The problem of computing equilibria for general equilibrium models with incomplete real asset markets, or GEI models
for the sake of brevity, is reconsidered. It is shown here that the rank-dropping behavior of the asset return matrix
could be dealt with in rather a simple fashion: We first compute its singular value decomposition, and then, through
this decomposition, construct, by the introduction of a homotopy parameter, a new matrix such that it has constant rank
before a desired equilibrium is reached. By adjunction of this idea to the homotopy method, a simpler constructive
proof is obtained for the generic existence of GEI equilibria. For the purpose of computing these equilibria, from this
constructive proof is then derived a path-following algorithm whose performance is finally demonstrated by means of
three numerical examples.