American Economic Association Experimental Confirmation of the Existence of a Giffen Good Author(s): Raymond C. Battalio, John H. Kagel, Carl A. Kogut Source: The American Economic Review, Vol. 81, No. 4 (Sep., 1991), pp. 961-970 Published by: American Economic Association Stable URL: http://www.jstor.org/stable/2006656 Accessed: 26/04/2010 13:36 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showpublisher?publishercode=aea. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. American Economic Association is collaborating with JSTOR to digitize, preserve and extend access to The American Economic Review. http://www.jstor.org
Experimental Confirmation of the Existence of a Giffen Good By RAYMOND C. BATTALIO, JOHN H. KAGEL, AND CARL A. KOGUT* We shall have to find a new example of the positively sloping demand curve or push our discussion of it deeper into footnotes. (George J. Stigler, 1947) This paper reports an example of a positively sloping demand curve or, equivalently, the existence of a Giffen-good phenomenon. Giffen goods have long held a special place in the theory of consumer choice. Search as they might, however, economists have not been able to find unequivocal evidence of this frequently cited "exception" to the simple law of demand (Stigler, 1947, 1948; A. R. Prest, 1948; Gerald P. Dwyer and Cotton M. Lindsay, 1984). Further, since most data relating to consumer demand behavior result from the interaction of supply and demand forces in a market system, there are sound theoretical reasons why observations of Giffen goods in market data are bound to be infrequent, or nonexistent (William R. Dougan, 1982; Dwyer and Lindsay, 1984). This has led some economists to suggest that we should "...begin our analysis of the demand side, in the theory of value, with the 'law of demand"' (E. J. Mishan, 1961 p. 10), mini- *Battalio: Department of Economics, Texas A&M University, College Station, TX 77843-4228; Kagel: Department of Economics, University of Pittsburgh, Pittsburgh, PA 15260; Kogut: Department of Economics, University of South Florida, Tampa, FL 33620. This research was supported by the National Science Foundation under grants SES 8708402 and SES 8509968. Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the National Science Foundation. We have profited from comments received at a seminar at the University of Wyoming and from detailed suggestions of Armen Alchian on an earlier draft of the paper. 961 mizing the significance of the distinction between income and substitution effects in theories of consumer behavior.1 It also means that the counterintuitive prediction of Slutsky-Hicks choice theory regarding the existence of Giffen-good effects, a prediction that distinguishes it from a number of rival explanations of consumer behavior, has yet to receive unequivocal empirical confirmation. The forces at the market level that inhibit observing Giffen-good effects can be overcome in a laboratory environment. The wealth constraint and the supply of the commodities in question can be created to induce inferior goods which take up a sizable portion of consumer expenditures, a commonly cited precondition in consumer demand theory for the observation of Giffen goods. In constructing such an environment within the bounds set by legal and ethical considerations and our limited research budget, we have used rats as individuals. Previous research shows that rats' (and pigeons') behavior is consistent with the Slutsky-Hicks theory of preference (Battalio et al., 1981a,b) and that there are significant parallels between human and animal behavior (Kagel, 1987). Our experiment demonstrates the existence of Giffen goods at the level of an individual's demand and identifies additional forces, heretofore unrecognized in the literature, inhibiting the observation of Giffen goods at the market demand level. IIn contrast, Richard G. Lipsey and Gideon Rosenbluth (1971) use the commodity-characteristics approach to consumer demand behavior (Kelvin J. Lancaster, 1966) to argue for a rehabilitation of the concept of Giffen goods, arguing for much more common occurrence than previously suspected. Nevertheless, instances of Giffen goods observed using marketlevel data are rare and typically subject to considerable dispute.
