraint. If the objective function is cost, it is the marginal cost of strengthening the constraint. In a business application, a shadow price is the maximum price that management is willing to pay for an extra unit of a given limited resource. For example, if a production line is already operating at its maximum 40-hour limit, the shadow price would be the maximum price the manager would be willing to pay for operating it for an additional hour, based on the benefits he would get from this change. In advance of adequate regulation or market pricing for some commodity items conservative organizations will place on their balance sheets a value they believe to be an accurate reflection of the value of those items to their operations. This is common for companies with a large carbon footprint or water footprint. As an example Microsoft has placed a $27/ton price on its carbon emissions which is then billed to the P&L of its individual business units and used to fund the company's renewable energy and efficiency programs. More formally, the shadow price is the value of the Lagrange multiplier at the optimal solution, which means that it is the infinitesimal change in the objective function arising from an infinitesimal change in the constraint. This follows from the fact that at the optimal solution the gradient of the objective function is a linear combination of the constraint function gradients with the weights equal to the Lagrange multipliers. Each constraint in an optimization problem has a shadow price or dual variable. Shadow pricing is frequently used to figure out the monetary values of intangibles and hard to quantify factors during cost-benefit analyses. In the context of public economics, shadow pricing is very useful for governments and policymakers to evaluate whether a public project should be pursued. This is because public goods are very rarely exchanged in the market, making it difficult to determine its price. To help determine the monetary value of these goods, these three tools are often used. Take the example of a government determining whether it wants to undertake a freeway project that would save commuters 500,000 hours a year, save 5 lives a year, and reduce air pollution due to decreased congestion but with a present value cost of $250 million. Contingent valuation estimates the value a person places on a good by asking him or her directly. It is essentially surveys for individuals on how much they would be willing to pay for some intangible benefits or to avoid some intangible harms. Typically, these surveys contain detailed descriptions of hypothetical public goods or services, ask respondents how much they would pay for it, and collect relevant demographic data of these respondents. Some common types of these survey questions include: open-ended, referendum-type, payment-card type, and double-bounded referendum-type. The advantage of contingent valuation is that it is sometimes the only feasible method for valuing a public good. This is especially the case when there is no obvious market price that one can use to determine the value. On the contrary, there are also many disadvantages of this method. For instance, how the survey is structured and how the questions are framed can lead to widely varying results and can induce bias into the results. Other times, the respondents may simply have no idea how much they value the public good in question.