Existence, uniqueness and determinacy of equilibrium in CAPM with a riskless asset

In this note, we study the problem of existence, uniqueness and determinacy of equilibrium in the two period mean-variance C.A.P.M, with a riskless as set and possibly an infinite number of assets. The existence, uniqueness an d determinacy problem is brought down to a two-dimensional problem. We cons truct a reduced two-dimensional economy which has the same equilibria as th e original economy. In particular, we provide a very elementary proof of ex istence of equilibrium. We then show that when utilities are additively sep arable in mean and variance, sufficient conditions for uniqueness of equili brium may be given in terms of 'risk aversion'. Lastly, we show that generi cally equilibria are determinate. (C) 1999 Elsevier Science S.A. All rights reserved.