Unit price as a useful metric in analyzing effects of reinforcer magnitude.

In this paper, we applied the behavioral-economic concept of unit price to the study of reinforcer magnitude in an attempt to provide a consistent account of the effects of reinforcer magnitude on behavior. Recent research in the experimental analysis of behavior and in behavioral pharmacology suggests that reinforcer magnitude interacts with the schedule of reinforcement to determine response rate and total consumption. The utility of the unit-price concept thus stems from its ability to quantify this interaction as a cost-benefit ratio (i.e., unit price = characteristics of the schedule of reinforcement divided by magnitude of reinforcement). Research employing the unit-price concept has shown that as unit price increases, a positively decelerating function exists for consumption (i.e., a function with an increasingly negative slope, when plotted on log coordinates) and a bitonic function exists for response rate. Based on these findings, the present analysis applied the unit-price concept to those studies of reinforcer magnitude and drug self-administration that examined the effects of reinforcer magnitude on response rate using simple schedules of reinforcement (e.g., fixed-ratio schedule). This resulted in three findings: (a) Reinforcer-magnitude manipulations and schedule manipulations interact in a manner that can be quantified in terms of unit price as benefit and cost factors, respectively; (b) different reinforcer-magnitude manipulations are functionally interchangeable as benefit factors in the unit-price ratio; and (c) these conclusions appear warranted despite the differences in reinforcers (food or drug), species (dogs, monkeys, or rats), and schedules (interval or ratio), and despite the fact that these studies were not designed for a unit-price analysis. In methodological terms, these results provide further evidence that employing the unit-price concept is a parsimonious method for examining the effects of reinforcer magnitude. In theoretical terms, these results suggest that a single process may underlie the effect of combined reinforcer-magnitude and schedule manipulations.     

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.     

An economic analysis of "demand" for food in baboons.

Responding of 6 adult male baboons (Papio c. anubis) was maintained under a fixed-ratio schedule of food reinforcement during daily 22-hr experimental sessions. Completion of the ratio requirement resulted in the delivery of a single 1-g food pellet; supplemental feeding was limited to a daily fruit ration. Ratio values were increased on Mondays, Wednesdays, and Fridays according to the following schedule: 2, 4, 8, 16, 32, 64, 96, 128. Responding under each ratio value was examined four times. Under the Fixed-Ratio 2 conditions, food intake ranged between 300 and 600 g. Ratios were increased for each baboon until food intake decreased to about 100 g (20% to 30% of Fixed-Ratio 2 intake). Increasing the response cost increased total time responding and total daily responding in all baboons, but this increase in responding was not sufficient to maintain stable food intake. Baboons responded between 90 and 180 min per day. The highest running response rates were observed under the Fixed-Ratio 2 and Fixed-Ratio 4 schedules. Running rate was similar across the larger ratio values (greater than Fixed-Ratio 8) but was lower than that observed under the Fixed-Ratio 2 and Fixed-Ratio 4 schedules. Similar results were observed the four times that each fixed-ratio value was tested. Intake as a function of cost was analyzed by fitting data to the nonlinear equation proposed by Hursh, Raslear, Shurtleff, Bauman, and Simmons (1988) for "demand" functions. Demand for food was inelastic over most of the ratio values until food intake decreased to 15% to 55% of baseline. The results indicate that demand functions are appropriate for the study of food intake in baboons, but also caution that intake at the cost when demand shifts from inelastic to elastic and its relationship to maximal intake should also be included in analyses of demand for a commodity.     

DOES PACKAGE SIZE MATTER? A UNIT-PRICE ANALYSIS OF “DEMAND” FOR FOOD IN BABOONS

In a study examining “demand” for food, responding of 8 adult male baboons (Papio c. anubis) was maintained under a fixed-ratio schedule of food reinforcement during daily 23-hr experimental sessions. Completion of the ratio requirement resulted in the delivery of one, five, or 10 1-g food pellets. Supplemental feeding was limited to fruit and a dog biscuit daily. Responding increased as “cost” was increased across a wide range of fixed-ratio values before reaching a maximum and then decreasing. Increasing the number of food pellets per delivery decreased total responding and the number of reinforcements per day. A unit-price analysis, in which intake was converted to grams per day and fixed-ratio values were converted to responses per gram, yielded demand functions that overlapped at lower unit prices. Under one or more multiple-pellet conditions, however, intake decreased more quickly than under the one-pellet condition as the fixed-ratio value was increased in all but 1 baboon. This indicates that even when using unit-price conversions, there was variability in total intake. Although unit-price conversions yielded intake data that were more consistent across conditions, conditions differed in response topography even at the same unit prices: Under the multiple-pellet conditions there were longer pauses in responding, running response rate was slower, and the first eating bout (i.e., “meal”) of the session was smaller than under the one-pellet condition. These findings (a) support the heuristic value of a unit-price analysis for studying responding for and consumption of commodities that have similar attributes, and (b) indicate that different response topographies may result in similar intakes of a commodity.     