962 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1991 I. Experimental Design To investigate the Giffen phenomenon, we established initial conditions resulting in a strongly inferior good. We settled on rats choosing between a quinine solution (0.1 gram per liter) and root beer, with the price of quinine always less than root beer. Rats given ad lib access to these fluids strongly prefer root beer to water and water to the quinine solution. In keeping the price of quinine less than root beer, rats would be trading off the good-tasting root beer for more fluid, but less-good-tasting, quinine. The quinine solution was intended to serve as the Giffen good. Experimental procedures were similar to our earlier studies (Kagel et al., 1975, 1981). Subjects were placed in an experimental chamber for approximately three hours each day, during which time they received their entire daily liquid food ration. Other solid food was always available free in the experimental chamber and also while the animals were housed in holding cages. A rat obtained quinine and root beer by pressing either of two levers mounted on a wall of the experimental chamber. Below each lever (one for quinine, one for root beer) was an opening for a dipper cup which was filled with liquid each time a lever was pressed. Income was controlled by restricting the number of lever presses that would result in obtaining liquid. Prices were changed by varying the amount of liquid obtained at each lever press. For example, if each press on the right lever produced 0.1 cc of liquid on the right, and each press on the left lever resulted in 0.05 cc of the liquid on the left, then the price of the liquid on the right would be one-half press per 0.05 cc, and the price of the liquid on the left would be one press per 0.05 cc.2 Income, the allotted number of effective lever presses, could be distributed in any desired combination across the two levers. Figure 1 shows an example of the constraint sets used. Each constraint set was maintained for a mini- 2Quantities were varied by changing the number of 0.05-cc dipper-cup presentations per response (i.e., a 0.1-cc payoff equals two 0.05-cc cup presentations. 10 (2) (3) 0 5 10 15 20 cc of Quinine FIGURE 1. CONSTRAINT SETS mum of ten days. Prices and income were not changed until the rats' choices remained within the bounds that had occurred during the previous ten days. This criterion helps to assure stability of preferences for the consumption bundle measured (mean consumption over the last five days of each condition). The Giffen experiment had four phases. First, we conducted a search for an income range over which we would reliably observe strong inferiority for the quinine solution. This was done over low income levels, where the relatively low price of quinine as a nutritive source would offset the strong taste-advantage of root beer, and was accomplished through lowering the budget from (1) to (2) as shown in Figure 1 (through reducing the effective number of lever presses). Second, also shown in Figure 1, income-constant price changes were imposed at these income levels by changing the budget constraint from (2) to (3) (through increasing the amount of quinine received per lever press) in order to demonstrate the existence of a Giffen-good phenomenon. Notice that these income-constant price changes occurred over a portion of the choice space in which inferiority was observed. The third phase consisted of tests for negative Slutsky substitution effects for those rats exhibiting the Giffen phenomenon. Fourth, this was followed by increases in income and additional income-constant price changes for the
VOL. 81 NO. 4 BATTALIO ETAL.: GIFFEN GOODS 963 TABLE 1 QUININE INCOME ELASTICITIES FOR INITIAL INCOME CHANGES (MEAN DATA FOR LAST FIVE DAYS IN PERIOD) Subject Variable 531 532 533 541 542 543 Total presses available, high income 110 110 110 110 110 110 Quinine consumptiona 4.80 5.02 5.36 7.52 3.04 3.90 (0.434) (0.246) (0.093) (0.637) (0.147) (0.416) Total presses available, low income 59 80 62 60 71 75 Quinine consumptiona 4.92 7.74 5.12 5.80 7.08 5.86 (0.222) (0.103) (0.588) (0.152) (0.020) (0.371) Change in quinine consumptiona +0.12 +2.72** -0.24-1.72* +4.04** +1.96** Income elasticity - 0.04-1.35 + 0.08 + 0.44-1.85-1.06 aquantity measured in cc; standard errors of means in parentheses. *Significantly different from zero at the 0.10 level (two-tailed test); **Significantly different from zero at the 0.01 level (two-tailed test). Giffen-good rats to determine whether behavior was still Giffen at the higher income level. II. Results Table 1 reports income elasticities during the first phase of the experiment, during which we identified strong inferiority of quinine consumption, for three of the subjects. All rats started this sequence of changes, beginning at an income constraint of 110 effective presses. In all cases, income was then decreased by an amount such that, if a subject switched consumption to all