A shadow price is the monetary value assigned to an abstract or intangible commodity which is not traded in the marketplace. This often takes the form of an externality. Shadow prices are also known as the recalculation of known market prices in order to account for the presence of distortionary market instruments (e.g. quotas, tariffs, taxes or subsidies). Shadow prices are the real economic prices given to goods and services after they have been appropriately adjusted by removing distortionary market instruments and incorporating the societal impact of the respective good or service. A shadow price is often calculated based on a group of assumptions and estimates because it lacks reliable data, so it is subjective and somewhat inaccurate.
The need for shadow prices arises as a result of “externalities” and the presence of distortionary market instruments. An externality is defined as a cost or benefit incurred by a third party as a result of production or consumption of a good or services. Where the external effect is not being accounted for in the final cost-benefit analysis of its production. These inaccuracies and skewed results produce an imperfect market mechanism which inefficiently allocates resources.
Market distortion happen when the market is not behaving as it would in a perfect competition due to interventions by governments, companies, and other economic agents. Specifically, the presence of a monopoly or monopsony, in which firms do not behave in a perfect competition, government intervention through taxes and subsidies, public goods, information asymmetric, and restrictions on labour markets are distortionary effects on the market.
Shadow prices are often utilised in cost-benefit analyses by economic and financial analysts when evaluating the merits of public policy & government projects, when externalities or distortionary market instruments are present. The utilisation of shadow prices in these types of public policy decisions is extremely important given the societal impacts of those decisions.
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The Hamiltonian is a function used to solve a problem of optimal control for a dynamical system. It can be understood as an instantaneous increment of the Lagrangian expression of the problem that is to be optimized over a certain time period. Inspired by—but distinct from—the Hamiltonian of classical mechanics, the Hamiltonian of optimal control theory was developed by Lev Pontryagin as part of his maximum principle. Pontryagin proved that a necessary condition for solving the optimal control problem is that the control should be chosen so as to optimize the Hamiltonian.
Pontryagin's maximum principle is used in optimal control theory to find the best possible control for taking a dynamical system from one state to another, especially in the presence of constraints for the state or input controls. It states that it is necessary for any optimal control along with the optimal state trajectory to solve the so-called Hamiltonian system, which is a two-point boundary value problem, plus a maximum condition of the control Hamiltonian.
The costate equation is related to the state equation used in optimal control. It is also referred to as auxiliary, adjoint, influence, or multiplier equation. It is stated as a vector of first order differential equations where the right-hand side is the vector of partial derivatives of the negative of the Hamiltonian with respect to the state variables. The costate variables can be interpreted as Lagrange multipliers associated with the state equations.
We propose a framework to find optimal price-based policies to regulate markets characterized by oligopolistic competition and in which consumers make a discrete choice among a finite set of alternatives. The framework accommodates general discrete choice ...
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