b,/(b. + by) = r./(r, + ry), (1)

JOURNAL OF THE EXPERIMENTAL ANALYSIS OF BEHAVIOR

THE SUBSTITUTABILITY OF REINFORCERS

LEONARD GREEN AND DEBRA E. FREED

WASHINGTON UNIVERSITY

Substitutability is a construct borrowed from microeconomics that describes a continuum of possibleinteractions among the reinforcers in a given situation. Highly substitutable reinforcers, which occupyone end of the continuum, are readily traded for each other due to their functional similarity. Com-plementary reinforcers, at the other end of the continuum, tend to be consumed jointly in fairly rigidproportion, and therefore cannot be traded for one another except to achieve that proportion. At thecenter of the continuum are reinforcers that are independent with respect to each other; consumptionof one has no influence on consumption of another. Psychological research and analyses in terms ofsubstitutability employ standard operant conditioning paradigms in which humans and nonhumanschoose between alternative reinforcers. The range of reinforcer interactions found in these studies ismore readily accommodated and predicted when behavior-analytic models of choice consider issues ofsubstitutability. New insights are gained into such areas as eating and drinking, electrical brainstimulation, temporal separation of choice alternatives, behavior therapy, drug use, and addictions.Moreover, the generalized matching law (Baum, 1974) gains greater explanatory power and com-prehensiveness when measures of substitutability are included.Key words: microeconomics, choice, substitutability of reinforcers, generalized matching law

The conceptualization of the nature of re-inforcers continues to expand. Reinforcers, longviewed as fixed stimulus events that simplystrengthen any response upon which they werecontingent, came to be understood as occurringwithin a context. Originating with Premack's(1965) probability-differential response the-ory of reinforcement, the behavioral view ofreinforcement broadened as response depri-vation (Timberlake & Allison, 1974), conser-vation of behavior (Allison, Miller, & Wozny,1979), and disequilibrium (Timberlake, 1980,1984) theories were elaborated. Herrnstein'smatching law (1961, 1970), which predicts thata given activity is influenced not only by thereinforcers contingent upon it but also by otherreinforcers within the situation, made explicitthe role that context plays in understandingreinforcement effects. The nature of reinforc-ers has been elaborated further by incorpo-rating economic principles, specifically that ofsubstitutability, into behavioral analyses in or-der to account for behavior when the outcomes(reinforcers) are not qualitatively identical(Rachlin, Battalio, Kagel, & Green, 1981;

We thank Howard Rachlin and William Timberlakefor their useful comments and suggestions, Joel Myersonfor his critique of an earlier version of this paper, andHeather Rehberg for making us aware of the literatureon social support and risk behavior. Requests for reprintsshould be addressed to Leonard Green, Department ofPsychology, Washington University, Campus Box 1125,St. Louis, Missouri 63130.

Rachlin, Green, Kagel, & Battalio, 1976). In-deed, it is reasonable to suggest that an ade-quate understanding of the interactions amongreinforcers and their influence on behavior isnot possible without a consideration of sub-stitutability. Moreover, this understanding willundoubtedly have implications for areas suchas choice, behavior therapy and behaviorchange, and the nature of addictions.The goal of the present paper is to bring

together the experimental psychological liter-ature on substitutability and, in so doing, dem-onstrate the importance of including economicanalyses, theory, and research in the psycho-logical study of choice and the understandingof the nature of reinforcement.

SUBSTITUTABILITYTraditionally, knowledge of the properties

of reinforcers was derived from examining theeffects of a single reinforcer on a single activity(e.g., Berlyne, 1969; Hull, 1943; Logan, 1960).Herrnstein's (1961, 1970) formalization of thematching law was revolutionary because itmade explicit the relativistic nature of rein-forcers; that is, the effect of a reinforcer isdependent upon the context of other reinforc-ers in which it appears. The matching lawstates:

B,/(B. + By) = R./(R, + Ry), (1)where B is some behavior, expressed in units

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1993, 609 141-158 NUMBER 1 (JULY)

LEONARD GREEN and DEBRA E. FREED

of either responses or time, allocated to alter-natives x and y, and R represents the rein-forcers obtained from that behavior. Expressedas a ratio,

BX/BY = Rx/RY- (2)

Following from this relation is the notionthat the effect of a given reinforcer is alwayscontext dependent; in other words, there arealways other reinforcers in an animal's currentenvironment from which to choose. By impli-cation, then, all behavior can be construed aschoice (Herrnstein, 1970). This can be derivedfrom Equation 1 as follows:

Bx= [(Bx + BY)Rx]/(Rx + Ry).Replacing the quantity (B. + By) with k, weobtain

Bx = kRx/(Rx + Ry). (3)

Furthermore, the specific source of reinforce-ment, Ry, may be more generally understoodas the "unknown, aggregate reinforcementf[rom] other alternatives" (Herrnstein, 1970,p. 255) and be represented as RO; Bo, then,would represent all behavior allocated to thosealternatives. This yields the following equa-tion:

Bx= kRx/(Rx + Ro)) (4)

where k now replaces the quantity (Bx + Bo).Thus, the effects of a given reinforcer (Rx) onan activity (Bx) are necessarily modulated bycontext (RO). Given that the effect of a rein-forcer cannot be understood apart from its re-lation to other reinforcers, the study of rein-forcer interactions is of paramount importance.

Behavior analysts have focused primarily oninvestigating the interactions of reinforcers thatdiffer in their frequency, amount, delay, orprobability. Rarely, however, have the inter-actions of reinforcers that differ along a qual-itative dimension been examined. It is to thislargely unexplored issue that consumer de-mand theory-specifically, the concept of sub-stitutability-is particularly relevant. Psy-chologists' study of animals choosing betweenreinforcers has a direct analogue to economists'study of consumers choosing between com-modities. Consequently, economic principlesregarding the relationship between commod-ities should be equally germane to the inter-actions of reinforcers.

Substitutability is not a property of a single

good, but rather is a characteristic of the re-lationship between commodities or reinforcers;thus, substitutability describes a continuum ofpossible interactions among reinforcers. Per-fect substitutability and perfect complemen-tarity define the ends of the continuum, withindependence falling between the two. Rachlin(1989) discusses substitutabilityin terms of theextent to which two commodities are quali-tatively similar. However, two commoditiesmay share many qualitative similarities yet notbe substitutable. For example, oranges andtennis balls are similar with regard to size,shape, weight, and firmness but quite dissim-ilar with respect to nutritional value. Are or-anges and tennis balls substitutable or not? Itdepends. For the purposes ofjuggling, orangesand tennis balls are relatively good substitutes;however, when it comes to eating, tennis ballsand oranges are highly nonsubstitutable. Con-sequently, a general definition of substitut-ability must take into account the function ofthe commodities in question. To this end, sub-stitutable goods may be defined as those thatserve similar purposes (Baumol, 1972). Somecommon examples of relatively substitutablegoods include raincoats and umbrellas, Coke®and Pepsi®, and zippers and buttons.

But what of goods that do not serve similarpurposes? Goods that are not functionally sim-ilar may be either complementary or indepen-dent commodities. When two commodities areused jointly, these goods can be consideredcomplementary (Baumol, 1972). Comple-ments might include commodities such as ba-gels and cream cheese, kites and string, paintand canvases. However, some pairs of com-modities are neither substitutes nor comple-ments, but rather are independent goods. Re-turning to our previous example, oranges andtennis balls are usually independent commod-ities (except when it comes to juggling). Ofcourse, a good need not serve only one function.Thus, substitutes and complements are notfixed categories or points on a continuum.

