Karl-Gustaf Löfgrena, Chuan-Zhong Lib
Author information
a School of Economics, Umeå University, Umeå 901 87, Sweden
b Department of Economics, Uppsala University, Uppsala 751 05, and The Beijer Institute, Royal Swedish Academy of Sciences, Stockholm 104 05, Sweden
E-mail: Chuanzhong.Li@nek.uu.se (Chuan-Zhong Li, corresponding author)
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.
Keywords
economic history, envelope theorems, dynamic optimization, environmental economics, cost-benefifit analysis
Karl-Gustaf Löfgren, Chuan-Zhong Li
. Envelope Theorems in Economics: Historical Development and Modern Cost-Benefit Applications.
Front. Econ. China,
2021, 16(2): 377−404 https://doi.org/10.54605/fec20210207
