Most models of plant competition represent competition as taking place between species when realistically competition takes place between individuals. We model individual plants as optimally choosing biomass in order to maximize net energy that is directed into reproduction. Competition is for access to light and a plant that grows more biomass adds to the leaf area index, creating negative feedback in the form of more self shading and shading of its neighbors. In each period and for given species densities, simultaneous maximization by all plants yields an equilibrium characterized by optimum biomasses. Between periods the net energies plants obtain are used to update the densities, and if densities change the equilibrium changes in the subsequent period. A steady state is attained when all plants have net energies that just allow for replacement. Four main predictions of the resource-ratio theory of competition are obtained, providing behavioral underpinnings for species level models. However, if individual plant parameters are not identical across species, then the predictions do not follow. The optimization framework yields many other predictions, including how specific leaf areas and resource stress impact biomass and leaf area indices.