Behavioral economics of drug self-administration. II. A unit-price analysis of cigarette smoking.

In behavioral economics, the ratio of response requirement to reinforcer magnitude is referred to as unit price. Previous research with nonhuman subjects has demonstrated that (a) comparable amounts of food are consumed at the same unit price even though different response requirements and reinforcer magnitudes comprise that unit price and (b) increases in unit price decrease food consumption in a positively decelerating fashion. The present study assessed the generality of these findings to the cigarette smoking of 5 human volunteers. During approximately 18 3-hr sessions, various combinations of response requirement (fixed-ratio 200, 400, and 1,600) and reinforcer magnitude (1, 2, and 4 puffs per bout) were arranged. Consumption (i.e., the number of puffs) generally was comparable at the same unit price independent of the response requirement and reinforcer magnitude comprising that unit price. In addition, increasing unit price generally decreased consumption in a positively decelerating fashion. These results extend the generality of the unit-price analysis to human cigarette smoking. Moreover, these results further support the position that reinforcer magnitude and response requirement are functionally equivalent and interact to determine consumption. The concept of unit price, by integrating and summarizing the effects of those two operations, provides a more parsimonious explanation of the results than do separate evaluations of the effects of response requirement and reinforcer magnitude.     

Unit price and choice in a token-reinforcement context

Pigeons were exposed to multiple and concurrent second-order schedules of token reinforcement, with stimulus lights serving as token reinforcers. Tokens were produced and exchanged for food according to various fixed-ratio schedules, yielding equal and unequal unit prices (responses per unit food delivery). On one schedule (termed the standard schedule), the unit price was held constant across conditions. On a second schedule (the alternative schedule), the unit price was either the same or different from the standard. Under conditions with unequal unit prices, near-exclusive preference for the lower unit price was obtained. Under conditions with equal unit prices, the direction and degree of preference depended on ratio size (number of responses per exchange period). When this ratio differed, strong preferences for the smaller ratio were observed. When this ratio was equal, preferences were nearer indifference. Response rates on the multiple schedule were generally consistent with the preference data in showing sensitivity to ratio size. Results are discussed in terms of a unit-price model that includes handling and reinforcer immediacy as additional costs. On the whole, results show that preferences were determined primarily by delay to the exchange period.     

Similar consumption and responding across single and multiple sources of drug

Two experiments were conducted to assess whether total response output and total consumption would be similar when drugs are available from single and multiple sources of reinforcement, as predicted by behavioral economics. In Experiment 1, cigarette-deprived smokers were exposed to a concurrent-chains schedule in which equal fixed-ratio schedules served as the initial links, and different reinforcer magnitudes (i.e., number of cigarette puffs) were arranged across alternatives. After the session, obtained unit price was calculated and imposed in the next session when a different number of puffs was available according to a single fixed-ratio schedule. Thus, the unit price at which cigarette puffs could be earned was yoked within subjects across the single and concurrent-chains schedules. When plotted as a function of unit price, similar consumption and response rates were usually obtained across these schedules. Experiment 2 addressed a weakness of Experiment 1, namely, that responding was allocated exclusively to the larger reinforcer magnitude in concurrent-chains conditions, and therefore this schedule may have functioned as a single schedule. In Experiment 2, subjects were instructed to alternate responding between the two alternative schedules. Instructions produced approximately equal response allocation between the two alternatives. Again, similar consumption and response rates were observed across the single and instructed concurrent-chains schedules. These findings are discussed in the context of direct effects and behavioral economics perspectives of drug self-administration.     

Three predictions of the economic concept of unit price in a choice context

Economic theory makes three predictions about consumption and response output in a choice situation: (a) When plotted on logarithmic coordinates, total consumption (i.e., summed across concurrent sources of reinforcement) should be a positively decelerating function, and total response output should be a bitonic function of unit price increases; (b) total consumption and response output should be determined by the value of the unit price ratio, independent of its cost and benefit components; and (c) when a reinforcer is available at the same unit price across all sources of reinforcement, consumption should be equal between these sources. These predictions were assessed in human cigarette smokers who earned cigarette puffs in a two-choice situation at a range of unit prices. In some sessions, smokers chose between different amounts of puffs, both available at identical unit prices. Individual subjects' data supported the first two predictions but failed to support the third. Instead, at low unit prices, the relatively larger reinforcer (and larger response requirement) was preferred, whereas at high unit prices, the smaller reinforcer (and smaller response requirement) was preferred. An expansion of unit price is proposed in which handling costs and the discounted value of reinforcers available according to ratio schedules are incorporated.     

