Psychological Review 1980, Vol. 87, No. 4, 355-374 Substitutability in Time Allocation Howard Rachlin State University of New York at Stony Brook John H. Kagel and Raymond C. Battalio Texas A&M University A characteristic of a group of commodities that influences the way they are chosen is their substitutability. For instance, an animal choosing between two solid foods (relatively substitutable for one another) allocates time in a different way from an animal choosing between solid food and water (relatively less substitutable for one another). We provide a method to measure substitutability using concurrent schedules of reinforcement. We assume that an animal allo- cates its time so as to maximize utility (according to a certain function) within the constraints imposed by the choice situation (the limited time available and the schedules of reinforcement). This assumption implies that when it chooses among various rates and amounts of a single reinforcer, the animal allocates time proportionally to the value of the alternatives (matching). But when the animal chooses among various rates and amounts of different rein- forcers, its time allocation deviates from matching. This deviation provides a measure of substitutability of the commodities. It would be convenient to be able to as- sign, to various commodities, numbers that indicate their values. Such numbers would form a scale by which one might predict (a) the power of a commodity to reinforce in- strumental responding and (b) choice among commodities. Premack (1965, 1971) has shown that the value of a consummatory response relative to the value of an instrumental response (as determined by responding in a baseline situ- ation) may be used to determine the power of the consummatory response to reinforce or punish the instrumental response. Herrn- stein's (1961) matching law asserts that in choice situations, relative responding (i.e., choice) is proportional to relative value, and that relative value, in turn, is a simple func- tion of the physical parameters of the com- The research was supported by grants from the Na- tional Science Foundation. The authors are grateful to Gary Becker and Alex- andra Logue for comments on a previous version of this manuscript. Requests for reprints should be sent to Howard Rach- lin, Department of Psychology, State University of New York at Stony Brook, Stony Brook, New York 11794. modities being chosen. The matching law has been applied to time allocation as well as choice among discrete responses (Baum & Rachlin, 1969). In both of these cases, value is assumed to be scalable independently of context. However, Rachlin and Burkhard (1978) have found, in the case of Premack's theory of reinforcement, that context (responses avail- able other than the instrumental response and consumption of the reinforcer) may de- termine whether reinforcement or punish- ment or no effect at all is found. Our object here is to provide a coherent account of context in time-allocation choice. Our at- tempt parallels Tversky's (1972) similar ac- count of context in probabilistic choice. The assignment of values to commodities and the assumption that such values are in- dependent of context corresponds to the notion of simple scalability in probabilistic choice situations. Luce's (1959) choice axiom, which implies that probability of choosing an alternative equals its scale value relative to the sum of the scale values of all other available alternatives, is equivalent to a simple form of Herrnstein's (1961) matching law as applied to time allocation Copyright 1980 by the American Psychological Association, Inc. 0033-295X/80/8704-0355$00.75 355