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Matching theory and linear system theory make different predictions about how the y-asymptote, k, of Herrnstein's (1970) hyperbola varies with reinforcer value. The present experiment tested both these predictions and linear system theory's account of how reinforcement rate and reinforcer value jointly govern response rate. Eight rats served as subjects. In Phase 1, 3 sucrose pellets of different concentration (5%, 75%, and 95%) were alternately paired with a fourth concentration (50%) on concurrent VI VI schedules. By fitting linear system theory's equation for concurrent choice, measures of reinforcer value were assigned to each concentration for each subject. The reinforcer values for the 50%, 75%, and 95% were roughly equivalent, and the reinforcer values for the 5% concentration were lower. In Phase 2 subjects were exposed to a series of single-alternative VI schedules (8, 17, 55, 150, and 250 sec) and each sucrose concentration was studied separately, with a :25% pellet added. Herrnstein's equation was fitted to response rate as a function of reinforcement rate for each concentration. The asymptote, k, was roughly equivalent under the 50%, 75%, and 95% pellets, but was lower for the 5% and 25% pellets. The measures of reinforcer value from Phase 1 suggest that the equivalent ks in Phase 2 were the result of equivalent reinforcer values . Matching theory predicts that k should remain constant across changes in reinforcer value . The value of k varied with reinforcer value, and the form of variability in k supported linear system theory's prediction of a positively accelerating function. Linear system theory's prediction about how reinforcement rate and reinforcer value jointly govern response rate was also supported. The results contradict matching theory's account and support linear system theory's account of single-alternative responding.