A behavioral economic analysis of concurrently available money and cigarettes.

In economic terms, consumption of a reinforcer is determined by its price and the availability and price of other reinforcers. This study examined the effects of response-requirement (i.e., price) manipulations on the self-administration of two concurrently available reinforcers. Six cigarette smokers participated in 4-hr sessions in which money and puffs on a cigarette were concurrently available according to fixed-ratio schedules of reinforcement. Once stable responding was obtained with both reinforcers available at Fixed Ratio 100, the response requirement for one reinforcer was systematically varied (Fixed Ratio 1,000 and 2,500), while the other reinforcer remained scheduled at Fixed Ratio 100. Increasing the fixed-ratio size for a reinforcer decreased its consumption, with a greater decrease occurring for monetary reinforcement. This finding was quantified in economic terms as own-price elasticity, with elasticity coefficients greater for money than cigarettes. The effects of fixed-ratio size on response output also differed across the two reinforcers. Although greater responding occurred for money at Fixed Ratio 100, increases in fixed-ratio size (for money) decreased responding for money, whereas the same increase in fixed-ratio size (for puffs) increased responding for puffs. Finally, increasing the fixed-ratio size for one reinforcer had little effect on consumption of the other concurrently available reinforcer. This finding was quantified as cross-price elasticity, with elasticity coefficients near 0.0 for most subjects, indicating little or no reinforcer interaction. The results indicate that the reinforcing effects of cigarettes and money in the setting studied here differed, and that the effects produced by changing the price of one reinforcer did not interact with the consumption of the other concurrently available reinforcer.     

Labor supply and consumption of food in a closed economy under a range of fixed- and random-ratio schedules: tests of unit price

The behavioral economic concept of unit price predicts that consumption and response output (labor supply) are determined by the unit price at which a good is available regardless of the value of the cost and benefit components of the unit price ratio. Experiment 1 assessed 4 pigeons' consumption and response output at a range of unit prices. In one condition, food was available according to a range of fixed-ratio schedules, whereas in the other condition, food was available according to a range of random-ratio schedules. Consistent with unit price predictions, consumption and response output were approximately equivalent across schedule types within the lower range of unit prices. However, at Unit Prices 64 (ratio value = 192) and greater, considerably more consumption and response output were observed in the random-ratio condition. Experiment 2 replicated these findings with 4 pigeons using the rapid demand curve assay procedure that is commonly used in the behavioral economics literature. Findings are integrated with two mathematical models of behavior under variable reinforcer delays.     

Applying the behavioral economics principle of unit price to DRO schedule thinning

Within the context of behavioral economics, the ratio of response requirements to reinforcer magnitude is called unit price. In this investigation, we yoked increases in reinforcer magnitude with increases in intervals of differential reinforcement of other behavior (DRO) to thin DRO intervals to a terminal value.     

Resistance to extinction following variable-interval reinforcement: reinforcer rate and amount

Rats obtained food-pellet reinforcers by nose poking a lighted key. Experiment 1 examined resistance to extinction following single-schedule training with different variable-interval schedules, ranging from a mean interval of 16 min to 0.25 min. That is, for each schedule, the rats received 20 consecutive daily baseline sessions and then a session of extinction (i.e., no reinforcers). Resistance to extinction (decline in response rate relative to baseline) was negatively related to the rate of reinforcers obtained during baseline, a relation analogous to the partial-reinforcement-extinction effect. A positive relation between these variables emerged, however, when the unit of extinction was taken as the mean interreinforcer interval that had been in effect during training (i.e., as an omitted reinforcer during extinction). In a second experiment, rats received blocks of training sessions, all with the same variable-interval schedule but with a reinforcer of four pellets for some blocks and one pellet for others. Resistance to extinction was greater following training with the larger (four pellets) than with the smaller (one pellet) reinforcer. Taken together, these results support the principle that greater reinforcement during training (e.g., higher rate or larger amount) engenders greater resistance to extinction even when the different conditions of reinforcement are varied between blocks of sessions.     

