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

Author

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  • MERTENS, Jean-François
  • RUBINCHIK, Anna

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.
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Suggested Citation

  • MERTENS, Jean-François & RUBINCHIK, Anna, 2014. "Essential properties of Lp,q spaces (the amalgams) and the implicit function theorem for equilibrium analysis in continuous time," LIDAM Reprints CORE 2549, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:2549
    Note: In : Journal of Mathematical Economics, 50, 187-196, 2014
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    2. Rubinchik, Anna, 2015. "The chase of a multi-armed economist for the elusive social discount rate," Working Papers WP2015/8, University of Haifa, Department of Economics, revised 18 Nov 2015.

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