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SECOND-ORDER SCHEDULES OF TOKEN REINFORCEMENT: COMBINED
EFFECTS OF TOKEN-PRODUCTION AND EXCHANGE-SCHEDULE
A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE
UNIVERSITY OF FLORIDA
I thank my parents for their support and encouragement throughout my graduate
studies. I would also like to thank my mentor, Timothy Hackenberg, for his
encouragement and guidance in the research and writing of this research project.
TABLE OF CONTENTS
A C K N O W L E D G M E N T S ......... ................................................................................... iii
LIST OF FIGURES .............. ... ................................ ......... ..v
ABSTRACT ........ .............. ............. ..... .......... .......... vi
1 IN TR O D U C TIO N ......................................................................... .... .. ........
2 M E T H O D .............................................................................. 5
Su objects ...................................... .................................... .................... 5
A p p a ratu s ................................................................................. 5
P rocedu re .......................................................................... . 6
3 R E S U L T S ........................................................................................................1 1
4 D ISC U SSIO N ..................................................... 18
L IST O F R E FE R E N C E S .............................................................................. 26
B IO G R A PH IC A L SK E T C H ........................................................................................ 28
LIST OF FIGURES
2-1. Sample of an FR 2 (FR 50) token-reinforcement schedule............................... ..10
3-1. Mean responses per minute and standard deviations for each pigeon under
constrained consumption conditions plotted as a function of small, medium, and
large token-production ratios, and as a function of exchange ratio........................ 13
3-2. Mean responses per minute plotted as a function of token-production segment for
each pigeon under constrained consumption conditions ....................................14
3-3. Mean latency plotted as a function of token-production segment for each pigeon
under constrained consumption conditions. .................................. .................15
3-4. Mean total responses for each pigeon under unconstrained consumption conditions
plotted as a function of unit price. ............................. .... ..................... 16
3-5. Mean consumption (total seconds access to food) for each pigeon under
unconstrained consumption conditions plotted as a function of unit price.............. 17
4-1. Mean consumption rate as a function of unit price for each pigeon under constrained
consumption conditions plotted on log-log coordinates. .......................................24
4-2. Mean reciprocal responses per minute and modified unit price for each pigeon
plotted as a function of unit price and exchange schedule .............. ...............25
Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science
SECOND-ORDER SCHEDULES OF TOKEN REINFORCEMENT: COMBINED
EFFECTS OF TOKEN-PRODUCTION AND EXCHANGE-SCHEDULE
Chair: Timothy D. Hackenberg
Major Department: Psychology
Four pigeons were exposed to second-order schedules of token reinforcement,
with stimulus lights serving as token reinforcers. Tokens were earned according to a
fixed-ratio (token-production) schedule and were exchanged for 2.5 s access to food
according to a fixed-ratio (token-exchange) schedule. The token-production and token-
exchange schedules were manipulated systematically across conditions. Response rates
varied inversely with the token-production schedule for a given token-exchange schedule
value. Response rates also varied inversely with the token-exchange schedule for a given
token-production value, particularly at the higher token-production ratios. Further, under
higher token-production and exchange-schedule values, response rates tended to increase
in token-production segments closer to exchange periods and food. Several probe
conditions were also studied in a closed economy that permitted unconstrained food
consumption. Under these conditions, response rates were less sensitive to token-
production schedule manipulations than under standard (constrained consumption)
conditions in which sessions were limited to 48 food presentations. Results were
analyzed using a modification of the behavioral economic concept of unit price (a cost-
benefit ratio comprising responses per unit of food delivery).
A second-order schedule of reinforcement is one in which a pattern of behavior
reinforced according to one schedule is treated as a unitary response reinforced according
to a second schedule (Kelleher, 1966). A token-reinforcement schedule is a second-order
schedule in which responses produce tokens according to one schedule (the token-
production schedule) and opportunities to exchange those tokens for primary
reinforcement according to a second schedule (the exchange schedule) (Kelleher, 1958;
Previous research has shown that response rates and patterns maintained under
token-reinforcement schedules vary systematically as a function of both the token-
production schedules (Kelleher, 1958) and the exchange schedules (Foster, Hackenberg
& Vaidya, 2001; Waddell, Leander, Webbe, & Malagodi, 1972; Webbe & Malagodi,
1978). Most research on token-reinforcement schedules has involved fixed-ratio (FR)
components (schedules that require a specified number of responses for reinforcement).
Similar to FR performance reinforced with food, response rates under FR token-
production and exchange schedules vary inversely with the FR value (Foster, et al., 2001;
Kelleher, 1958; Malagodi, 1967; Webbe & Malagodi, 1978;). Kelleher (1958), for
example, found that chimpanzees' rates of lever pressing decreased as the FR token-
production requirement increased from 30 to 100 with the exchange ratio held constant at
FR 60. Foster et al. (2001) found that pigeons' response rates decreased as the FR
exchange schedule increased from 1 to 8 with the token-production ratio held constant at
FR 50. In both studies, response-rate decrements were mainly a function of increased
pausing early in an FR cycle.