Contrast and reallocation of extraneous reinforcers as a function of component duration and baseline rate of reinforcement

Four pigeons responded on multiple schedules arranged on a “main” key in a two-key experimental chamber. A constant schedule component was alternated with another component that was varied over conditions. On an extra response key, conjoint schedules of reinforcement that operated in both components were arranged concurrently with the multiple schedule on the main key. On the main key, changes in reinforcement rate in the varied component were inversely related to changes in response rates in the constant component (behavioral contrast). On the extra key, some reinforcers were reallocated between components, depending on the schedules in effect on the main key in the varied component. In the varied component, the obtained rates of reinforcement on the extra key were inversely related to main-key reinforcement rate. In the constant component, extra-key reinforcer rates were positively related to main-key reinforcer rates obtained in the varied component, and were not a function of response rates on the extra key. In two comparisons, the rate at which components alternated and the value of the main-key schedule in the constant component were varied. Consistent with earlier work, long components reduced the extent of contrast. Reductions in contrast as a function of component duration were accompanied by similar reductions in the extent of reinforcer reallocation on the extra key. In the second comparison, lowering the rate of reinforcement in the constant component increased the rate at which extra-key reinforcers were obtained, reduced the extent of reinforcer reallocation, and reduced contrast. Overall, the results are consistent with the suggestion that some contrast effects are due to the changes in extraneous reinforcement during the constant component, and that manipulations of component duration, and manipulations of the rate of reinforcement in the constant component, affect contrast because they influence the extent of extraneous reinforcer real-location.     

Extended pausing by humans on multiple fixed-ratio schedules with varied reinforcer magnitude and response requirements

We conducted three experiments to reproduce and extend Perone and Courtney's (1992) study of pausing at the beginning of fixed-ratio schedules. In a multiple schedule with unequal amounts of food across two components, they found that pigeons paused longest in the component associated with the smaller amount of food (the lean component), but only when it was preceded by the rich component. In our studies, adults with mild intellectual disabilities responded on a touch-sensitive computer monitor to produce money. In Experiment 1, the multiple-schedule components differed in both response requirement and reinforcer magnitude (i.e., the rich component required fewer responses and produced more money than the lean component). Effects shown with pigeons were reproduced in all 7 participants. In Experiment 2, we removed the stimuli that signaled the two schedule components, and participants' extended pausing was eliminated. In Experiment 3, to assess sensitivity to reinforcer magnitude versus fixed-ratio size, we presented conditions with equal ratio sizes but disparate magnitudes and conditions with equal magnitudes but disparate ratio sizes. Sensitivity to these manipulations was idiosyncratic. The present experiments obtained schedule control in verbally competent human participants and, despite procedural differences, we reproduced findings with animal participants. We showed that pausing is jointly determined by past conditions of reinforcement and stimuli correlated with upcoming conditions.     

Behavioral momentum in computer-presented discriminations in individuals with severe mental retardation

Behavioral momentum was examined in 2 individuals with severe mental retardation via within-subject manipulations of obtained reinforcer rates. Subjects performed self-paced discrimination problems presented on a touch screen computer monitor. Two different problems, Tasks A and B, alternated in blocks of 15 trials on a multiple schedule. Reinforcers were snack foods. The reinforcement schedule for Task A was continuous (fixed-ratio 1) and the schedule for Task B was continuous in some conditions and variable ratio in other conditions. Behavioral momentum was assessed in test sessions by prefeeding, presenting response-independent food, and making available alternatives to the tasks. When the obtained reinforcer rate for Task A was at least twice that for Task B, resistance to change was greater for Task A. When both reinforcer rates and response rates were a pproximately equal for the two tasks, resistance to change was approximately equal. These results are consistent with behavioral momentum effects. They extend previous findings with humans by examining momentum in self-initiated discrete-trial discrimination tasks with ratio schedules, and by isolating relative reinforcer rates as a controlling variable via within-subject manipulations.     

