What Is Shadow Price?

Shadow price is basically a term from Economics. It is change in the objective value of an optimal solution. The optimal value is of an optimization problem that is obtained by relaxing the constraint by one unit.

Practically, the shadow price is the maximum price that a company is willing to pay for an extra unit of a given resource. Shadow price provides powerful insights into problems to the decision makers.

This can be shown with the help of an example. If a person has a constraint which limits the labor to 60 hours per week. In this case, the shadow price tells how much that person will be willing to pay for an additional hour of labor. Another example can be that the price of keeping a production line operational for an additional hour is the shadow price.

In a more formal setting, it is considered as the value of Lagrange multiplier at optimal solution. Thus the infinitesimal change in the objective function arising from an infinitesimal change in the constraint.

Shadow Price is a concept used while dealing with maximization problems having constraints. Shadow price represents the amount by which the objective function of maximization changes due to a change of one unit in the constraint. It is also very useful in cost-benefit analysis to analysis the benefit related to a cost that you will have to incur and you can see if it is worth it.

In addition, in accounting shadow price is a term that refers to the maximum amount any management would be willing to pay for extra capacity.

A mathematical programming term; it is the rate at which the objective value changes by increasing the supply of a particular resource (for example, a metabolite).