Envelope theo­rems in economics: Historical development and modern cost-benefit applications

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-benefit rules with special reference to environmental projects involving the green or comprehensive net national product(CNNP). Finally, we illustrate how to extend the cost-benefit rules to a stochastic economic growth setting.

Keywords: cost-benefit analysis, dynamic optimization, economic history, envelope theorems, environmental economics

Löfgren, K.G. and C.Z. Li. 2021. Envelope theo­rems in economics: Historical development and modern cost-benefit applications. Frontiers of Economics in China 16: 377-404.