Concurrent nonindependent fixed‐ratio schedules of alcohol self‐administration: Effects of schedule size on choice

Choice behavior was studied under concurrent nonindependent fixed‐ratio fixed‐ratio (nFR) schedules of reinforcement, as these schedules result in frequent changeover responses. With these schedules, responses on either operandum count toward the completion of the ratio requirements of both schedules. Five monkeys were subjects, and two pairs of liquid reinforcers were concurrently available: 16% (w/v) and 0% ethanol or 16% and 8% ethanol. For each pair of reinforcers, the nFR sizes were systematically altered across sessions while keeping the schedule size equal for both liquids. Responding varied as a function of reinforcer pair and nFR size. With the 16% and 0% pair, higher response rates were maintained by 16% and were an inverted U‐shape function of nFR size. With 16% and 8%, a greater number of responses initially occurred on the schedule that delivered 8% ethanol. However, as nFR size increased, preference reversed such that responses that delivered 16% ethanol were greater. When the nFR size was subsequently decreased, preference reverted back to 8%. Number of responses emitted per delivery was a dependent variable and, in behavioral economic terms, was the price paid for each liquid delivery. With 16% and 0%, changeover responses initially increased and then decreased as schedule size became larger. In contrast, with the 16% and 8% pair, changeover responses increased directly with schedule size. Responding under nFR schedules is sensitive to differences in reinforcer magnitude and demonstrates that relative reinforcing effects can change as a function of schedule size.     

Every reinforcer counts: reinforcer magnitude and local preference

Six pigeons were trained on concurrent variable-interval schedules. Sessions consisted of seven components, each lasting 10 reinforcers, with the conditions of reinforcement differing between components. The component sequence was randomly selected without replacement. In Experiment 1, the concurrent-schedule reinforcer ratios in components were all equal to 1.0, but across components reinforcer-magnitude ratios varied from 1:7 through 7:1. Three different overall reinforcer rates were arranged across conditions. In Experiment 2, the reinforcer-rate ratios varied across components from 27:1 to 1:27, and the reinforcer-magnitude ratios for each alternative were changed across conditions from 1:7 to 7:1. The results of Experiment 1 replicated the results for changing reinforcer-rate ratios across components reported by Davison and Baum (2000, 2002): Sensitivity to reinforcer-magnitude ratios increased with increasing numbers of reinforcers in components. Sensitivity to magnitude ratio, however, fell short of sensitivity to reinforcer-rate ratio. The degree of carryover from component to component depended on the reinforcer rate. Larger reinforcers produced larger and longer postreinforcer preference pulses than did smaller reinforcers. Similar results were found in Experiment 2, except that sensitivity to reinforcer magnitude was considerably higher and was greater for magnitudes that differed more from one another. Visit durations following reinforcers measured either as number of responses emitted or time spent responding before a changeover were longer following larger than following smaller reinforcers, and were longer following sequences of same reinforcers than following other sequences. The results add to the growing body of research that informs model building at local levels.     

Tolerance to effects of cocaine on behavior under a response-initiated fixed-interval schedule

Tolerance to effects of cocaine can be modulated by schedules of reinforcement. With multiple ratio schedules, research has shown an inverse relationship between ratio requirement and amount of tolerance that resulted from daily administration of the drug. In contrast, tolerance to the effects of cocaine on behavior under multiple interval schedules generally has developed regardless of interval value. Under interval schedules reinforcement depends on the animal making one response following a time interval. Thus, as time to respond increases, the time to reinforcement decreases. On the other hand, fixed ratio schedules require a specified number of responses to be made prior to reinforcement. Therefore, delaying the initiation of responding does not coincide with a significant decrease in the time to reinforcement. In the current experiment, 6 pigeons were trained to respond under a three-component multiple schedule, with a different tandem fixed-ratio 1 fixed-interval schedule in each component. The multiple schedule required one response, which was followed by one of three fixed-interval values (5, 15, or 60 s). Thus, the multiple schedule was interval-like because after the fixed-ratio 1, only one more response was required for reinforcement, but it was also ratio-like because the length of the pause at the beginning of each interreinforcer interval affected the time until the next reinforcer. Acute administration of cocaine generally resulted in dose-dependent decreases in responding. Chronic (i.e., daily) administration of a rate-decreasing dose resulted in tolerance patterns similar to those usually obtained with multiple ratio schedules. That is, the magnitude of tolerance was related inversely to schedule size. These results suggest that delay to reinforcement from the initial response may play a role in the development of schedule-parameter-related tolerance.     