Substitutability and complementarity can bejudged by the degree to which consumption ofone commodity changes as the value of an al-ternative commodity is altered. (See Samuel-son, 1974, for a discussion of six tests for sub-stitutability and complementarity thathistorically have been attempted, none of whichneed be incompatible with the informal defi-nition given here.) For both substitutable andcomplementary goods, altering the price of one

SUBSTITUTABILITY OF REINFORCERS

commodity in a pair produces specifiablechanges in consumption of both commodities:If the price of one commodity were to decrease,its consumption would increase while that ofits substitute would decrease, whereas con-sumption of its complement would increase.For independent goods, altering the price ofone commodity has little or no effect on con-sumption of the other (Schwartz, 1989).

Substitutability may be understood in termsof Figure 1. The solid line is a budget con-straint determined by the price of CommoditiesX and Y and total income available. The filledcircle on the solid line represents one possible"package" of Commodities X and Y chosen.The dashed line is a new budget constraintimposed by decreasing the price of CommodityY and increasing the price of Commodity X.In economic terms, the dashed line representsan income-compensated price change from thesolid line. Under an income-compensated pricechange, total income is adjusted to keep realincome constant so that the identical packageof commodities can still be obtained under thenew set of prices as was obtained under theprevious budget constraint. The same packagecan be chosen under the new budget becausethis line passes through the filled circle-thepreviously chosen combination of X and Y.Consequently, any change in consumption ofthe two commodities must be due to the dif-ference in the slopes of the two budget con-straint lines. If the price of one commoditywere decreased without adjusting total income(i.e., a noncompensated price change), then theamount of real income available would in-crease. A change in the consumption of thecommodities, then, might reflect an increase inreal income, a substitution effect, or both.However, when income is adjusted to keep realincome constant as prices are changed, theoriginal package of commodities may still bepurchased at the new prices. Therefore, anychange in consumption from that originalpackage is indicative of a substitution effectrather than an income effect. (See Green, Ka-gel, & Battalio, 1982, for further explanation.)The degree of substitutability between the twocommodities shown in Figure 1 is representedby the degree to which consumption shifts inthe direction of the other symbols, with thetriangle, square, and cross representing in-creasing degrees of substitution from Com-modity X into the made-cheaper (relatively)Commodity Y. (For a fuller description, in-

>- \

0 \02

0IL60

h

AMOUNT OF COMMODITY XFig. 1. An economy in which Commodities X and Y

may be purchased. The solid line represents a budgetconstraint as determined by the prices of the two com-modities, X and Y, and total income. The filled circlerepresents one possible "package" of X and Y purchased.The dashed line shows another budget constraint deter-mined by decreasing the price of Commodity Y and in-creasing the price of Commodity X. This budget con-straint, referred to as an income-compensated price change(see text for a more detailed explanation), is selected sothat it passes through the filled circle, thus allowing thesubject to obtain amounts of both commodities identical tothose obtained under the original budget constraint. Thetriangle, square, and cross on the dashed line representsuccessively greater degrees of substitutability of Com-modity Y for Commodity X.

volving, as it must, the details of indifferencecontours, see Rachlin, 1989.)

Consider the following hypothetical exam-ple. If the price of Coke were to remain con-stant while the price of Pepsi were to decrease,we would expect a large decrease in con-sumption of Coke, assuming that Coke andPepsi were highly substitutable. If, in fact,Coke and Pepsi were perfect substitutes, thenfor every amount, X, of Coke given up, con-sumption of Pepsi would increase by amountpX (Allison, 1989).1 Conversely, decreasing

I The constant p allows that the exchange between per-fect substitutes may not necessarily be in the ratio of 1:1.For example, if both Coke and Pepsi came in 1 6-oz bottles,then for every bottle of Coke given up, consumption ofPepsi would increase by one bottle and the exchange wouldbe in the ratio of 1:1. However, if Coke came only in 16-oz bottles and Pepsi came only in 12-oz bottles, then forevery bottle of Coke given up, consumption of Pepsi wouldincrease by 1.33 bottles-an exchange ratio of 1:1.33.

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the price of Pepsi might produce an increasein consumption of Doritoss even though theprice of Doritos had not changed, because softdrinks and snack foods tend to be consumedjointly. Finally, decreasing the price of Pepsiwould probably have little effect on the con-sumption of automobiles; these two commod-ities are independent.One reason that substitutability has received

little attention in the operant conditioning lit-erature may be the fact that psychological stud-ies of choice have, almost exclusively, exam-ined the effects of variables that control choicebetween qualitatively similar (usually identi-cal), and therefore substitutable, reinforcers.A typical choice experiment involves hungrypigeons choosing between identical food re-inforcers that differ in their frequency, dura-tion, delay, or probability. Hursh and Bauman(1987) have suggested that this is akin tostudying consumer behavior in a store that sellsonly one product.

Economists, on the other hand, have for themost part studied the interactions among non-substitutable commodities. However, theiranalyses have taken place in the absence ofempirical tests with individual animals (Hursh& Bauman, 1987). Psychologists recently havebegun to fill this gap predominantly, althoughnot exclusively, by studying nonhuman sub-jects, and in so doing have found cause to revisetheir theories of choice and reinforcement.The value of integrating economic with psy-

chological analyses that incorporate substitut-ability is evident from Hursh's (1991) consid-eration of the use of methadone in the treatmentof heroin abuse. Methadone treatment has beena common form of therapy for heroin addicts.However, the extent to which methadone willeffectively decrease heroin use is dependent onhow substitutable methadone is for heroin.Methadone is less than perfectly substitutablefor heroin for a variety of reasons. One of theseis that methadone is administered in doses de-signed specifically not to induce the same de-gree of euphoria as heroin. Moreover, meth-adone, because it is dispensed at regularintervals in a clinical setting rather than "ondemand," is not as readily available as heroin.(And, as we will discuss in a later section,temporal separation between two otherwiseidentical reinforcers reduces the degree to whichthey are substitutable.) The lack of comple-ments may be another variable that strongly

attenuates the degree of substitutability be-tween methadone and heroin. Heroin is fre-quently administered as part of an elaboratesocial ritual that may function as a complementto drug taking. "To the extent that the sub-stitute, methadone, must be consumed in aclinical, nonsocial environment, its value willbe diminished as an adequate substitute forheroin because it is not accompanied by im-portant complementary social reinforcers"(Hursh, 1991, p. 384).

PSYCHOLOGICAL STUDIES OFSUBSTITUTABILITY

In one early examination of substitutability(Kagel et al., 1975; Rachlin et al., 1976), rats'responding for two different reinforcers (eitherroot beer and Tom Collins mix or food andwater) was studied under concurrent fixed-ratio (conc FR) schedules of reinforcement.Each of the two reinforcers was associated witha unique response lever and FR requirement.However, unlike the short-duration sessions ofmore typical operant experiments, the rats livedin the experimental chamber and were limitedto a fixed number of lever presses in a given24-hr period. This paradigm has obvious par-allels to an economy: The pairs of reinforcersconstitute different commodities, the FR re-quirements determine the price of each good,and the total number of level presses allottedspecify the rat's income. Thus, it is possible tostudy substitution effects between differentcommodities with rats as consumers.