quinine, total liquid consumption would remain constant. If strong inferiority was not observed with the initial decrease in income, a further reduction in income was imposed to attempt to locate an inferior range of quinine consumption. The animals' total fluid consumption and weights were monitored daily to insure their health.3 Income decreases resulted in significant decreases in quinine consumption for rat 541 (quinine is normal over this range for 3Liquid consumption averaged about 6 cc at the low-income levels. While the animals can (and did) remain healthy at these levels, these fluid levels are considerably lower than the amount of water the rats this subject), no significant change in quinine consumption for rats 531 and 533, and large increases in quinine consumption for the remaining three rats, 532, 542, and 543.4 For these last three, income elasticities are greater than 1 in absolute value, so quinine is strongly inferior in this region. The effects of income-constant reductions in the price of quinine on quinine consumption are presented in Table 2. The resulting demand curves for the three subjects exhibiting strong quinine inferiority are shown in Figure 2.5 For rats 532 and 543 in periods 1-3, we observe a reversible (A-B-A) sequence of Giffen points. The next period (4) was also Giffen, but the strength of the effect had weakened. For subject 542, the first price decrease resulted in a sharp reduction in quinine consumption, but the baseline was not recovered. However, price changes imposed during the next four peri- would consume on an ad lib basis. During this phase of the experiment, the rats varied in weight from 210 grams for the smallest individual to over 400 grams for the largest individual. 4The subject numbers represent a numbering scheme used to identify rats in our laboratory. Data are reported for all rats used in this experiment. 5Straight lines were fitted to the mean data points using ordinary least-squares regressions.
964 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1991 TABLE 2-QUININE CONSUMPTION FOR INITIAL PRICE CHANGES (MEAN DATA FOR LAST FIVE DAYS IN PERIOD) Subject Variable 531 532 533 541 542 543 Income elasticity - 0.04-1.35 + 0.08 + 0.44-1.85-1.06 High price 1/2 1/2 1/2 1/2 1/2 1/2 Quinine consumptiona 4.92 7.74 5.12 5.80 7.08 5.86 (0.222) (0.103) (0.588) (0.152) (0.020) (0.371) Low price 1/3 1/3 1/3 1/3 1/3 1/3 Quinine consumptiona 4.95 6.87 6.54 7.89 4.38 4.74 (0.394) (0.438) (0.387) (0.485) (0.537) (0.215) Change in quinine consumptiona 0.03-0.87 1.44 2.09-2.70-1.12 t statistic 0.07-1.93 2.02 4.11-5.02-2.61 Significance levelb 0.95 0.12 0.08 0.01 < 0.01 0.04 Giffen? no yes no no yes yes aquantity measured in cc; standard errors of means in parentheses. btwo-tailed test for difference in means. ods produced a Giffen response (relative to the new, reduced level of quinine consumption) similar to those of the other two subjects. The reversible behavior in response to price changes observed for rats 532, 542, and 543 provides strong evidence that the positively sloped demand curves are due to the changing price of quinine and not due to chance. Table 2 also shows the t statistics that result from a test of differences in means over the first phase (A-B) of these price changes. Two of the three differences are significant at better than the 0.05 level, with the third significant at the 0.12 level. Further, using Fisher's Z statistic for combining independent t tests, a value of 4.78 is obtained, which is significant at less than the 0.01 level. Demand curves for the three subjects not showing strong inferiority of quinine consumption are shown in Figure 3. In all three cases, the price changes yield standard, negatively sloped, demand curves, which stand in marked contrast to those in Figure 2.6 6In this case, price-change reversals were not conducted, since the existence of downward-sloping demand curves for rats, in the case of normal goods, is well documented elsewhere (Kagel et al., 1981). The t statistics resulting from a test of differences in means are also reported in Table 2. Two of the differences are significant at better than the 0.10 level, while for rat 531, the change in consumption was not significant (P = 0.95). We implemented income-compensated price changes, which pivot the budget line through the original consumption bundle, for rats 532, 542, and 543 following the income-constant price changes reported in Table 2. Rats 542 and 543 showed a small, statistically nonsignificant (P > 0.30) decrease in quinine consumption in response to an increase in its relative price (as the Slutsky-Hicks theory requires), while rat 532 showed a small, statistically nonsignificant (P = 0.52) increase in consumption when the relative price was increased. However, a further income-compensated increase in the relative price of quinine for rat 532, directed through this new choice point, produced a statistically significant reduction in quinine consumption (t = 4.23, P < 0.01). Note that, although Giffen responses were rare (occurring in only three of the six rats), even under conditions designed to produce them, they were reliably associated with the initial conditions specified in the theory: namely, strong inferiority for the commodity in question in conjunction with a relatively small substitution effect. Equally important,
