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Shadow prices and optimal cost in economic applications

Author

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  • Nikolay Khabarov
  • Alexey Smirnov
  • Michael Obersteiner
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).

Suggested Citation

  • Nikolay Khabarov & Alexey Smirnov & Michael Obersteiner, 2022. "Shadow prices and optimal cost in economic applications," Papers 2211.03591, arXiv.org, revised Nov 2022.
    • Handle: RePEc:arx:papers:2211.03591
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    References listed on IDEAS

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    1. Arslan, AslIhan, 2011. "Shadow vs. market prices in explaining land allocation: Subsistence maize cultivation in rural Mexico," Food Policy, Elsevier, vol. 36(5), pages 605-613, October.
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    3. Wen, Xiaojie & Yao, Shunbo & Sauer, Johannes, 2022. "Shadow prices and abatement cost of soil erosion in Shaanxi Province, China: Convex expectile regression approach," Ecological Economics, Elsevier, vol. 201(C).
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    5. Mariani, Francesca & Recchioni, Maria Cristina & Ciommi, Mariateresa, 2019. "Merton’s portfolio problem including market frictions: A closed-form formula supporting the shadow price approach," European Journal of Operational Research, Elsevier, vol. 275(3), pages 1178-1189.
    6. Yagi, Michiyuki & Managi, Shunsuke, 2018. "Shadow price of patent stock as knowledge stock: Time and country heterogeneity," Economic Analysis and Policy, Elsevier, vol. 60(C), pages 43-61.
    7. Wang, Zhaohua & Song, Yanwu & Shen, Zhiyang, 2022. "Global sustainability of carbon shadow pricing: The distance between observed and optimal abatement costs," Energy Economics, Elsevier, vol. 110(C).
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