TY - JOUR

T1 - Fixed Points in Grassmannians with Applications to Economic Equilibrium

AU - Keiding, Hans

PY - 2017

Y1 - 2017

N2 - In some applications of equilibrium theory, the fixed point involves not only a state and a value of a parameter in the dual of the state space, but also a particular subspace of the state space. Since the set of all subspaces of a finite-dimensional Euclidean space has a structure which does not allow immediate application of fixed point theorems, the problem must be reformulated using a suitable parametrization of subspaces. One such parametrization, the Plücker coordinates, is used here to prove a general equilibrium existence theorem. Applications to economic problems involving hierarchies of consumers or incomplete markets with real assets are outlined.

AB - In some applications of equilibrium theory, the fixed point involves not only a state and a value of a parameter in the dual of the state space, but also a particular subspace of the state space. Since the set of all subspaces of a finite-dimensional Euclidean space has a structure which does not allow immediate application of fixed point theorems, the problem must be reformulated using a suitable parametrization of subspaces. One such parametrization, the Plücker coordinates, is used here to prove a general equilibrium existence theorem. Applications to economic problems involving hierarchies of consumers or incomplete markets with real assets are outlined.

KW - Faculty of Social Sciences

KW - Existence

KW - hierarchic equilibrium

KW - pseudoequilibrium

KW - Plücker coordinates

U2 - 10.22606/jaef.2017.21003

DO - 10.22606/jaef.2017.21003

M3 - Journal article

VL - 2

SP - 29

EP - 39

JO - Journal of Advances in Economics and Finance

JF - Journal of Advances in Economics and Finance

SN - 2519-5980

IS - 1

ER -