VOL. 81 NO. 4 BATTALIO ETAL.: GIFFEN GOODS 965 532 531 0,.50 t (1) 3 &.50 ~~~~~~~(2).33 (4) a.50 \0(1) 4.25 (3) o 3 6 9 542 533 (4) (5) (2) ) b.50 0.25 543 541 &.50 (1 & 3)?.33 (2 (4) o 3 6 9 50 y.50 ~~~~~~~~~~~(2) c.25.; ~~~~~~~~~~~~(3) FIGURE 2. INCOME-CONSTANT DEMAND CURVES FOR RATS SHOWING STRONG INFERIORITY IN QUININE CONSUMPTION (Numbers in parentheses indicate chronological sequence of price changes) FIGURE 3. INCOME-CONSTANT DEMAND CURVES FOR RATS SHOWING WEAK INFERIORITY OR NORMALCY IN QUININE CONSUMPTION (Numbers in parentheses indicate chronological sequence of price changes)
966 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1991 TABLE 3-QUININE INCOME ELASTICITIES AT HIGHER INCOME LEVELS (MEAN DATA FOR LAST FIVE DAYS IN PERIOD) Subject Variable 532 542 543 Total presses available, low income 104 71 94 Quinine consumptiona 7.48 3.78 6.88 (0.227) (0.983) (0.263) Total presses available, high income 150 150 150 Quinine consumptiona 7.18 2.94 5.02 (0.407) (0.175) (0.231) Change in quinine consumptiona - 0.30-0.84-1.86** Income elasticity -0.11-0.35-0.68 aquantity measured in cc; standard errors of means in parentheses. **Significantly different from zero at the 0.01 level (two-tailed test). standard negatively sloped demand curves resulted for those rats whose quinine consumption was normal or only mildly inferior. Indeed, the difficulty in designing an experiment to identify the existence of a Giffen good was in identifying a commodity set in which one of the goods would show strong inferiority.7 The implication is that it is not the Giffen phenomenon per se that is difficult to generate as much as it is the initial conditions of strong inferiority that the theory calls for. After these income-compensated price changes, the Giffen subjects were moved to a higher level of income. Table 3 reports the effects of these changes in income on quinine consumption. In all cases, the change in quinine consumption is computed relative to the nearest period (in time) with lower income at these same relative prices. Quinine consumption continues to be inferior for all three subjects, but the change is statistically significant only for subject 543. 7Earlier research showed that rats preferred both root beer and saccharin to water. Using six rats choosing either between root beer and water or between saccharin and water, we were unable to find an area in the choice space that would reliably generate strong inferiority similar to what was found here with the quinine solution. However, for one subject, we did observe strong inferiority for water and a Giffen response was observed following a price decrease. In addition, the income elasticities are all less than 1 in absolute value at these higher income levels and are far less than those reported in Table 1. Income-constant price changes were again imposed on the three subjects. Table 4 reports the consumption levels under the different prices. Figure 4 shows the resulting demand curves. In all three cases, consumption increased with a decrease in price, with two changes in consumption statistically significant (P < 0.10). The breakdown of the Giffen response here is consistent with the substantially smaller (in absolute size) income elasticities of demand for quinine over this portion of the choice space (see Table 3). As Slutsky-Hicks demand theory suggests, inferiority is a necessary, but not a sufficient, condition for a Giffen good to exist. The income effects here are simply not large enough (in absolute value) to offset the substitution effects of the price changes. Given the heterogeneity in consumption patterns among these genetically similar consumers (rats from the same inbred strain) raised in similar environments, it is of interest to examine the aggregate per capita data to determine whether the "market" demand curve for quinine is negatively sloped. Using the consumption data for quinine during the first phase of price changes reported in Table 2 and averaging across rats,
