## Abstract

To extend the analysis of continuous-time general-equilibrium macro models we study 2 parameter variants L_{p,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 ℓ_{p} and w.r.t. q like the spaces L_{q} 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.

Original language | English |
---|---|

Pages (from-to) | 187-196 |

Number of pages | 10 |

Journal | Journal of Mathematical Economics |

Volume | 50 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2014 |

## Keywords

- Asymptotic behaviour
- Convolution
- General equilibrium
- Implicit function theorem
- Lebesgue spaces

## ASJC Scopus subject areas

- Economics and Econometrics
- Applied Mathematics

## Fingerprint

Dive into the research topics of 'Essential properties of L_{p,q}spaces (the amalgams) and the implicit function theorem for equilibrium analysis in continuous time'. Together they form a unique fingerprint.