### Abstract

This paper is concerned with generic properties of the set of price equilibria of overlapping-generations economies that include money. It is shown (in a C^{1} topology) that if generations live for m periods and if there are n goods available in each period, then most economies will feature equilibrium price sets of dimension at most (m-1)n. It is likewise shown that for every k that ranges between 0 and (m-1)n there are open sets of economies which possess locally k-dimensional, C^{1} manifolds of equilibria. In the process of establishing these facts, a transversality theorem is proved which applies to maps, not necessarily Fredholm, between open subsets of non-separable, infinite-dimensional spaces.

Original language | English (US) |
---|---|

Pages (from-to) | 209-230 |

Number of pages | 22 |

Journal | Journal of Mathematical Economics |

Volume | 18 |

Issue number | 3 |

DOIs | |

State | Published - 1989 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Economics and Econometrics
- Applied Mathematics

### Cite this

*Journal of Mathematical Economics*,

*18*(3), 209-230. https://doi.org/10.1016/0304-4068(89)90022-0

**On the structure of the equilibrium price set of overlapping-generations economies.** / Santos, Manuel; Bona, Jerry L.

Research output: Contribution to journal › Article

*Journal of Mathematical Economics*, vol. 18, no. 3, pp. 209-230. https://doi.org/10.1016/0304-4068(89)90022-0

}

TY - JOUR

T1 - On the structure of the equilibrium price set of overlapping-generations economies

AU - Santos, Manuel

AU - Bona, Jerry L.

PY - 1989

Y1 - 1989

N2 - This paper is concerned with generic properties of the set of price equilibria of overlapping-generations economies that include money. It is shown (in a C1 topology) that if generations live for m periods and if there are n goods available in each period, then most economies will feature equilibrium price sets of dimension at most (m-1)n. It is likewise shown that for every k that ranges between 0 and (m-1)n there are open sets of economies which possess locally k-dimensional, C1 manifolds of equilibria. In the process of establishing these facts, a transversality theorem is proved which applies to maps, not necessarily Fredholm, between open subsets of non-separable, infinite-dimensional spaces.

AB - This paper is concerned with generic properties of the set of price equilibria of overlapping-generations economies that include money. It is shown (in a C1 topology) that if generations live for m periods and if there are n goods available in each period, then most economies will feature equilibrium price sets of dimension at most (m-1)n. It is likewise shown that for every k that ranges between 0 and (m-1)n there are open sets of economies which possess locally k-dimensional, C1 manifolds of equilibria. In the process of establishing these facts, a transversality theorem is proved which applies to maps, not necessarily Fredholm, between open subsets of non-separable, infinite-dimensional spaces.

UR - http://www.scopus.com/inward/record.url?scp=38249024986&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38249024986&partnerID=8YFLogxK

U2 - 10.1016/0304-4068(89)90022-0

DO - 10.1016/0304-4068(89)90022-0

M3 - Article

AN - SCOPUS:38249024986

VL - 18

SP - 209

EP - 230

JO - Journal of Mathematical Economics

JF - Journal of Mathematical Economics

SN - 0304-4068

IS - 3

ER -