Neural systems face the challenge of optimizing their performance with limited resources, just as economic systems do. Here, we use tools of neoclassical economic theory to explore how a frugal visual system should use a limited number of neurons to optimize perception of motion. The theory prescribes that vision should allocate its resources to different conditions of stimulation according to the degree of balance between measurement uncertainties and stimulus uncertainties. We find that human vision approximately follows the optimal prescription. The equilibrium theory explains why human visual sensitivity is distributed the way it is and why qualitatively different regimes of apparent motion are observed at different speeds. The theory offers a new normative framework for understanding the mechanisms of visual sensitivity at the threshold of visibility and above the threshold and predicts large-scale changes in visual sensitivity in response to changes in the statistics of stimulation and system goals.