VOL. 81 NO. 4 BATTALIO ETAL.: GIFFEN GOODS 967 TABLE 4-QUININE CONSUMPTION FOR PRICE CHANGES AT HIGHER INCOME LEVELS (MEAN DATA FOR LAST FIVE DAYS IN PERIOD) Subject Variable 532 542 543 High price 1/2 1/2 1/2 Quinine consumptiona 7.18 2.94 5.02 (0.407) (0.175) (0.231) Low price 1/3 1/3 1/3 Quinine consumptiona 9.87 3.12 5.91 (0.198) (0.145) (0.337) Change in quinine consumptiona 2.69 0.18 0.89 t statistic 5.95 0.79 2.18 Significance levelb < 0.01 0.45 0.07 aquantity measured in cc; standard errors of means in parentheses. btwo-tailed test for difference in means. consumption was 6.09 cc per capita under the original baseline prices (standard error of 0.453 across individuals) and 5.90 cc per capita following the income-constant decrease in the price of quinine (SE = 0.574), for an average reduction in quinine consumption of 0.19 cc, some 3 percent of baseline consumption. Averaged across individuals, this difference is not significantly different from zero (t = 0.26, P = 0.40). Thus, at the market level, the differences in consumption patterns of the different subjects resulted in a negligible, statistically nonsignificant, reduction in quinine consumption in response to reductions in price. These differences in consumption patterns across individuals may be another reason, heretofore unrecognized in the literature, for why the Giffen-good phenomenon is so difficult to identify in market-level data.8 III. Implications for Alternative Models of Choice The empirical validation of a Giffen-good phenomenon has profound effects on the status of two alternative theories of choice popular among animal psychologists. (i) The existence of Giffen goods brings into question the "law of effect," which states that increasing reward (i.e., positive reinforcement) for an activity increases the probability of engaging in that activity (where probability is typically measured in terms of the amount of time spent in the activity; Howard Rachlin, 1976 pp. 228-31). For example, a lower price of a commodity (increased positive reinforcement) increases consumption of the commodity as the consumer gets more for each dollar (for each lever press). As such, consumers would buy more (allocate more lever presses to the activity). However, with the Giffen-good phenomenon, not only does the rate of total expenditure on the commodity decrease with decreased prices, but the rate of consumption also decreases. As such, the existence of Giffen goods is inconsistent with simple strengthening mechanisms exemplified in the law of effect that would have the animal respond only to relative prices, with no income effect. (ii) The existence of Giffen-good behavior also contradicts "melioration" theory 8Hicks (1956) argued that heterogeneity across consumers would lend support to the existence of downward-sloping market demand curves, since different consumers would be at different income levels and the Giffen phenomenon is, of necessity, a local rather than global characteristic of individual demand. This is quite different from the heterogeneity observed here, (i.e., different consumers with markedly different preference maps at comparable income levels).
968 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1991 532 a.50 (3).0.50 (1) 542 033 (2) 543 :a. 50 (4) 0( (2) (Richard J. Herrnstein and William Vaughan, Jr., 1980; Vaughan, 1981) and its implication, the "matching" law (Herrnstein, 1961, 1970). Under melioration theory, the average, rather than the marginal, rate of reward (or cost) guides behavior; it is unaffected by the overall rate of reinforcement. As such, pure changes in income, which do not affect the average reward rate, have no role to play in consumption. The existence of inferior goods, the necessary initial condition for the existence of Giffen goods, stands in marked violation of this implication of melioration theory. The strong inferiority of quinine for the Giffen subjects resulted in a change from a majority of all responses being allocated to root beer consumption, to an overwhelming majority of responses being allocated to quinine consumption. Further, under the conditions of our experiments, a reduction in the price of a commodity corresponds to an increase in the commodity's average reinforcement rate (quantity of the good received divided by responses required to obtain the good). According to melioration theory, this should result in increased expenditure (responding) on the commodity in question. However, with Giffen goods, not only does total expenditure on the commodity decrease, but the rate of physical consumption of the Giffen good decreases as well.9 IV. Conclusions The results obtained in this series of experiments support the conventional preference-map model of individual choice and (2) (3) FIGURE 4. INCOME-CONSTANT DEMAND CURVES FOR ORIGINAL GIFFEN RATS AT HIGHER INCOME LEVELS (Numbers in parentheses indicate chronological sequence of price changes) 9For further discussion, we refer the interested reader to Alan Silberberg et al. (1987), who have recently reported inferior-good and Giffen-good effects in monkey choice behavior. In their experiment, two monkeys chose between a large bitter-tasting food pellet and a small pleasant-tasting food pellet. Prices were altered by varying the probability that choice would result in delivery of a reward. Both monkeys showed Giffen behavior, increasing consumption of the large bitter-tasting food pellet in response to reduced probability of payoff. Silberberg et al. discuss how the existence of inferior and Giffen goods cannot be explained in terms of melioration theory and the matching law.
