Essential properties of Lp,q spaces (the amalgams) and the implicit function theorem for equilibrium analysis in continuous time
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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Volume (Year): 50 (2014)
Issue (Month): C ()
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- Mertens, Jean-Francois & Rubinchik, Anna, "undated". "Regularity And Stability Of Equilibria In An Overlapping Generations Growth Model," Working Papers WP2014/2, University of Haifa, Department of Economics.
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- Jean-François Mertens & Anna Rubinchik, 2013. "Equilibria in an overlapping generations model with transfer policies and exogenous growth," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 537-595, November.
- Mertens, Jean-Francois & Rubinchik, Anna, "undated". "Equilibria in an overlapping generations model with transfer policies and exogenous growth," Working Papers WP2012/5, University of Haifa, Department of Economics.
- MERTENS, Jean-François & RUBINCHIK, Anna, 2012. "Equilibria in an overlapping generations model with transfer policies and exogenous growth," CORE Discussion Papers 2012032, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-392, May.
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- Debreu, Gerard, 1976. "Regular Differentiable Economies," American Economic Review, American Economic Association, vol. 66(2), pages 280-287, May. Full references (including those not matched with items on IDEAS)
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