Each set of prices and income constitutedan experimental condition. The Tom Collins/root beer rats initially had an income of 300lever presses, and the price of both the TomCollins and root beer was an FR 1 scheduledelivering 0.05 mL of fluid. As can be seen inFigure 2 (top and middle graphs, Budget Line1), both rats strongly preferred root beer toTom Collins. In the next condition, the priceof Tom Collins was halved (by doubling theamount delivered each time) and the price ofroot beer was doubled while the income of eachrat was adjusted so that it could still obtainthe same combination of root beer and TomCollins as it had in the first condition. Thisincome-compensated price change is repre-sented by Budget Line 2 in the top and middlegraphs. In this second condition, the rats con-

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25 .sumed much more of the now-cheaper Tom', Rat 1 Collins mix than the more expensive root beer.

When prices and income were returned to their20i * initial baseline values, consumption likewise

returned to or near baseline levels (not shown15 in Figure 2). When for Rat 1 the price of rootW

_ beer was halved, the price of Tom Collins_ 10 doubled, and total income again adjusted so0 that baseline amounts could still be obtained0 5 (Budget Line 3 in the top graph), consumption

of the cheaper root beer increased while con-,13 1 sumption of the more expensive Collins de-

0- creased, with the rat now consuming 10 times0 5 10 15 2D 25 30 as much root beer as Tom Collins. As Rachlin

TOM COLLINS MIX (ml) et al. (1976) suspected, root beer and TomCollins proved to be highly substitutable com-modities: When the price of one liquid was

25- increased, consumption of that liquid de-Rat 2 creased and consumption of the alternative

drink increased. It is important to note thatE these substitution effects occurred indepen-

dently of preference-when the price of rootIY 15--_ beer and Tom Collins was equal, root beerffi \ ~~-_ was the highly preferred commodity, yet that

10- \ ~ ~ -__ preference was eliminated entirely when theO 10 - price of root beer was increased.0 The same basic procedure was also used to

5 examine the degree of substitutability between\1 food and water. At baseline (Figure 2, bottom

0 5 1 1 graph, Budget Line 1), Rat 3 had an income0| 5 10 15 S 25 30)of 2,500 presses, the price of five food pellets

TOM COLLINS MIX (ml) was 10 presses, and the price of 0.10 mL ofwater was 10 presses. In the next condition, theprice of food was increased 67% (10 pressesnow delivered three food pellets), while incomewas also increased so as to allow baseline

Rat 3amounts of food and water to be purchased

\ Rat 3 (Budget Line 2). Although a slight shift inconsumption in the direction of the relativelycheaper water did occur, this shift was con-siderably less dramatic than that in the TomCollins/root beer case, providing support that

8 Xfood and water are highly nonsubstitutable and,

0 in fact, relatively complementary goods.0U20 Hursh (1978) provided further evidence that

10 ~.

1 %%%2

0 graphs present the combinations of root beer and Tom0 5 10 15 z25 30 Collins chosen by Rats 1 and 2, respectively; the bottom

WATER (m) graph shows the combinations of food and water chosenby Rat 3. Baseline budget conditions are represented by

Fig. 2. Individual rats' data under different budget solid lines (Line 1), and income-compensated price changesconstraints in which the commodities were root beer and are represented by the dashed lines. (Adapted from KagelTom Collins mix or food and water. The top and middle et al., 1975, and Rachlin et al., 1976.)

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Table 1Responses and reinforcers per hour for the constant food and water as the frequency of thealternative food was varied. Data are from Hursh's (1978) Experiment 1 (closed economy) andExperiment 2 (open economy).

Closed economy Open economy(Experiment 1) (Experiment 2)

Alternative Responses/hr Reinforcers/hr Responses/hr Reinforcers/hrfood Constant Constant Constant Constant

Subject schedule (VI) food Water food Water food Water food Water

SM2 4,668 275 58 44 -480 3,808 612 58 47 3,196 543 57 46240 3,449 610 58 46 3,428 716 56 47120 1,518 1,968 56 52 2,576 690 57 4360 734 2,652 49 55 2,088 1,085 56 5130 288 3,888 40 58 2,209 697 59 47

SM3 1,891 183 32 34480 1,578 403 60 52 2,241 613 59 53240 1,171 730 57 54 2,586 552 55 45120 444 1,173 50 55 2,113 168 57 3360 264 1,046 36 54 1,983 293 56 4030 241 2,095 25 61 1,112 381 57 51

food and water are complements in a pair ofexperiments with rhesus monkeys. Identicalfood pellets were available for responding ontwo levers; water was available for respondingon a third lever. The water and one food source(the constant food) were always available onvariable-interval (VI) 60-s schedules, while therate of access to the alternative food sourcevaried from VI 30 s to VI 480 s across con-ditions. In one condition, no alternative foodsource was available. If the alternative food issubstitutable for the constant food, then re-sponding for and consumption of the constantfood should decrease as the alternative foodincreases in frequency. If the alternative foodis a complement for water, then respondingfor and consumption of the water are expectedto increase with increased availability of thealternative food.The first experiment studied the monkeys

under a closed economy. In a closed economy,the subjects earn their total daily consumptionof the reinforcers during the experimental ses-sion. No postsession feeding is given (Hursh,1980). Hursh found that the presence of thealternative food resulted in decreased respond-ing for the constant food but increased re-sponding for the water: As shown in Table 1,when the alternative food was introduced ona VI 480-s schedule, SM2 decreased respond-ing for the constant food by 18% and increased

responding for water by 123%. SM3 demon-strated a similar pattern, decreasing its re-sponding by 17% for the constant food andincreasing its responding by 120% for waterwhen the alternative food was added on a VI480-s schedule.

Furthermore, changes in the frequency withwhich the alternative food was obtained pro-duced direct changes in responding for andconsumption of the water, but produced in-verse changes in responding for and consump-tion of the constant food. Thus, when the al-ternative food was made more readily available,the monkeys reduced responding for and con-sumption of the constant food and substitutedinto the now-cheaper alternative, but increasedresponding for and consumption of the water,even though its availability had not changed.This result is clearly demonstrated in the com-parison of response rates when the alternativefood was changed from a VI 480-s scheduleto a VI 30-s schedule: SM2 reduced its re-sponding for the constant food by 92% andincreased its responding for water by 535%;similarly, SM3 reduced its responding for theconstant food by 85% and increased its re-sponding for water by 420%. Similar, thoughless dramatic, patterns of change occurred inconsumption rates (reinforcers per hour). In-creasing the rate of the alternative food fromVI 480 s to VI 30 s reduced consumption of

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the constant food by 31% for SM2 and by 58%for SM3; consumption of water increased by23% and 17% respectively.

In Hursh's (1978) second experiment, thesame monkeys were exposed to the conditionsof an open economy under which consumptionof food and water was held constant acrosssessions. That is, total daily intake of food andwater was regulated by consumption both dur-ing experimental sessions and by postsessionfeedings. In short, deprivation was constantfrom session to session (Hursh, 1980). There-fore, unlike the closed economy, daily intakeof food and water was not determined exclu-sively by the monkeys' interactions with theexperimental contingencies. In all other re-spects, however, the procedures replicated thoseof the first experiment.