Demand for food on fixed-ratio schedules as a function of the quality of concurrently available reinforcement

Six rats lever pressed for food on concurrent fixed-ratio schedules, in a two-compartment chamber. In one compartment, mixed diet pellets were delivered on fixed-ratio schedules of 1, 6, 11, and 16; in the other, either no food was delivered, or sucrose or mixed diet pellets were delivered on fixed-ratio 8. The number of pellets obtained in the first compartment declined as a function of fixed-ratio size in that compartment in all three conditions, but the decline was greatest overall with mixed diet pellets concurrently available in the other compartment, and least with no food concurrently available. The result is discussed in terms of economic demand theory, and is consistent with the prediction that elasticity of demand for a commodity (defined in operant terms as the ratio of the proportionate change in number of reinforcements per session to the proportionate change in fixed-ratio size) is greater the more substitutable for that commodity are any concurrently available commodities.     

Effects of economy type and nicotine on the essential value of food in rats

The exponential demand equation proposed by Hursh and Silberberg (2008) provides an estimate of the essential value of a good as a function of price. The model predicts that essential value should remain constant across changes in the magnitude of a reinforcer, but may change as a function of motivational operations. In Experiment 1, rats' demand for food across a sequence of fixed-ratio schedules was assessed during open and closed economy conditions and across one- and two-pellet per reinforcer delivery conditions. The exponential equation was fitted to the relation between fixed-ratio size and the logarithm of the absolute number of reinforcers. Estimates of the rate of change in elasticity of food, the proposed measure of essential value, were compared across conditions. Essential value was equivalent across magnitudes during the closed economy, but showed a slight decrease across magnitudes during the open economy. Experiment 2 explored the behavioral mechanisms of nicotine's effects on consumption with the results from Experiment 1 serving as a within-subject frame of reference. The same subjects were administered nicotine via subcutaneously implanted osmotic minipumps at a dose of 3 mg/kg/day and exposed to both the one- and two-pellet conditions under a closed economy. Although nicotine produced large decreases in demand, essential value was not significantly changed. The data from the present experiments provide further evidence for the adequacy of the exponential demand equation as a tool for quantifying the rate of change in elasticity of a good and for assessing behavioral mechanisms of drug action.     

The effects of differing response types and price manipulations on demand measures

Animals' behavioral needs have become an important component of animal welfare legislation. Behavioral economics provides a framework for the study of such needs. A function, analogous to a demand function relating consumption rate to price, can be obtained by increasing the price (or work) required for access to a commodity. This experiment investigated the effects of different response types and price manipulations on these functions. Six hens pushed a door or pecked a key for food under open economic conditions (short experimental sessions and supplementary food). In Part 1, the number of door pushes required (fixed-ratio schedule) was increased each session, and the force needed to push the door was increased across conditions. In Part 2, the force needed to push the door was increased session to session, and the fixed-ratio schedule was increased across conditions. In Part 3, the number of key pecks required was increased each session. Both response types produced similarly shaped (approximately linear in logarithmic coordinates and downward sloping) demand functions when price was increased by increasing the number of responses required. These imply an elastic demand for food under these conditions. In contrast, increasing the force required to push the door resulted in highly curvilinear functions. These functions indicated little change in consumption across lower door forces and abrupt drops in consumption at higher force requirements, implying mixed elasticity in the animals' demand for food. The differences between the shapes of the two functions seem to arise from the different ways that the two price manipulations alter the time taken to complete the work required. Increasing the fixed-ratio requirement necessarily increases the time needed to complete each response unit, whereas increasing the force requirement does not. The different shapes of the functions were robust when either force or number was varied across sessions and the value of the other was varied over conditions. They were also robust when the price increases were taken from different conditions, showing that the shapes of the functions were independent of the place in the experiment in which the price was examined. Unit price (which combines number and force into a single price measure) unified the data from the two price manipulations to a large degree, producing moderately curved functions. However, there was some variance around the unit price functions, and this was attributable to the different shapes of the underlying functions. The data suggest that different price manipulations may give different measures of animal demand but that unit price might provide some unification.     

