Shadow price

Shadow price is a term from the field of microeconomics and welfare economics . There are two interpretations of the shadow price which are equivalent within the framework of a general equilibrium . The shadow price of a good is either 1. the marginal contribution of this good to the utility function of a representative actor or 2. the price of this good in a perfect market.

definition

The shadow price is defined as "the price that reflects social costs and benefits". It is the result of a total analysis and not just a partial analysis of the directly affected market. So it is the price in a market in which all externalities have been internalized. In the societal optimum it corresponds to the social opportunity costs . Formally, the shadow price of a good is its marginal contribution to the utility function of a representative agent:

${\displaystyle p={\frac {\partial U}{\partial x}}}$

where the shadow price, the utility function and the amount of the divisible good. It can also be shown as the result of a Lagrange optimization - the shadow price of a good corresponds to its Lagrange multiplier . ${\displaystyle p}$ ${\displaystyle U}$ ${\displaystyle x}$

A special case of shadow price is the social discount rate . This is an intertemporal shadow price . Since Frank Ramsey, the social discount rate has usually been defined as:

${\displaystyle r=\delta +\gamma g}$

where (sometimes also ) is the discount rate, the rate of time preference , the growth rate of consumption and a weighting factor for these, the relative aversion to intertemporal inequality. ${\displaystyle r}$ ${\displaystyle \rho }$ ${\displaystyle \delta }$ ${\displaystyle g}$ ${\displaystyle \gamma }$

→ Main article : Social discount rates

detection

Shadow prices can be estimated using various valuation methods. This includes in particular methods of revealed preferences ( travel expense method , hedonic method ) and methods of expressed preferences ( contingent evaluation method , choice experiment ). In doing so, marginal willingness to pay is calculated, which is considered an approximation of shadow prices. The determination of shadow prices takes place particularly frequently in the context of environmental economic assessment .

See also

• Cost-benefit analysis

literature

• Partha Dasgupta : Human Well-Being and the Natural Environment . Oxford University Press, Oxford 2001, ISBN 0-19-924788-9 .
• Partha Dasgupta, Amartya Sen , Stephen Marglin : Guidelines for Project Evaluation . United Nations, New York 1972.

Individual evidence

1. ↑ P. Kanbur: Shadow pricing . In: The New Palgrave Dictionary of Economics . Palgrave Macmillan, Basingstoke 1998, pp. 316 .
2. ↑ Optimization , a script from the University of Cambridge , p. 29, accessed December 15, 2016.