Essential properties of <i>L_p,q</i> spaces (the amalgams) and the implicit function theorem for equilibrium analysis in continuous time

• Type: Article in International Scientific Journal
• Date: 2014

Authors

Mertens, JF (Author) Other; Rubinchik, A (Author) Other

Journal

Title: Journal of Mathematical Economics

Vol. 50

Pages: 187-196

ISSN: 0304-4068

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 1 Citation

Scopus - 1 Citation

Other information

Authenticus ID: P-017-3S8

DOI: 10.1016/j.jmateco.2013.06.002

Abstract (EN): To extend the analysis of continuous-time general-equilibrium macro models we study 2 parameter variants Lp,q of the Lebesgue spaces, thus gaining separate control on the asymptotic behaviour (p) and the local behaviour (q): they behave w.r.t. p like the spaces ¿p and w.r.t. q like the spaces Lq on a probability space. Such spaces might naturally contain equilibrium variables (paths) as well as time-dependent policies of a macro model. Convolution behaves very well on those spaces, which can be used as a basis for the classical "comparative statics" (see e.g. Mertens and Rubinchik (2011)). Finally, we generalise the classical implicit function theorem (ift) for a family of Banach spaces, with the resulting implicit function having derivatives that are locally Lipschitz to very strong operator norms. © 2013 Elsevier B.V.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 10