This experiment demonstrated that substi-tutes and complements are differentially af-fected by economy type. In this open economy,responding for the constant food decreasedmuch less sharply compared to that in the closedeconomy as the frequency of the alternativefood increased. As shown in Table 1, as thefrequency of the alternative food was increasedfrom VI 480 s to VI 30 s, SM2 decreasedresponding for the constant food by 31%, andSM3 decreased its responding by 50%.Whereas responding for water had increasedwith increases in the frequency of the alter-native food under the closed economy, the openeconomy produced no consistent changes inwater responding or water consumption as thefrequency of the alternative food source varied.This pattern of results suggests that respond-ing for substitutable (or at least identical) com-modities is not as strongly affected by the "eco-nomic conditions of daily consumption"(Hursh, 1978, p. 475) as is responding forcomplementary commodities. That is to say,responding for the constant food showed qual-itatively similar changes under both open andclosed economies, whereas responding for thewater was affected differently by the open andclosed economies as the frequency of the al-ternative food was varied.What is it about the open economy that

brought about such minimal effects on re-sponding for water? One possibility is that theavailability of postsession water increased thedemand elasticity of water during the session(Hursh, 1980). Demand elasticity can bethought of as the degree to which consumption

of a commodity is affected by changes in pricefor that commodity. If demand is elastic, thenconsumption is strongly influenced by changesin price. If, however, demand is inelastic, thenconsumption is relatively unaffected by changesin price. One of the factors influencing demandelasticity is the availability of substitutes (Al-lison, 1986). In the open economy the postses-sion water provided a substitute-albeit a tem-porally distant one-for the water availableduring the session, thus resulting in the in-creased demand elasticity of water. Stated dif-ferently, in the closed economy the monkeysworked to defend a certain "water balance"or ratio of water to food, thereby increasingresponding for water when more food wasavailable. In the open economy, however, thewater balance did not have to be so stronglydefended through responding because a con-stant daily intake was maintained via postses-sion access to water (Hursh, 1984).

It is worth noting that a complementaryrelationship has not always been obtained be-tween food and water. Allison and Mack (1982)demonstrated that within a closed economy,food and water can serve as complements un-der some circumstances but can serve as sub-stitutes under others. In one experiment, ratswere permitted free access to food and waterduring a baseline phase. In subsequent phases,the rats continued to have free access to water,but food delivery was arranged through fixed-time (FT) schedules such that the total amountof food delivered was less than that consumedduring the baseline phase. These conditionsproduced the familiar schedule-induced poly-dipsia: The rats consumed substantially greaterquantities of water than they had during base-line and made a greater number of licks. More-over, an interesting substitution effect was alsoevident: As total food intake was increased un-der the FT schedules (but kept below baselinelevels), the total number of water licks de-creased linearly. In terms of Allison's (1976)conservation model, water consumption roseabove baseline because drinking had some sub-stitute value for the experimentally suppressedeating behavior.

In their Experiment 4, Allison and Mack(1982) ascertained whether eating and drink-ing are mutually substitutable-even thoughdrinking was shown to be substitutable foreating, such a result need not imply that eatingis substitutable for drinking. To this end, rats

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were exposed to FT schedules of water deliv-ery with food now freely available, followinga baseline phase of free access to both the foodand water. The FT schedules of water deliveryrestricted water intake below baseline levels.Unlike the first experiment, clear complemen-tarity was evident: Food intake decreased aswater intake decreased. According to Allisonand Mack, these results indicate that eatingand drinking are substitutable when eating issuppressed (increases in water intake can helpalleviate hunger) but are complementary whendrinking is suppressed (dry food cannot alle-viate thirst).

Rachlin and Krasnoff (1983) confirmed thisasymmetry in substitutability effects betweenfood and water. They studied rats deprived ofeither food or water in an open economy. Dur-ing 3-hr sessions, food-deprived rats had freeaccess to water, but could have either free orrestricted (via variable-time [VT] schedules)access to food. Similarly, water-deprived ratshad free access to food, but access to water waseither continuous or determined by VT sched-ules. With regard to their major findings,Rachlin and Krasnoff's results verified thoseof Allison and Mack (1982). Under conditionsof food deprivation, rats spent more timedrinking when food was restricted than whenit was freely available, demonstrating poly-dipsia and thus a substitution of water for food.However, under conditions of water depriva-tion, rats did not evidence polyphagia (exces-sive eating), but instead spent slightly less timeeating when water was restricted than whenit was continuously available, thereby indict-ing complementarity between food and water.Hursh (1978) suggested that responding

controlled by nonsubstitutable commoditiessuch as food and water is affected by economytype. However, Rachlin and Krasnoff (1983),with their use of an open economy, replicatedthe findings of Allison and Mack (1982), whoemployed a closed economy. That is, the re-lationship between food and water was deter-mined by which one of the commodities wasrestricted below baseline levels, and not byeconomy type. In Hursh's experiment, thesubjects' access to both commodities was re-stricted below baseline levels, and it is thisdifference (aside from the obvious species dif-ference) that might make responding for non-substitutable commodities sensitive to type ofeconomy.

Substitution effects between reinforcers neednot occur only along some physiological di-mension. In fact, substitutability has beendemonstrated in situations in which it wouldbe difficult to identify a common physiologicalneed. In one such demonstration, Bernsteinand Ebbesen (1978) studied human subjectsliving for several weeks in isolated laboratoryenvironments. During an initial baseline pe-riod, the subjects were free to engage in a va-riety of activities (e.g., sewing, reading, can-dlemaking, and painting). Following the freebaseline, access to one of the activities wasrestricted to below-baseline levels and wasmade contingent on engaging in another of theactivities. Bernstein and Ebbesen found thatsubstitution of other activities for the restrictedactivity was selective; that is, the additionaltime was not proportionately distributed amongthe nonrestricted activities but instead was fo-cused on one or two of them. In some cases,time was redistributed to activities quite unlikethe one that was restricted. For example, whenaccess to sewing was restricted for 1 subject,there was a disproportionate increase in read-ing magazines. If this subject had redistributedher additional time to the nonrestricted activ-ities in proportion to their baseline levels, thepercentage of time spent reading magazineswou:d have increased 5%, from 14% to 19%of her waking hours. However, this subjectincreased her magazine reading 13%, to a totalof 27% of her waking hours.

In a similar demonstration (Burkhard,Rachlin, & Schrader, 1978), nursery schoolchildren were allowed to play freely with avariety of toys during a baseline period. Foreach child, a toy was then classified as high,medium, or low, based on the amount of timespent playing with it. Several weeks later, thechildren were studied under an experimentalcontingency in which only three toys, one eachfrom the high, medium, and low categories,were available. Access to the high toy was re-stricted below baseline level, and was contin-gent on playing with either the low toy for onegroup or the medium toy for another group.For both groups, the third toy was freely avail-able. Children in both groups increased abovebaseline levels the time spent playing with theirrespective instrumental toys, demonstrating theexpected "Premackian" reinforcement effect.In addition, the group for whom the mediumtoy was freely available greatly increased the

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time spent playing with this toy; in fact, thetime spent with it was equal to that of thegroup for whom playing with the medium toywas the instrumental response. Rachlin andBurkhard (1978) interpret this result as dueto the substitution of the medium toy for therestricted high toy, much like the substitutionof magazine reading for sewing shown byBernstein and Ebbesen's (1978) subject.The experiments reported by Bernstein and

Ebbesen (1978) and Burkhard et al. (1978)serve to demonstrate that substitutes need notsatisfy a common physiological need, nor arethey necessarily related in any obvious way.Instead, substitution effects may have their ba-sis in individual experience (Hursh & Bau-man, 1987). For example, Allison and Mack(1982) have suggested that through classicalconditioning, lever pressing might come to serveas a learned substitute for eating.