Second-order schedules of token reinforcement with pigeons: implications for unit price

Four pigeons were exposed to second-order schedules of token reinforcement, with stimulus lights serving as token reinforcers. Tokens were earned according to a fixed-ratio (token-production) schedule, with the opportunity to exchange tokens for food (exchange period) occurring after a fixed number had been produced (exchange-production ratio). The token-production and exchange-production ratios were manipulated systematically across conditions. Response rates varied inversely with the token-production ratio at each exchange-production ratio. Response rates also varied inversely with the exchange-production ratio at each token-production ratio, particularly at the higher token-production ratios. At higher token-production and exchange-production ratios, response rates increased in token-production segments closer to exchange periods and food. Some conditions were conducted in a closed economy, in which the pigeons earned all their daily ration of food within the session. Relative to comparable open-economy conditions, response rates in the closed economy were less affected by changes in token-production ratio, resulting in higher levels of food intake and body weight. Some of the results are consistent with the economic concept of unit price, a cost-benefit ratio comprised of responses per unit of food delivery, but most are well accounted for by a consideration of the number of responses required to produce exchange periods, without regard to the amount of reinforcement available during those exchange periods.     

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.     

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.     

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.     

Quantification of rats' behavior during reinforcement periods

What is treated as a single unit of reinforcement often involves what could be called a reinforcement period during which two or more acts of ingestion may occur, and each of these may have associated with it a series of responses, some reflexive, some learned, that lead up to ingestion. Food-tray presentation to a pigeon is an example of such a “reinforcement period.” In order to quantify this behavior, a continuous-reinforcement schedule was used as the reinforcement period and was chained to a fixed-ratio schedule. Both fixed-ratio size and reinforcement-period duration were manipulated. Rats were used as subjects, food as reinforcement, and a lever press as the operant. Major findings included (a) a rapid decline in response rates during the first 15 to 20 seconds of the reinforcement periods, and (b) a strong positive relationship between these response rates and the size of the fixed ratio. Also revealed was a short scallop not normally found in fixed-ratio response patterns, whose length was a function of fixed-ratio size and reinforcement-period duration. It is suggested that rapidly fluctuating excitatory processes can account for many of these findings and that such processes are functionally significant in terms of behavioral compensation.     

Ratio size and cocaine concentration effects on oral cocaine-reinforced behavior.

Monkeys were given a choice between cocaine solutions and water under concurrent fixed-ratio reinforcement schedules. The operant response was spout contact. Six rhesus monkeys served as subjects. The cocaine concentration was varied from 0.0125 to 0.8 mg/ml, and the fixed-ratio value was varied from 8 to 128. Cocaine maintained higher response rates than did water over a wide range of conditions. Response rate and number of cocaine deliveries per session were inverted U-shaped functions of concentration. These functions were shifted to the right as the fixed ratio was increased. The number of cocaine deliveries was more persistent as fixed-ratio value was increased when the unit dose was larger rather than smaller. Cocaine consumption was analyzed as a function of unit price (fixed-ratio value divided by cocaine concentration), and unit price accounted for between 77% and 92% of the variance in cocaine consumption for individual monkeys. The current data support the claim that a drug's reinforcing effects increase directly with dose and underscore the need to gather parametric data when examining the effects of experimental manipulations on a drug-reinforced baseline.     

Modifying drug-reinforced behavior by altering the economic conditions of the drug and a nondrug reinforcer.