VOL. 81 NO. 4 BATTALIO ETAL.: GIFFEN GOODS 969 demand. The Giffen responses shown in Figure 2 are associated with large, negative income effects (strong inferiority of quinine consumption) and small substitution effects. At higher income levels, quinine is weakly inferior, and price changes result in standard, negatively sloped demand curves (Table 4, Fig. 4). Further, the three subjects for which an initial strongly inferior range of consumption was not found showed standard, negatively sloped demand curves (Fig. 3). Finally, the large variations in individual consumption patterns observed, even though the subjects used in this study were genetically similar and had similar environmental histories, adds one more reason why a Giffen response is unlikely to be observed at the market demand level. The data also clearly reveal that the Giffen phenomenon is a property of the preference map of an individual at a point in the choice space and not solely a property of the good. As is frequently pointed out (see e.g., Jack Hirshleifer, 1988 pp. 102-3), commodities are not Giffen, but rather, over some range of income and prices for a given preference structure and choice set, the individual's demand can be Giffen. The positively sloped demand curves observed at low income levels for rats 532, 542, and 543 (Fig. 2), along with the conventional, negatively sloped demand curves at higher incomes for the same subjects (Fig. 4), support this argument. We believe that the results of this experiment are important, not because they suggest that Giffen goods are likely to be observed in aggregate market demand, but because of their ability to test between competing representations of consumer behavior and to validate the counterintuitive prediction of the Slutsky-Hicks theory regarding the existence of the Giffen phenomenon. Simple theories that imply that demand curves are always negatively sloped or that subjects always respond to relative prices by consuming more of the good whose relative price has fallen are rejecting an important implication of consumer behavior. The suggestion that modern choice theory be dropped in favor of a more restrictive structure (Louis De Alessi, 1968) that would eliminate the possibility of a Giffen good would therefore be a mistake. Instead, the very small likelihood of its existence has to be admitted. From a methodological point of view, we note that determining that the class of Giffen goods is not empty would have been very difficult without using experimental methods or if we had been restricted to using human consumers. Previous results have validated "well-known" principles of economic behavior with rats using the same research protocol as employed here (Kagel, 1987). We interpret the present results as strong support for the existence of a Giffen-good response under appropriate, even if rare, initial conditions of strong inferiority for the commodity in question. REFERENCES Battalio, Raymond C., Green, Leonard and Kagel, John H., (1981a) "Income-Leisure Tradeoffs of Animal Workers," American Economic Review, September 1981, 71, 621-32., Kagel, John H., Rachlin, Howard and Green, Leonard, (1981b) "Commodity Choice Behavior with Pigeons as Subjects," Journal of Political Economy, February 1981, 84, 116-51. De Alessi, Louis, "A Methodological Appraisal of Giffen's Paradox," Weltwirtschaftliches Archiv, December 1968, 101, 287-96. Dougan, William R., "Giffen Goods and the Law of Demand," Journal of Political Economy, August 1982, 90, 809-15. Dwyer, Gerald P., Jr. and Lindsay, Cotton M., "Robert Giffen and the Irish Potato," American Economic Review, March 1984, 74, 188-92. Herrnstein, Richard J., "Relative and Absolute Strength of Response as a Function of Frequency of Reinforcement," Journal of the Experimental Analysis of Behavior, July 1961, 4, 267-72.,_ "On the Law of Effect," Journal of the Experimental Analysis of Behavior, March 1970, 13, 243-66. Herrnstein, Richard J. and Vaughan, William,
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