Although the results from additional studiesdemonstrating substitutability might not beterribly surprising, they do provide validity forthe use of substitutability as a factor in ac-counting for reinforcement interactions. In onesuch experiment, Lea and Roper (1977) stud-ied rats responding in a chamber with twocompartments. In one compartment, mixed dietpellets were available under fixed-ratio sched-ules that ranged from FR 1 to FR 16 acrossconditions. In the second compartment, an al-ternative food source (either the identical mixeddiet pellets or sucrose pellets), when it wasavailable, could be obtained on an FR 8 sched-ule. Lea and Roper found that for hungry rats,mixed diet pellets were highly substitutable foran identical and concurrently available food.However, a concurrent source of sucrose pel-lets was not as highly substitutable for mixeddiet pellets. These conclusions were drawnfrom differences in demand elasticity for mixeddiet pellets when the concurrently availablealternative was the identical food versus su-crose pellets. For example, as the price of themixed diet pellets increased from FR 1 to FR16, the number of mixed diet pellets obtainedin the first compartment declined by approx-imately 79% when the concurrently availablefood was identical, whereas the number ofmixed diet pellets obtained decreased by ap-proximately 63% when the concurrently avail-able food was sucrose pellets. Demand for themixed diet pellets was least elastic when noalternative food source was available, as dem-

onstrated by the roughly 45% decrease in ob-tained reinforcements across the same rangeof prices.Some research, however, has generated re-

sults contrary to conventional wisdom. In onesuch case, Green and Rachlin (1991) studiedrats in an open economy, choosing betweenpairs of reinforcers available under concurrentvariable-ratio (VR) schedules. The pairs ofreinforcers were food and water, food and elec-trical stimulation of the brain (EBS), and wa-ter and EBS. The procedure employed wasthat of Rachlin et al. (1976): For each pair ofreinforcers, an income of total responses thatvaried across conditions was allotted, with ses-sions terminating once the total number of re-sponses had been spent. In addition, each re-inforcer in a pair was assigned a price,determined by a VR schedule. Subsequentconditions comprised income-compensatedprice changes. With respect to choices betweenfood and water, the results generally confirmedthose of Rachlin et al. (1976) (i.e., a highlynonsubstitutable relation was evident). Inter-estingly, food and EBS proved to be highlysubstitutable: When both EBS and food wereavailable on a VR 15 schedule, all the ratspreferred EBS to food. When EBS was madecheaper, the rats increased their "consump-tion" of EBS while decreasing their consump-tion of food. When food became the cheapercommodity, food consumption markedly in-creased and EBS consumption decreased dra-matically. Although introductory psychologytexts (e.g., Gleitman, 1991) report that whengiven a choice between food and EBS, hungryrats choose to self-stimulate "even though itliterally brings starvation" (p. 97), Green andRachlin clearly demonstrated that even a smallincrease in the price of EBS (from VR 15 toVR 30) dramatically decreased responding forEBS. Similarly, Hursh and Natelson (1981)have shown that rats' demand for EBS is highlyelastic whereas demand for food is relativelyinelastic, and Hollard and Davison (1971) haveadditional evidence to suggest that food andEBS are completely substitutable for pigeons.

Perhaps the most striking aspect of the Greenand Rachlin (1991) results is that EBS alsoproved to be fairly substitutable for water, al-though food and water were not substitutablefor each other. Based on these data, Green andRachlin suggest that EBS may function as ageneral reinforcer-substitutable for other

149


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Fig. 3. Individual data from Rat A, showing the in-teractions between food and water, food and EBS, andwater and EBS under a series of budget constraints. Eachsolid line represents a unique budget constraint, and each

- goods that are not themselves substitutable-in much the same way that money functionsas a general economic good in a human econ-omy.The individual data from Rat A (the only

subject exposed to all experimental treatments)presented in Figure 3 depict the interactionsGreen and Rachlin (1991) found between foodand water, food and EBS, and water and EBS.Each numbered line represents a budget con-straint imposed by concurrent VR schedulesfor the two commodities and a total numberof responses allotted. Each filled circle repre-

100 sents the combination of reinforcers obtainedunder that budget constraint. For example, inthe food versus EBS graph (middle graph),when EBS and food were equally priced (Bud-

- get Line 1), EBS was strongly preferred overfood. When EBS was made cheaper than food(Budget Line 2) Rat A responded almost ex-clusively for EBS. When prices were reversedso that food was made relatively cheaper, EBSmade relatively more expensive, and incomeadjusted (Budget Line 3), Rat A increased con-sumption of food reinforcers 10-fold over itsconsumption of EBS reinforcers. These samedramatic changes in relative consumption as afunction of income-compensated price changesare also evident in the water versus EBS (bot-torr) graph. However, changing the relative

1O0 prices of food and water had substantially dif-ferent effects on the consumption of those re-inforcers (top graph); that is, even with sizabledecreases in the price of water (Budget Lines2 and 3), there was only a minor decrease inconsumption of the now more expensive food.Many of the studies reviewed to this point

have made unique contributions to the psy-chological literature because they are, to someextent, experiments that could not have beenconducted or interpreted without the consid-eration of economic factors. One such factorfor which this may be particularly true is lei-sure, or nonresponding. An adequate discus-sion of leisure is beyond the scope of this paper,except to mention that a variety of studies (seeRachlin et al., 1981, and Schrader & Green,

F 1990, for reviews) indicate that under some

filled circle represents the combination of reinforcers ob-tained under that constraint. (Adapted from Green &Rachlin, 1991.)

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conditions leisure can substitute for income(typically food for nonhuman subjects; e.g.,Green, Kagel, & Battalio, 1982, 1987), andthe degree of substitutability is affected byvariables such as need (Green & Green, 1982),type of leisure activity available, and so forth.

SUBSTITUTABILITY AND THEMATCHING LAW

Baum (1974) proposed a generalized ver-sion of the matching law:

BX/BY = b(Rx/Ry)s, (5)where B, as before, represents the behaviorallocated to alternatives x and y, R representsthe reinforcers obtained from that behavior,and the constants b and s denote bias and sen-sitivity to those reinforcement alternatives. Biasreflects a systematic asymmetry between thealternatives, such as position or color prefer-ence for one of the two alternatives. A completelack of bias would be the case in which b = 1.Sensitivity is manifest as the slope of the linethat plots the logarithm of the behavior ratioBX/BY as a function of the logarithm of thereinforcement ratio Rx/Ry. When s < 1, thebehavior is called undermatching (i.e., the sub-ject overvalues the leaner schedule of rein-forcement); when s > 1, the behavior is calledovermatching (the subject overvalues the richerschedule of reinforcement). When the con-stants b and s both equal 1, the generalizedmatching equation reduces to Equation 2.These additional parameters allow Equation5 to account for a greater variety of data fromchoice situations than does Equation 2 (Baum,1979).The vast majority of data described by the

generalized matching law have been gatheredin experiments that used qualitatively similar(indeed identical) reinforcers. Early on, Rach-lin (1971) noted that in choices between qual-itatively different reinforcers (such as betweenorange juice and grape juice), relative obtainedreinforcement value would not equal relativeamount consumed; yet if one assumes thematching relation to be true, then some otherfactor must be incorporated to preserve therelation between relative obtained reinforce-ment value and relative amount consumed forqualitatively different reinforcers. Addition-ally, as Baum (1974) has pointed out, devia-tions of s from unity are poorly understood.

