Isaac Scientific Publishing

Journal of Advances in Economics and Finance

Fixed Points in Grassmannians with Applications to Economic Equilibrium

Download PDF (517.9 KB) PP. 29 - 39 Pub. Date: February 23, 2017

DOI: 10.22606/jaef.2017.21003


  • Hans Keiding*
    Department of Economics, University of Copenhagen, Denmark


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.


Existence, hierarchic equilibrium, pseudoequilibrium, Plücker coordinates


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