Capital accumulation of a firm facing environmental constraints

• Published in: Optimal control applications & methods Vol. 17; no. 4; pp. 253 - 266
• Main Authors: Hartl, Richard F., Kort, Peter M.
• Format: Journal Article
• Language: English
• Published: Chichester Wiley Subscription Services, Inc., A Wiley Company 01.10.1996; Wiley
• Subjects: Applied sciences; environmental problems; Exact sciences and technology; Firm modelling; history-dependent equilibria; input substitution; Inventory control, production control. Distribution; Operational research and scientific management; Operational research. Management science; optimal control; Optimization. Search problems; Skiba point; Upper bound; Business model; Pollution; Mathematical analysis; Environmental policy; Optimal control; Maximum principle; Capital accumulation; Equilibrium; Investment
• ISSN: 0143-2087; 1099-1514
• DOI: 10.1002/(SICI)1099-1514(199610/12)17:4<253::AID-OCA574>3.0.CO;2-E

In this paper we consider the dynamic behaviour of a firm subject to environmental regulation. As a social planner the government wants to reduce the level of pollution. To reach that aim, it can, among other actions, set an upper limit on polluting emissions of the firm. The paper determines how this policy instrument influences the firm's decisions concerning investments and abatement efforts. Using standard control theory in determining the firm's optimal dynamic investment decisions it turns out that it is always optimal to approach a long‐run optimal level of capital. In some cases this equilibrium is reached within finite time, but usually it will be approached asymptotically. Also, a necessary condition is determined under which history‐dependent equilibria can occur. Some of them are saddle point equilibria and others are unstable nodes or spirals (focuses). These history‐dependent equilibria can be identified as being good or bad for society. We show that it is possible to eliminate bad equilibria through government intervention. Finally we derive conditions under which equilibrium capital stock and equilibrium investment rate in the regulated case decrease compared with the unregulated case.