One attempt to understand these deviationshas been made by Rachlin et al. (1981), whosuggested that the exponent s in the general-ized matching law should also be interpretedas substitutability. If this were so, s wouldapproach unity for perfectly substitutable re-inforcers, would approach negative infinity forperfect complements, and would be equal tozero for independent reinforcers. As an illus-tration, Rachlin et al. (1981) noted that inexperiments with pigeons, rats, and monkeyschoosing between food and water, s was ap-proximately -10, whereas in choices betweenfood and food or water and water, s was closeto 1.

Rachlin et al.'s (1981) assessment of s assubstitutability has not been universally ac-cepted. Baum and Nevin (1981), for example,acknowledge that variation in s may, to someextent, incorporate choice between qualita-tively different reinforcers, but find the sub-stitutability interpretation to be premature.Baum (1974) noted that deviations of s fromunity may be due in part to level of deprivation(and cites evidence to the effect that relativeresponding more closely matches relative re-inforcement as level of deprivation is de-creased; Herrnstein & Loveland, 1974, undermultiple schedules; but see McSweeney, 1975,who did not find an effect of body weight onrelative responding in concurrent schedules)or to poor discrimination between alternatives.For example, if an animal is responding ontwo manipulanda, each of which produces re-inforcement, the inability to distinguish whichmanipulandum produced the reinforcer or theinability to distinguish between the reinforcersthemselves would result in undermatching.This latter proposition does not seem compel-ling in the case of qualitatively different re-inforcers, which certainly would be morereadily discriminable than identical reinforc-ers. In addition to Baum's suggestions, Herrn-stein (1974, 1981) argued that differing ratesof satiation between qualitatively different re-inforcers can account for observed deviationsfrom matching.The general proposal has been that quali-

tative differences between reinforcers can betreated in much the same way as differencesin amount of the same reinforcer-that is tosay, by introducing a constant scaling factor.For example, 1 g of food might have twice thevalue of 1 mL of water, given constant depri-

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vation. We contend, not that this approach iswrong or even without merit, but rather thatit is insufficient to deal with qualitatively dif-ferent reinforcers.The notion of accounting for qualitatively

different reinforcers by introducing a scalingfactor has received some empirical attention(e.g., Hollard & Davison, 1971). In an elegantdemonstration of this approach, Miller (1976)conducted pairwise comparisons of pigeons'preferences for three different grains (hemp,buckwheat, and wheat). In the first compari-son, pigeons chose between concurrent VIschedules delivering hemp and buckwheat,thereby assessing the scaling factor of the rel-ative value of hemp to buckwheat. The secondcomparison was of wheat to buckwheat. Thisallowed the determination of the scaling factorof the relative value of wheat to buckwheat.The scaling of wheat and hemp each to buck-wheat provided a common unit of value, andthus a prediction as to the relative value ofwheat to hemp. Miller found that actual com-parisons of wheat to hemp strongly supportedthe prediction based on scaling.A problem with this type of analysis is that

"value is assumed to be scalable independentlyof context" (Rachlin, Kagel, & Battalio, 1980,p. 355). The essential aspect missing in a scal-ing approach is well stated by Lancaster (1966,p. 134): "Goods in combination may possesscharacteristics different from those pertainingto goods separately." Miller selected reinforc-ers that were highly substitutable with respectto each other and were, therefore, easily ame-nable to scaling. Such might not be the casewith nonsubstitutable reinforcers.

Consider another experiment in which pair-wise comparisons of three different reinforcerswere conducted. Green and Rachlin (1991)found food to be substitutable for EBS andwater to be substitutable for EBS, but foodand water were highly nonsubstitutable. As-sume, for the sake of argument, that when foodwas compared to EBS, EBS was found to havea value of x and food a value of 1.lx; that is,each food reinforcer was worth a little morethan each EBS reinforcer. When water wascompared to EBS, suppose that water wasfound to have a value of 0.9x-each waterreinforcer was worth slightly less than oneEBS reinforcer. In accordance with the logicof scaling, knowing the values of food and wa-ter in the common currency of EBS allows us

to determine that the relative value of food towater is 1.2; in other words, one food reinforcershould be worth marginally more than onewater reinforcer. That the value of one com-modity can be expressed in terms of its worthrelative to another presupposes that those com-modities can be traded for each other. How-ever, the results Green and Rachlin obtainedclearly contradict such a universal approach;food and water were consumed in fairly rigidproportion to one another. Thus, Miller (1976)found that, with a scaling factor, A = C andB = C implies A = B. Such a transitive resultholds only with substitutable commodities.Without taking into account the degree of sub-stitutability between commodities, the wrongprediction would be made with complementswhere, as Green and Rachlin showed, A = Cand B = C, but A # B.

Finally, consider behavior under concurrentratio schedules of reinforcement. With iden-tical reinforcers for each of the response al-ternatives, the matching law predicts exclusivepreference for the cheaper alternative (i.e., thealternative with the lower ratio requirement)(Herrnstein & Vaughan, 1980). Indeed, sucha result has been obtained (Green, Rachlin, &Hanson, 1983; Herrnstein & Loveland, 1975).However, nonexclusive responding is pre-dicted and obtained when the reinforcers arenot substitutable.

It is precisely because of results such as thesethat the notion of substitutability warrants in-clusion in psychological models of choice ingeneral and the matching law in particular.Although it is true that substitutability derivesfrom a theory that assumes maximization ofutility, one need not accept views of maximi-zation in order to accept the notion of substi-tutability. Allison (1983) has noted that it ispossible for an animal's behavior to obey thedemand law without maximizing utility; thatis to say, changes in price can produce inversechanges in consumption by some mechanismother than optimization (see Becker, 1962).The demand law can be derived without ref-erence to utility. A similar argument can bemade with regard to substitutability. It is pos-sible to adopt an economic view of the fun-damental interactions of reinforcers withoutnecessarily adopting maximization theory.Granted that determination of scaling and sub-stitutability both must be accomplished posthoc, substitutability has the advantage because

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it encompasses a broader range of possible in-teractions among reinforcers.

APPLICATIONSThe matching law is receiving increasing

attention in applied behavior analysis (e.g.,Epling & Pierce, 1983; McDowell, 1981, 1982,1988; Myerson & Hale, 1984). Application ofthe matching law suggests two interventionstrategies for the elimination of inappropriatebehavior, in addition to standard treatmentprocedures of punishment and extinction.These are (a) increasing the rate of reinforce-ment for a concurrently available response (in-creasing R in Equation 1) and (b) increasingthe rate of noncontingent reinforcement (in-creasing Ro in Equation 4) (McDowell, 1981,1982). Either of these interventions would havethe effect of decreasing the occurrence of theinappropriate behavior, Bx (with RX being thereinforcement for that behavior).An example of the first intervention strategy

was reported by Ayllon and Roberts (1974)with 5 fifth-grade boys who were disruptivein the classroom. Rather than attempting todecrease or eliminate the disruptive behaviors(Bx) by directly modifying the reinforcementfor such behavior (R.), Ayllon and Robertsinstead instituted a token-reward system inwhich the children could earn points (Ry), ex-changeable for a variety of activities and priv-ileges, based upon their reading performance(By). When the points-for-reading-perfor-mance contingency was instituted, readingperformance increased, as expected. Interest-ingly, BX-the disruptive behavior-markedlydecreased in frequency. When the reinforce-ment for reading performance was then with-drawn, disruption increased; the reinstatementof reinforcement (Ry) dramatically increasedreading performance and nearly eliminateddisruption.