Six rhesus monkeys were trained to self-administer orally delivered phencyclidine (0.25 mg/mL) and saccharin (0.03% wt/vol) under concurrent fixed-ratio 16 schedules. In Condition 1 the fixed-ratio requirement for phencyclidine was changed from 16 to 4, 8, 16, 32, 64, 128 and 16 while the fixed-ratio requirement for saccharin deliveries remained constant at 16. In Condition 2 the fixed-ratio value for saccharin was systematically altered while the fixed-ratio requirement for phencyclidine remained at 16, and in Condition 3 the fixed-ratio requirements for both phencyclidine and saccharin were altered simultaneously. Water was then substituted for saccharin, and the series of fixed-ratio manipulations was replicated. The phencyclidine concentration was reduced to 0.125 mg/mL and Conditions 1 and 3 were repeated. When the fixed-ratio requirement for phencyclidine was increased and the fixed-ratio requirement for saccharin or water remained fixed at 16, phencyclidine deliveries decreased when saccharin (vs. water) was concurrently available. The magnitude of the decrease ranged from 20% to 90% (of the concurrent water condition) as the fixed-ratio requirement for phencyclidine increased from 4 to 128. When the fixed-ratio requirement for phencyclidine remained at 16 and the fixed-ratio requirements for concurrent saccharin or water varied between 4 and 128, phencyclidine deliveries decreased by 30% to 40% due to the concurrent availability of saccharin (vs. water). This decrease occurred only at the three lowest fixed-ratio values when saccharin intake was relatively high. When the fixed-ratio requirements for both phencyclidine and concurrent saccharin or water were varied simultaneously, phencyclidine deliveries were reduced from 20% to 45% when saccharin (vs. water) was concurrently present. There was little effect of reducing the phencyclidine concentration when the data were analyzed in terms of unit price (responses per milligram). Thus, changes in the fixed-ratio requirement or drug concentration were functionally similar, and unit price of phencyclidine was the variable that was influenced by the presence of concurrent saccharin. These data indicate that drug-reinforced behavior is substantially reduced when the environment is enriched with an alternative nondrug reinforcer. The economic context in which these substances are presented is an important determinant of drug-reinforced behavior.     

An experimental analysis of the cost of food in a closed economy.

Rats lived in individual chambers in which the only food available was delivered for lever pressing. During Stage I, a fixed number of presses was required for each food pellet. As this fixed ratio of presses per food pellet was increased daily, a rat's daily intake of food was reduced. During Stage II, the cost of a food pellet was increased by replacing each fixed ratio with its interval equivalent. Each interval was a rat's mean time between the first press of a ratio and the delivery of a pellet during Stage I. During Stage II, only two presses were every required for a food pellet: The first press initiated a delay and the second activated the pellet dispenser after that delay elapsed. Food intakes for the series of fixed ratios and a rat's series of delay equivalents were very similar when plotted as a function of delay, but not when plotted as a function of presses per pellet. Consequently, the fixed ratio reduced food intake because larger ratios increased delay to food from the first press of a ratio. Observations and an analysis of interresponse times further revealed that as the fixed ratio increased, and local as well as overall rate of food intake decreased, lever pressing became more stereotyped. Because this increased stereotypy resulted in greatly increased rates of lever pressing, delay to food was minimized, and perhaps more importantly, so too was the reduction of a rat's baseline daily intake.     

The relationship between feeding rate and patch choice.

Rats in a laboratory foraging simulation searched for sequential opportunities to feed in two patches that differed in the rate at which food pellets were delivered (controlled by fixed-interval schedules) and in the size of the pellets. The profitability of feeding in each patch was calculated in terms of time (grams per minute) and in terms of effort (grams per bar press). These values were the result of the imposed fixed interval, the size of the pellets, and the rate at which the rats pressed the bar in each condition. The rats ate more food and larger meals, but not more frequent meals, at the patch offering the higher rate of food consumption, calculated as grams per minute. The relative intake at any patch was a function of the relative rate of intake during meals at that patch compared to the other patch. Rats respond to explicit manipulations of feeding time in the same manner as they respond to manipulations of feeding effort.     

Food and water intake as functions of resource consumption costs in a closed economy.

In two experiments, rats living in a closed economy were offered continuous, concurrent access to four resources: food, water, a nest, and a running wheel. Costs of consuming food and water were imposed with bar-press requirements, and the price of either one or both resources was raised. As the consumption cost increased, less was consumed in each bout of resource use. Bout frequency increased, but not sufficiently to compensate for the fall in bout size, and total intake fell. Food and water tended to be complementary resources, in that as intake of one fell with its price, intake of the other also decreased. This interaction was accounted for by the defense of the ratio of body water to lean body mass. As amount consumed decreased, increases in feed efficiency (weight gain per unit of food ingested) and the use of stored calories compensated for the reduced energy intake. There was evidence of competition between feeding and drinking at the higher costs: When both commodities were expensive, the decline in the intake of each one was greater than when only one commodity was expensive. Although the time spent nesting, running, and in unmonitored activity was adjusted when feeding or drinking took more of the rat's day, there was no particular activity that was sacrificed.     