Response Form, Force, And Number: Effects On Concurrent-schedule Performance

Six hens responded on concurrent variable-interval (key-peck) variable-interval (door-push) schedules of reinforcement in which the second-order (fixed-ratio) requirements on the alternatives (Experiment 1) or the required door forces (Experiment 2) were varied. The key-peck and door-push response (measured as fixed-ratio completion) and time data were well described by the generalized matching law. However, the manipulations of fixed-ratio requirement and required response force differed in their effects. The manipulations of fixed-ratio size affected the response and time measures differently, producing fairly constant, multiplicative biases only in terms of response allocation. It was argued that variations in fixed-ratio size necessarily change the time allocated to that response unit, and thus changes in time bias were not necessarily a fundamental effect of changing the ratio. In contrast, the changes in response bias were a fundamental result of changes in ratio size. The response-force manipulations produced similar bias shifts in terms of response and time allocation, but they appeared to combine with relative reinforcement rate to affect choice interactively. Specifically, behavior appeared to be biased towards the least effortful (i.e., key-peck) response, but the increases in door force had a larger effect on bias when the hens were making this response infrequently (on a lean schedule). The different effects of the fixed-ratio and response-force manipulations on concurrent performance were partially accounted for by the differing times required to complete each response unit under those manipulations, but this would not account for the interaction. The interaction would be consonant with increased response effort decreasing the effective value of the associated reinforcement schedule.     

Pavlovian contingencies and resistance to change in a multiple schedule

According to theoretical accounts of behavioral momentum, the Pavlovian stimulus—reinforcer contingency determines resistance to change. To assess this prediction, 8 pigeons were exposed to an unsignaled delay-of-reinforcement schedule (a tandem variable-interval fixed-time schedule), a signaled delay-of-reinforcement schedule (a chain variable-interval fixed-time schedule), and an immediate, zero-delay schedule of reinforcement in a three-component multiple schedule. The unsignaled delay and signaled delay schedules employed equal fixed-time delays, with the only difference being a stimulus change in the signaled delay schedule. Overall rates of reinforcement were equated for the three schedules. The Pavlovian contingency was identical for the unsignaled and immediate schedules, and response—reinforcer contiguity was degraded for the unsignaled schedule. Results from two disruption procedures (prefeeding subjects prior to experimental sessions and adding a variable-time schedule to timeout periods separating baseline components) demonstrated that response—reinforcer contiguity does play a role in determining resistance to change. The results from the extinction manipulation were not as clear. Responding in the unsignaled delay component was consistently less resistant to change than was responding in both the immediate and presignaled segments of the signaled delay components, contrary to the view that Pavlovian contingencies determine resistance to change. Probe tests further supported the resistance-to-change results, indicating consistency between resistance to change and preference, both of which are putative measures of response strength.     

Stimulus Equivalence: Effects Of A Default-response Option On Emergence Of Untrained Stimulus Relations

Human subjects were exposed to a concurrent-chains schedule in which reinforcer amounts, delays, or both were varied in the terminal links, and consummatory responses were required to receive points that were later exchangeable for money. Two independent variable-interval 30-s schedules were in effect during the initial links, and delay periods were defined by fixed-time schedules. In Experiment 1, subjects were exposed to three different pairs of reinforcer amounts and delays, and sensitivity to reinforcer amount and delay was determined based on the generalized matching law. The relative responding (choice) of most subjects was more sensitive to reinforcer amount than to reinforcer delay. In Experiment 2, subjects chose between immediate smaller reinforcers and delayed larger reinforcers in five conditions with and without timeout periods that followed a shorter delay, in which reinforcer amounts and delays were combined to make different predictions based on local reinforcement density (i.e., points per delay) or overall reinforcement density (i.e., points per total time). In most conditions, subjects' choices were qualitatively in accord with the predictions from the overall reinforcement density calculated by the ratio of reinforcer amount and total time. Therefore, the overall reinforcement density appears to influence the preference of humans in the present self-control choice situation.     

