Economic growth theory and theoretical ecology represent independent traditions of modeling aggregate consumer-resource systems. Both focus on different but equally important forces underlying the dynamics of human societies. Though the two traditions have unknowingly converged in some ways, they each have curious conventions from the perspective of the other. These conventions are reviewed, and two separate modeling frameworks that integrate the two traditions in a simple and straightforward fashion are developed and analyzed. The resulting models represent a consumer species (e.g. humans) that both produces and consumes its resources and then reproduces biologically according to the consumption of its resources. Depending on the balance between production, consumption, and reproduction, the models can exhibit stagnant behavior, like some predator-prey models, or growth, like many mutualism and economic growth models. When growth occurs, in the long term it takes one of two forms. Either resources per capita grow and the human population size converges to a constant, which may be zero, or resources per capita converge to a constant and the human population grows. The difference depends on initial conditions and the particular mix of biological conditions and human technology.