In one clinical intervention exemplifying thesecond strategy, McDowell (1981) introduceda token-reinforcement contingency in whichpoints were awarded for behaviors unrelatedto the extreme oppositional behavior (refusalto follow instructions, aggressiveness, etc.) dis-played by the client, a mildly retarded adultmale. The oppositional behavior (B,) ap-peared to be reinforced by attention (Rx) fromthe client's parents. The use of token rewardswas chosen over other treatments aimed at di-

rectly decreasing reinforcement for the oppo-sitional behavior (Rx), such as withdrawal ofattention, because ignoring the client's out-bursts could result in his becoming violent.The client earned points, later exchangeablefor money, for activities such as reading, shav-ing, and helping with dinner. In other words,reinforcing alternative behavior is tantamountto increasing Ro and should therefore decreasethe incidence of the target oppositional behav-ior. Prior to implementation of the token-re-ward contingency, oppositional behavior oc-curred almost daily. During the first few weeksof intervention, oppositional behavior had de-creased by approximately 80%, even thoughthe reinforcement contingency for the oppo-sitional behavior had not been changed.

Reinforcement for one behavior may influ-ence the emission of other behavior in less thandesirable ways. As an example, consider thetoken-reward system studied by Fisher et al.(1978). They examined the effects of differentwages (tokens earned) for toothbrushing in apsychiatric population at a large state hospital,and measured the income (total tokens) earnedweekly. As is apparent in Figure 4A, rein-forcement for toothbrushing worked well: In-come from toothbrushing increased as thenumber of tokens received for it increased fromzero, to one, to five. However, there were sig-nificant effects of the changes in the wage fortoothbrushing on the emission of other typesof token-earning behavior, as can be seen inFigure 4B. The subjects decreased nontooth-brushing income earned, with greater reduc-tions under the five- than under the one-tokenwage rate. As Fisher et al. state: "Thus, a wagefor toothbrushing and, especially, a relativelyhigh wage for toothbrushing discouraged pa-tients from engaging in other token-reinforced,presumably therapeutic, behaviors" (p. 401).Clearly, then, a behavioral intervention occurswithin a system, and attention to only the tar-get behavior may blind the clinician, teacher,or parent to other, beneficial or detrimental,behavior changes (see Winkler & Burkhard,1990).The preceding interventions follow directly

from the generalized matching law and do notnecessitate an economic interpretation. How-ever, our discussion of substitutability makesclear that interventions based on the matchinglaw will be effective only to the extent that Ryand Ro are substitutable for Rx. If Ry or Ro

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in which toothbrushing earned zero, one, or five tokens. (Adapted from Fisher et al., 1978.)

are nonsubstitutable for Rx, then the unfor-tunate consequence of increasing the alterna-tive reinforcers (Ry or RO) in the attempt toreduce inappropriate behavior may at best bean ineffective treatment (in the case of inde-pendent reinforcers) and may at worst resultin increasing inappropriate behavior (if thereinforcers are complements). For example, itis not difficult to imagine the case of a harriedparent who drops everything to play with ascreaming child. If this parent also "spoils"the child by giving him many noncontingenttoys (RO), the result may be a child who screamsa great deal because play time and toys tendto be consumed together-increasing the num-ber of toys increases the demand for play time.The results from Fisher et al. (1978) notedabove are also consistent with this view. Sim-ilarly, if Rx and Ro are complements, thendecreasing alternative reinforcers (RO) mayprovide an effective means for decreasing thetarget response (B). Applied behavior ana-lysts who do not take the time and effort toevaluate the substitutability of reinforcers indesigning behavior-change programs do so atperil to their clients.The concept of substitutability may also be

relevant to an understanding of addictions.Stigler and Becker (1977) have proposed twotypes of addictions-positive and negative (seeHerrnstein, 1990, for an alternative behavioralaccount of addictions). Positive addictions areacquired when demand for that good is elastic(i.e., equivalently priced substitutes are avail-able) and when the price of that good decreases

with increased consumption. Stigler and Beckergive the following example: The more "good"music one listens to, the more good music isappreciated, thus effectively decreasing the"price" of listening to music-one begins torecognize themes, styles, and so forth, and sothe music is not as difficult to follow. The resultis an increase in music consumption becausemusic is now cheap relative to other substi-tutable goods.

Negative addictions are acquired when de-mand for that good is inelastic (because equiv-alently priced substitutes are unavailable) andthe price of that good increases with increasedconsumption. Demand, according to Stigler andBecker (1977), is not for the good itself, butfor the satisfaction that good offers (i.e., "eu-phoria"). Euphoria is a good that presumablyis largely inaccessible to those living in con-ditions of extreme poverty or neglect, exceptthrough consumption of drugs such as alcoholand cocaine. However, the more alcohol orcocaine is consumed, the less euphoria is ob-tained (this is what is meant by tolerance to adrug). Tolerance can be thought of as an ef-fective increase in the price of the drug; con-sequently, consumption of the drug must in-crease to produce the initial degree of euphoria(see, however, Elsmore, Fletcher, Conrad, &Sodetz, 1980, for an indication that in baboons,demand for heroin is much more elastic thanis demand for food). Because addicts' demandfor drugs such as heroin and alcohol is inelas-tic, exogenous increases in price (e.g., decreas-ing the available supply or imposing harsh

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penalties for use) will have relatively little in-fluence on consumption. Exogenous price in-creases, as Stigler and Becker note, affect onlypositively addictive commodities because de-mand for these is elastic. If Stigler and Becker'sanalysis is accurate, the implications for cur-rent social policy are enormous. (See Hursh,1991, for a cogent discussion of drug abuseand public policy with regard to behavioraleconomic issues including substitutability.)

It is admittedly speculative to venture thatthere may be substitutability between suchseemingly disparate reinforcers as social sup-port and substance abuse. But in keeping withour general definition of substitutable com-modities, we note that both social support anddrug taking serve similar purposes-they re-duce negative feelings and increase positivefeelings. The apparent link between copingwith unpleasant feelings and involvement inrisky behavior (e.g., drug and alcohol con-sumption, cigarette smoking, problem eating)(Wills & Shiffman, 1985) suggests that socialsupport and risky behavior may substitute foreach other in times of emotional distress. Con-sequently, during times of hardship, socialsupport from close personal relationships maybe sought by those to whom it is available,whereas persons lacking such relationships maybe more likely to engage in risky behavior.Furthermore, social support may provide aneffective substitute for the drug use that is un-dertaken to alleviate loneliness; to the extentthat they are related to one another (Newcomb& Bentler, 1986), social support, as a substi-tute for drug taking, may reduce loneliness andthus the likelihood of engaging in such riskybehavior.