With FR token-production and exchange schedules, a potentially relevant variable
emerges: the ratio of responses per unit of reinforcer, closely related to the economic
concept of unit price (DeGrandpre, Bickel, Hughes, Layng, & Badger, 1993; Hursh,
1978). When the exchange ratio is manipulated with token-production ratio held
constant, changes in reinforcer magnitude are proportional to changes in exchange ratio.
As a result, the unit price remains constant across variations in the exchange schedule.
For example, in the Foster et al. (2001) study, with a token-production ratio of 50 and an
exchange ratio of 2, FR 2 [FR 50], to use the standard nomenclature,100 responses
produced 2 tokens (each exchangeable for 2 s access to food), or 25 responses per second
access to food. So too under the FR 8 [FR 50] condition, 400 responses produced 8
tokens (16 s access to food), or 25 responses per second access to food. According to a
literal version of the unit price concept, response output should be roughly constant under
such conditions of equivalent unit price, without regard to the specific values of its cost
and benefit components(Madden, Bickel, & Jacobs, 2000). Contrary to these predictions,
however, response output varied substantially across conditions of equal unit price.
Responding then was governed not by responses per unit of food delivery (unit price) but
by responses per exchange period (exchange ratio).
Another way of examining the viability of the unit price concept with token-
reinforcement procedures is through manipulations of the token-production ratio. Unlike
exchange-ratio manipulations, altering the token-production ratio while holding constant
the exchange ratio changes the unit price. For example, in the Kelleher (1958) study,
with an FR 30 token-production schedule and an FR 60 exchange schedule, 1800
responses produced 60 tokens, a unit price of 30. When the token-production schedule
was increased to 100, while holding constant the exchange schedule ratio at 60, 6000
responses produced 60 tokens, a unit price of 100. In accordance with unit price
predictions, rates of lever pressing decreased as the FR requirement and unit price of the
token-production schedule increased. Thus, unlike exchange-ratio manipulations, in
which unit price is invariant with respect to changes in ratio requirements; with token-
production manipulations, unit price changes with changes in ratio requirements.
The purpose of the present experiment was to clarify how both the token-
production schedule and exchange schedule contribute to maintaining behavior on token-
reinforcement schedules while assessing the applicability of unit price in accounting for
this behavior. Although response rates and patterns in token-reinforcement procedures
have been shown to vary with the values of both FR token-production and exchange
schedules, previous studies have typically manipulated only one of these variables while
holding the other constant. The effects of manipulating one of the schedules in a token-
reinforcement procedure may depend on the others value. Using a preparation similar to
that of Foster et al. (2001), with stimulus lights serving as token reinforcers, FR token-
production and exchange schedules were parametrically manipulated on a within-subject
basis across a wider range of schedule values than examined in prior research, allowing
for a more detailed analysis of their effects. The present experiment included three
token-production values (small, medium, and large) and three exchange values (2, 4, and
8); and was designed such that most of the possible combinations of these two schedules
were experienced by the subjects.
Unit price experiments are typically conducted in a closed economy, where all food
is obtained via interaction with the experimental conditions (Hursh, 1980). A closed
economy is often contrasted with an open economy, where supplemental feeding occurs
outside of experimental sessions. In the Foster et al. (2001) study, birds received all or
nearly all of their daily food intake within sessions (functionally a closed economy).
However, because supplementary feeding was sometimes necessary, it can be argued that
this was not a genuine closed economy, rendering a unit-price analysis inappropriate. In
the present study, therefore, three probe conditions were conducted under a closed
economy where all food was obtained via interaction with experimental contingencies.
Parametric evaluation of token-production and exchange ratios in closed and open
economic contexts allows for a stronger investigation of the unit price concept and for an
extension of previous token-reinforcement studies. Unit price considerations aside, the
study had as its main objective the extension of previous work in the realm of token-
reinforcement procedures. The results should further clarify the contributions of token-
production and exchange schedules to performance on token-reinforcement procedures.
Four male White Carneau pigeons (Columba livia) (numbered 702, 732, 774,
1855) served as subjects. Each pigeon had prior experience with token-reinforcement
schedules. Subjects were housed individually under a 16.5 hour / 7.5 hour light dark
cycle and had continuous access to water and health grit in home cages. Pigeons were
maintained at approximately 20g of their 80% free feeding weights for most conditions of
the experiment. In a few conditions (see below), the weight restrictions were removed,
such that weights were free to vary above the 80% level.
