THE APPLICATION OF THE MATCHING LAW TO SIMPLE RATIO SCHEDULES

where P is number of responses, k is a constant, n is the average number of responses required for one reinforcement, and R. is the reinforcement for other alternatives.2 This paper considers briefly the empirical adequacy of this equation in predicting responding under ratio schedules. Equation 1 predicts two effects of questionable generality: (a) responding should decrease as the average value of the ratio increases until (b) at some value of the ratio, responding goes to zero. The prediction of an inverse relation between number of responses and ratio size appears contradicted by considerable data. In fixed-ratio (FR) schedules the most common finding is a direct relation between number of responses and ratio size for low to moderate ratio values. For example, between FR 1 and FR 20, increased ratio requirement for a food reward is accompanied by increased key pecking in pigeons (Ferster and Skinner, 1957; Findley, 1962), and manipulation responses in rats (Barofsky and Hurwitz, 1968; Boren, 1961; Collier, Hirsch and Hamlin, 1972; Teitelbaum, 1957), gerbils (Vanderweele, Abelson, and Tellish, 1973), guinea pigs (Hirsch and Collier, 1974), goldfish (Rozin and Mayer, 1964), monkeys (Findley, 1959; Hamilton and Brobeck, 1964), and humans (Hutchinson and Azrin, 1961). A further increase in ratio size often produces a decline in number of responses. Increases in the size of variableand random-ratio schedules appear to produce changes similar to those that occur in the fixed-ratio case, though the relation is not always as marked (eg., Brandauer, 1958; Kelly, 1974; Priddle-Higson, Lowe, and Harzem, 1976). Performance on these latter schedules may be affected by