Shadow prices and optimal cost in economic applications

Khabarov, N. ORCID: https://orcid.org/0000-0001-5372-4668, Smirnov, A. ORCID: https://orcid.org/0000-0003-1765-0782, & Obersteiner, M. ORCID: https://orcid.org/0000-0001-6981-2769 (2022). Shadow prices and optimal cost in economic applications. arXiv (Submitted)

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Abstract

Shadow prices are well understood and are widely used in economic applications. However, there are limits to where shadow prices can be applied assuming their natural interpretation and the fact that they reflect the first order optimality conditions (FOC). In this paper, we present a simple ad-hoc example demonstrating that marginal cost associated with exercising an optimal control may exceed the respective cost estimated from a ratio of shadow prices. Moreover, such cost estimation through shadow prices is arbitrary and depends on a particular (mathematically equivalent) formulation of the optimization problem. These facts render a ratio of shadow prices irrelevant to estimation of optimal marginal cost. The provided illustrative optimization problem links to a similar approach of calculating social cost of carbon (SCC) in the widely used dynamic integrated model of climate and the economy (DICE).

Item Type:	Article
Research Programs:	Advancing Systems Analysis (ASA) Advancing Systems Analysis (ASA) > Exploratory Modeling of Human-natural Systems (EM) Biodiversity and Natural Resources (BNR) Biodiversity and Natural Resources (BNR) > Agriculture, Forestry, and Ecosystem Services (AFE)
Depositing User:	Luke Kirwan
Date Deposited:	29 Jan 2024 12:03
Last Modified:	29 Jan 2024 12:03
URI:	https://pure.iiasa.ac.at/19441

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