Essential properties of Lp,q spaces (the amalgams) and the implicit function theorem for equilibrium analysis in continuous time

Jean-François Mertens and Anna Rubinchik ()

Journal of Mathematical Economics, 2014, vol. 50, issue C, 187-196

Abstract: 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 ℓp 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.

Keywords: Lebesgue spaces; Asymptotic behaviour; Convolution; General equilibrium; Implicit function theorem (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (1)

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Working Paper: Essential properties of Lp,q spaces (the amalgams) and the implicit function theorem for equilibrium analysis in continuous time (2014)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:50:y:2014:i:c:p:187-196

DOI: 10.1016/j.jmateco.2013.06.002

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