Sensitivity to relative reinforcer rate in concurrent schedules: independence from relative and absolute reinforcer duration

Twelve pigeons responded on two keys under concurrent variable-interval (VI) schedules. Over several series of conditions, relative and absolute magnitudes of reinforcement were varied. Within each series, relative rate of reinforcement was varied and sensitivity of behavior ratios to reinforcer-rate ratios was assessed. When responding at both alternatives was maintained by equal-sized small reinforcers, sensitivity to variation in reinforcer-rate ratios was the same as when large reinforcers were used. This result was observed when the overall rate of reinforcement was constant over conditions, and also in another series of concurrent schedules in which one schedule was kept constant at VI ached 120 s. Similarly, reinforcer magnitude did not affect the rate at which response allocation approached asymptote within a condition. When reinforcer magnitudes differred between the two responses and reinforcer-rate ratios were varied, sensitivity of behavior allocation was unaffected although response bias favored the schedule that arranged the larger reinforcers. Analysis of absolute response rates ratio sensitivity to reinforcement occurrred on the two keys showed that this invariance of response despite changes in reinforcement interaction that were observed in absolute response rates on the constant VI 120-s schedule. Response rate on the constant VI 120-s schedule was inversely related to reinforcer rate on the varied key and the strength of this relation depended on the relative magnitude of reinforcers arranged on varied key. Independence of sensitivity to reinforcer-rate ratios from relative and absolute reinforcer magnitude is consistent with the relativity and independence assumtions of the matching law.     

Effects of shifts in food reinforcement context on rats’ consumption of concurrently available water or sucrose solution

The purpose of this study was to investigate the effects of signaled transitions from relatively rich to lean conditions of food reinforcement on drinking concurrently available water or sucrose‐sweetened water in rats. Past research demonstrated that these negative incentive shifts produce behavioral disruption in the form of extended pausing on fixed‐ratio schedules. Four male Long‐Evans rats operated on a two‐component multiple fixed‐ratio fixed‐ratio schedule. In one manipulation, the ratio was held constant and the components arranged either a large six‐pellet reinforcer (rich) or small one‐pellet reinforcer (lean). In a second manipulation, the components both produced a one‐pellet reinforcer but differed in terms of the ratio requirement, with the rich and lean conditions corresponding to relatively small and large ratios. In both manipulations, components were pseudorandomly presented to arrange four transitions signaled by retractable levers: lean‐to‐lean, lean‐to‐rich, rich‐to‐rich, and rich‐to‐lean (the negative incentive shift). During experimental conditions, a bottle with lickometer was inserted in the chamber, providing concurrent access either to tap water or a 10% sucrose solution. The negative incentive shift produced considerably more drinking than the other transitions in all rats during both manipulations. The level of drinking was not polydipsic; rather, it appears that the negative incentive shift enhanced the value of concurrently available reinforcers relative to food reinforcement.     

Negative reinforcement and choice in humans

Participants chose between reinforcement schedules differing in delay and/or duration of noise offset. In Experiment 1 it was found that (1) immediate reinforcement was preferred to delayed reinforcement when amounts (durations) of reinforcement were equal; (2) a relatively large reinforcer was preferred to a smaller one when both reinforcers were obtained immediately; and (3) preference for an immediate, small reinforcer versus a delayed, large reinforcer increased as the delay preceding the large reinforcer increased, a sign of “impulsivity”. In Experiment 2, the schedules differed in amount or delay and equal intervals were added either to the constant parameter or the varied parameter. A shift from virtually exclusive preference to indifference occurred in the latter case but not the former, a result supporting a model of self-control that assumes that the value of a schedule depends on the ratio of amount and delay, and that choice between schedules depends on the ratio of these values.