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
SN - 2519-5980
VL - 2
SP - 29
EP - 39
JO - Journal of Advances in Economics and Finance
JF - Journal of Advances in Economics and Finance
IS - 1
ER -