In this paper we propose the concept of an affine cost share equilibrium and show that under natural assumptions any optimal allocation corresponds to an affine cost share equilibrium. With linear cost functions and under mild regularity assumptions we show that an optimal allocation is a ratio equilibrium with redistribution. In an appendix to the paper we propose a new proof of the existence of a ratio equilibrium when the preferences of the agents are representable by strictly quasi-concave, continuous and strictly monotonically increasing utility functions.