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.

The prices reflect the real values of factors of production. The shadow prices or accounting prices are used in calculating the social costs and social costs and benefits. These prices are the prices of all the inputs and outputs. These, thus, comprise shadow price, shadow wages, shadow interest, shadow foreign exchange rate and shadow product prices. There are unreal and hypothetical prices increases that these do not exist. The actual prices may however differ from these, and will be confined only to factors and items that are bought and sold in the market.

The shadow prices for the sake of project appraisal and investment have been introduced by the economists like Tinbergen, Frisch, Chenery and Kretschmer etc.Shadow prices are the prices which represent the real values of factors and prices. These prices go on changing along with change in time and profession. These prices differ from the market prices.

In a UN report the concept of shadow prices has been explained with the help of opportunity cost of these factors. It means that they represent that loss of the economy which could arise due to reduction in one unit of that factor. The factor which is scare in a country, its shadow price will be more than the market price. While the factor which is in abundance its shadow price will be less than the market price

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.