Envelope Theorems in Economics: Historical Development and Modern Cost-Benefit Applications

IF 1.5 4区 经济学 Q2 ECONOMICS Frontiers of Economics in China Pub Date : 2021-12-15 DOI:10.54605/fec20210207
K. Löfgren, C. Li
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Abstract

This paper reviews some historical development and modern applications of the envelope theorems in economics from a static to a dynamic context. First, we show how the static version of the theorem surfaced in economics, which had eventually lead to the well-known Shephard’s lemma in microeconomics. Second, we present its dynamic version in terms of the classical calculus of variations and optimal control theory via the optimized Hamiltonian function. Third, we show some applications of the theorem for deriving dynamic cost-benefifit rules with special reference to environmental projects involving the green or comprehensive net national product (CNNP). Finally, we illustrate how to extend the cost-benefifit rules to a stochastic economic growth setting.
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经济学中的包络定理:历史发展与现代成本效益应用
本文回顾了包络定理在静态和动态背景下的一些历史发展和现代应用。首先,我们展示了该定理的静态版本是如何在经济学中出现的,它最终导致了微观经济学中著名的谢泼德引理。其次,利用经典变分法和最优控制理论,通过最优哈密顿函数给出了其动态版本。第三,我们展示了推导动态成本效益规则定理的一些应用,特别是涉及绿色或综合净国民生产总值(CNNP)的环境项目。最后,我们说明了如何将成本-收益规则扩展到随机经济增长设置。
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CiteScore
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0.00%
发文量
373
期刊介绍: Frontiers of Economics in China seeks to provide a forum for a broad blend of peer-reviewed academic papers of economics in order to promote communication and exchanges between economists in China and abroad. It will reflect the enormous advances that are currently being made in China in the field of economy and society. In addition, this journal also bears the mission of introducing the academic achievements on Chinese economics research to the world.
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