Twelve female Long-Evans rats were exposed to concurrent variable (VR) ratio schedules of sucrose and wheel-running reinforcement (Sucrose VR 10 Wheel VR 10; Sucrose VR 5 Wheel VR 20; Sucrose VR 20 Wheel VR 5) with predetermined budgets (number of responses). The allocation of lever pressing to the sucrose and wheel-running alternatives was assessed at high and low body weights. Results showed that wheel-running rate and lever-pressing rates for sucrose and wheel running increased, but the choice of wheel running decreased at the low body weight. A regression analysis of relative consumption as a function of relative price showed that consumption shifted toward sucrose and interacted with price differences in a manner consistent with increased substitutability. Demand curves showed that demand for sucrose became less elastic while demand for wheel running became more elastic at the low body weight. These findings reflect an increase in the difference in relative value of sucrose and wheel running as body weight decreased. Discussion focuses on the limitations of response rates as measures of reinforcement value. In addition, we address the commonalities between matching and demand curve equations for the analysis of changes in relative reinforcement value.