Choice for aperiodic versus periodic ratio schedules: A comparison of concurrent and concurrent-chain procedures

Choice between mixed-ratio schedules, consisting of equiprobable ratios of 1 and 99 responses per reinforcement, and fixed-ratio schedules of food reinforcement was assessed by two commonly used procedures: concurrent schedules and concurrent-chains schedules. Rats were trained under concurrent fixed-ratio mixed-ratio schedules, in which both ratio schedules were simultaneously available, and under a concurrent-chains schedule, in which access to one of the mutually exclusive ratio schedules comprising the terminal links was contingent on a single “choice” response. The distribution of responses between the two ratio schedules was taken as the choice proportion under the concurrent procedure, and the distribution of “choice” responses was taken as the choice proportion under the concurrent-chains procedure. Seven of eight rats displayed systematic choice; of those, each displayed nearly exclusive choice for fixed-ratio 35 to the mixed-ratio schedule under the concurrent procedure, but each displayed nearly exclusive choice for the mixed-ratio schedule to fixed-ratio 35 under the concurrent-chains procedure. Thus, preference for a fixed or a mixed schedule of reinforcement depended on the procedure used to assess preference.     

Tests of behavioral-economic assessments of relative reinforcer efficacy II: economic complements

This experiment was conducted to test the predictions of two behavioral-economic approaches to quantifying relative reinforcer efficacy. The normalized demand analysis suggests that characteristics of averaged normalized demand curves may be used to predict progressive-ratio breakpoints and peak responding. By contrast, the demand analysis holds that traditional measures of relative reinforcer efficacy (breakpoint, peak response rate, and choice) correspond to specific characteristics of non-normalized demand curves. The accuracy of these predictions was evaluated in rats' responding for food or water: two reinforcers known to function as complements. Consistent with the first approach, predicted peak normalized response output values obtained under single-schedule conditions ordinally predicted progressive-ratio breakpoints and peak response rates obtained in a separate condition. Combining the minimum-needs hypothesis with the normalized demand analysis helped to interpret prior findings, but was less useful in predicting choice between food and water--two strongly complementary reinforcers. Predictions of the demand analysis had mixed success. Peak response outputs predicted from the non-normalized water demand curves were significantly correlated with obtained peak responding for water in a separate condition, but none of the remaining three predicted correlations was statistically significant. The demand analysis fared better in predicting choice--relative consumption of food and water under single schedules of reinforcement predicted preference under concurrent schedules significantly better than chance.     

Oral self-administration of pentobarbital by rhesus monkeys: maintenance of behavior by different concurrently available volumes of drug solution.

For 4 rhesus monkeys, mouth-contact responses with either of two brass spouts were reinforced according to fixed-ratio schedules by 0.65-mL liquid deliveries during daily 3-hr sessions. Three experiments were conducted. In each experiment, independent fixed-ratio schedules were concurrently in effect at the two spouts. Following completion of each fixed ratio on a spout, a specified number of liquid deliveries were available from that spout under a continuous-reinforcement schedule. The number of such deliveries available at each spout was manipulated independently. In Experiment 1, a 1-mg/mL pentobarbital solution was simultaneously available with water (the drug vehicle) under concurrent fixed-ratio schedules of 32 responses for 3 subjects and 64 responses for the remaining subject. The number (N) of liquid deliveries that were available after completion of each fixed ratio was varied in the following order: 8, 4, 2, 1, and 8 (retest). For each subject at each condition, drug maintained more responding than water. The number of drug deliveries obtained per session was directly related to the amount of drug available per fixed ratio (i.e., to N), whereas the number of fixed ratios completed per session generally was inversely related to the value of N. In Experiment 2, fixed-ratio size was the same for each subject as in Experiment 1, but deliveries of a 1-mg/mL pentobarbital solution were available at both spouts. The number of drug deliveries available under one fixed-ratio schedule (Ns, the "standard" reinforcer amount) was held at eight, and the number of drug deliveries available under the second schedule (Nc, the "comparison" reinforcer amount) was changed across blocks of six sessions of stable responding in the following order: 1, 2, 4, 8, 4, 2, and 1. The identical series of comparison reinforcer amounts (Nc) was then tested twice more, but with the standard reinforcer (Ns) held first at four and then at two deliveries. Across the three choice series, reinforcing effects were directly related to reinforcer magnitude. In Experiment 3, deliveries of a 1-mg/mL pentobarbital solution again were available at both spouts. However, the two reinforcer amounts were held constant at N = 8 deliveries under one schedule and N = 4 deliveries under the second schedule, and fixed-ratio size was systematically varied. Across the range of fixed-ratio sizes from low to high, the degree to which behavior was better maintained by the larger of the two drug quantities was an inverted U-shaped function of fixed-ratio size.(ABSTRACT TRUNCATED AT 400 WORDS)