Dynamic externalities:Comparing conditions for Hopf bifurcationunder laissez‐faire and planning

Franz Wirl

Annals of Operations Research, 1999, vol. 89, issue 0, 177-194

Abstract: Consider an economy described by two states. The first state describes a private stocksubject to a firm's (or a consumer's) control, while the second state captures market interactionsand is exogenous data to the individual firm. Considering rational expectations, amarket equilibrium can be derived. This set‐up is typical, in particular for the recentlyinvestigated new endogenous growth models. In contrast to the market outcome, planningattempts to internalise this externality. In both cases, the policies ‐ either the optimal intertemporalpolicy of competitive firms exposed to this externality, or the social optimum ‐are characterised by a two‐dimensional plane. Thus, complex solutions in particular limitcycles are possible. This paper compares the conditions of stability and, in particular, theconditions for limit cycles under these two different institutional set‐ups, when the externalityis or is not properly internalised. This comparison is first theoretical and then applied to adeliberately simple economic example: firms accumulate a capital stock (e.g., sewage treatment,energy saving technologies) involving convex investment costs and this stock lowersemissions (or kinds of waste) that add to a stock of pollution (e.g. global warming, pollutionof water and soil, etc.). Copyright Kluwer Academic Publishers 1999

Date: 1999
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1023/A:1018971506197 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:annopr:v:89:y:1999:i:0:p:177-194:10.1023/a:1018971506197

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10479

DOI: 10.1023/A:1018971506197

Access Statistics for this article

Annals of Operations Research is currently edited by Endre Boros

More articles in Annals of Operations Research from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().