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 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.
| 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
On the structure of the equilibrium price set of overlapping-generations economies. / Santos, Manuel; Bona, Jerry L.
In: Journal of Mathematical Economics, Vol. 18, No. 3, 1989, p. 209-230.Research output: Contribution to journal › Article
}
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 -