In this paper, we improve a characterization of the Riesz decomposition property, obtained in Aliprantis et al. (J Math Econ 92:55–76, 2000). As an application of this result, we show that the existence of weakly Pareto optimal allocations in some economic models is equivalent to the finite dimensional nature of the commodity space. This result enables us to give a characterization of infinite dimensional \(C(K)\) spaces in terms of general equilibrium theory.