Prochaska and DiClemente (1985) have alsonoted the connection between unpleasant feel-ings and drug abuse. They state that "emo-tional distress is one of the most common rea-sons people relapse in attempts to overcomeaddictive behaviors" (p. 345). Social supportmay be effective in handling such distress andthereby provide an effective approach to theproblem of relapse.Of course, chemical substances are very

powerful short-term reinforcers, whose rein-forcing effects are immediate and thus quiteeffective. Less is understood about which com-ponents of social support are effective, let alonehow best to implement it and educate peoplein its use (Thoits, 1986). Still, this seems to

be a fertile area for continued research. (Fora discussion of some of the research on socialsupport and risk behavior, see Rehberg, 1992.)

CONCLUSIONSWe noted in an earlier section that deter-

minations of the substitutability of reinforcersare made post hoc. Given that this is so, theconcept of substitutability would seem to be oflimited utility. The goal of any science, afterall, is to adopt concepts that are predictive andexplanatory as well as descriptive. There is nodoubt that substitutability is descriptive, butcan it in fact predict and explain extant andfuture findings?As one example, consider the relationship

between food and water. A number of studieswith rats (Allison & Mack, 1982; Green &Rachlin, 1991; Rachlin & Krasnoff, 1983;Rachlin et al., 1976) have generally found foodand water to be highly nonsubstitutable. Thisrelationship is also true in primates (Hursh,1978) and has been obtained, albeit not con-sistently, in pigeons (Battalio, Kagel, Rachlin,& Green, 1981). Similarly, the substitutablerelationship between EBS and food is evidentin both rats (Green & Rachlin, 1991) andpigeons (Hollard & Davison, 1971). That theinteractions between food and water and be-tween EBS and food hold across species lendsa measure of generality, and therefore pre-dictability, to notions of substitutability.That one cannot predict, in the absence of

additional information, how two reinforcerswill interact for a given species does not di-minish the validity of the concept of substi-tutability, just as the concept of reinforcementis not discredited when one cannot predict ifan outcome will function as a reinforcer. How-ever, the factors that affect substitutability, be-yond the reinforcers themselves, should be pre-dictable once delineated (just as rate,magnitude, and delay of reinforcement havepredictable effects that are largely independentof the nature of the reinforcer). The work ofLea and Roper (1977) and analysis by Hurshand Bauman (1987) suggest that one of thesefactors is the temporal separation between al-ternatives, and this separation attenuates thedegree of substitutability even in otherwiseperfect substitutes. Hursh and Bauman's anal-ysis compares demand curves generated underthree different temporal situations: concurrent

155


schedules, multiple schedules, and across con-ditions of the same experiment. These threesituations are likened to comparing prices ofidentical items on the same shelf, comparingprices of identical items in different stores, andcomparing prices of identical items over monthsof shopping, respectively. The demand curves(in which consumption of food from one al-ternative is analyzed as a function of its relativeprice when an alternative but identical food ispresent) reveal that the greater the temporalseparation between identical commodities, thelower their substitutability.

In terms of the generalized matching law,one would predict that decreased substitut-ability would be manifest by decreases in thevalue of s as the temporal separation betweenalternatives increases. One way to increase thetemporal separation between alternative re-inforcers is to hold the relative rate of rein-forcement constant across concurrent variable-interval schedules while decreasing the overallrate of reinforcement. Indeed, when Alsop andElliffe (1988) studied pigeons responding un-der this procedure, they found that the valueof s decreased as the overall rate of reinforce-ment was decreased. Additional confirmationof this prediction is found in the work of LaFiette and Fantino (1988), who similarly ob-tained lower values of s as the duration of thecomponents in multiple VI schedules was in-creased (thereby increasing the temporal sep-aration between reinforcement alternatives)when their subjects were studied in an openeconomy. Additionally, in a reanalysis of thedata of Shimp and Wheatley (1971), La Fietteand Fantino calculated values of s that in-creased from 0.41 to 0.95 when equal com-ponent durations in a multiple schedule weredecreased from 180 s to 10 s.

It would be unwise to place too much em-phasis on this one example, especially in lightof other evidence to the contrary. La Fiette andFantino (1988), for example, obtained increas-ing values of s as component durations wereincreased in a closed economy. Nonetheless,this example does suggest the predictive utilityof substitutability, which may be further re-fined in light of contradictory findings. More-over, the effect of temporal separation on sub-stitutability itself may in turn be modulatedby the nature of the commodities in question;any temporal separation between goods thatmust be consumed immediately (such as heat)

may produce any degree of substitutability be-tween them.

Finally, the heuristic value of substitutabil-ity cannot be overemphasized. Notions of sub-stitutability cause one to examine interactionsamong reinforcers that otherwise might nothave been considered. Moreover, without aneconomic framework, researchers cannot pre-dict an animal's future preference based solelyon its current preference. This was vividlydemonstrated in the studies of Green andRachlin (1991) and Hursh and Natelson(1981), in which animals chose between foodand brain stimulation. An additional exampleis provided by Elsmore et al. (1980), who foundthat when heroin-addicted baboons were of-fered periodic opportunities to choose betweenfood and heroin infusion, the baboons wererelatively indifferent between food and heroinwhen the intertrial interval was short. How-ever, as the intertrial interval was increased(effectively increasing the prices of food andheroin equally), the baboons gave up heroininfusions but not food, indicating that demandfor food, compared to that for heroin, is largelyinelastic.The matching law was developed to account

for choice between qualitatively identical re-inforcers, and in that domain it fares quitewell. But it can be easily argued that choicesin the world beyond the laboratory are rarelymade between identical outcomes that differonly with respect to magnitude, frequency, ordelay. In short, many of our choices are be-tween oranges and tennis balls, not necessarilybetween Coke and Pepsi. The implicit as-sumption of the matching law is that all re-inforcers are perfectly substitutable. Resultswith qualitatively different reinforcers aretherefore accommodated by appeal to a scalingfactor. But, as we have seen, this approachworks only when the reinforcers are in factsubstitutable. When the reinforcers are notsubstitutable, as is the case with food and wa-ter, appeal is then made to, say, differentialrates of satiation as an explanation. Further-more, it is only with the matching law's as-sumption of perfect substitutability that all al-ternative sources of reinforcement are predictedto affect Bx equivalently, and thus can be sub-sumed under the single term Ro. The economicconcept of substitutability as a continuum ofpossible interactions among reinforcers ex-plicitly denies this assumption, thereby gen-

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SUBSTITUTABILITY OF REINFORCERS 157

erating new research, interpretation, and anal-ysis.

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pression, and conservation. Journal of the ExperimentalAnalysis of Behavior, 25, 185-198.

Allison, J. (1983). Behavioral substitutes and comple-ments. In R. L. Mellgren (Ed.), Animal cognition andbehavior (pp. 1-30). Amsterdam: North-Holland.

Allison, J. (1986). Economic interpretations of animalexperiments. In A. J. MacFadyen & H. W. Mac-Fadyen (Eds.), Economic psychology: Intersections intheory and application (pp. 219-245). Amsterdam: El-sevier.

Allison, J. (1989). The nature of reinforcement. In S.B. Klein & R. R. Mowrer (Eds.), Contemporary learn-ing theories: Instrumental conditioning theory and the im-pact of biological constraints on learning (pp. 13-39).Hillsdale, NJ: Erlbaum.

Allison, J., & Mack, R. (1982). Polydipsia and auto-shaping: Drinking and leverpressing as substitutes foreating. Animal Learning & Behavior, 10, 465-475.

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Received April 17, 1992Final acceptance November 24, 1992

b,/(b. + by) = r./(r, + ry), (1)

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