Experimental sessions were conducted in an enclosure 36 cm high by 50 cm long
by 36 cm wide. An intelligence panel on a wall of the enclosure was equipped with
three response keys centered vertically 11.5 cm from the ceiling to the key center and 9
cm from each other (center to center). Thirty-four evenly spaced red light emitting
diodes (LEDs) were centered 5 cm above the keys and 1.25 cm apart from each other
(center to center) and protruded 0.3 cm into the enclosure. The LEDs (hereafter referred
to as tokens) were always illuminated left to right, in sequential order. The presentation
and removal of tokens was controlled by an electromechanical stepping switch (Lehigh
Valley Electronics, model 1427, Lehigh Valley, PA), the operation of which also
provided auditory feedback each time a token was presented or removed. Centered above
the token array was a yellow house light that provided the enclosure with diffuse
illumination. When active, side keys were illuminated green, and the center key was
illuminated red. Pecks exceeding approximately 11 to 14 g of force were counted. A
hopper aperture was centered 11.5 cm below the left key. A solenoid-operated food
hopper could be raised into this opening, allowing access to mixed grain. Food
presentation was accompanied by illumination of a yellow light located inside the
opening. A photo-beam mounted across the aperture recorded head entry into the hopper.
Continuous white noise and ventilation fans were active during experimental sessions to
mask extraneous sounds. Experimental contingencies were programmed, and data
collected, using a computer equipped with Med-pc software, located in a separate room.
Because the pigeons had previous experience with token-reinforcement schedules,
no training was necessary. A session began with the illumination of a green side key
(key position counterbalanced across subjects). Responses on this key (designated the
token-production key), were reinforced according to a FR schedule, that is, a fixed
number of responses illuminated one token. A separate exchange schedule was arranged
with respect to the number of tokens needed to produce an exchange period. During this
exchange period, signaled by illumination of the red center key, a single response
darkened the rightmost token and produced 2.5 s access to food (timed from head entry
into hopper). The exchange period continued until all tokens earned during that cycle
were exchanged, followed immediately by the illumination of the green side key and the
beginning of the next cycle. Sessions continued until 48 tokens had been exchanged for
food. (Because Pigeon 774 was consistently overweight, sessions from the last 5
conditions ended after only 32 tokens had been exchanged). Figure 1 is a procedural
schematic of an FR 50 token production FR 2 exchange token-reinforcement schedule.
All pigeons were exposed to a series of conditions in which FR values of both the
token-production and exchange schedules were varied systematically across conditions.
Conditions included FR exchange-schedule values of 2, 4, and 8 and FR token-
production values of 25, 50, and 100. A variable ratio (VR) schedule 12.5 (on which
reinforcement depended with equal probability on either 12 or 13 responses) was added
as the lowest token-production schedule for Pigeon 1855 because response rates could
not be maintained reliably at the highest ratios. Table 1 shows the sequence of conditions
and the number of sessions conducted under each. (When reporting the results of this
experiment, conditions are referred to by the values of the token-production and
exchange schedules. The token exchange-schedule value is listed first, followed by the
value of the token-production schedule listed in brackets. For example, a condition with
an FR 50 token production FR 2 token exchange would be referred to by the abbreviation
FR 2 [FR 50] or simply as 2 .) The experiment consisted of two parts. In Part 1
(constrained consumption conditions) pigeons were maintained at approximately 80% of
their free-feeding weights. This was accomplished by holding constant the number of
food deliveries each session at 48, and providing supplementary post-session feedings as
needed. In Part 2 (unconstrained consumption conditions) sessions lasted until 10 min
elapsed without a response. Because pigeons in this phase were usually above 80%
weights, generally no supplementary feeding was needed. For some conditions in this
phase for Pigeons 702 and 1855, not enough food was earned to maintain their respective
80% free feeding weights. Supplementary feedings were therefore provided. In three
instances, when responding had weakened to the point that sessions were not being
completed consistently, or 80% weight not maintained in unconstrained consumption
conditions, conditions were changed arbitrarily in the absence of stability. Data from
these conditions were not included in the analysis. Further, several conditions with no
tokens were also run, but were not included in the present analysis.
In Part 1 conditions, the token-production ratio and the exchange ratio were
systematically varied across conditions. In Part 2 conditions, the token-exchange
schedule was held constant at FR 2, while the token-production schedule was varied
across conditions. During this phase a limited hold of 10 s was placed on hopper cycles,
such that the amount of time the hopper was raised was restricted. The expiration of the
10 s limited hold was treated as a hopper entry, starting the 2.5 s food timer.
Each condition was in place for a minimum of 20 sessions and until performance
was deemed stable via visual inspection of daily response rates. For several conditions,
due to a programming error, the initial-link latencies to respond were sometimes lost for
given exchange cycles. In those instances where greater than 5% of the total initial-link
latencies were lost from the last 5 sessions of a condition, the condition was replicated.
For two of the subjects, Pigeons 774 and 1855, five replications were required (Table 2-
Table 2-1. Order of conditions and number of sessions per condition listed as:
exchange schedule [production schedule] (number of sessions)
702 732 774 1855
a Condition ended arbitrarily
b 32 reinforcers per session
50 pecks produce
2 tokens produce an
A peck on the center key darkens one token
and produces 2.5-s access to food.
After all tokens are exchanged
the cycle repeats.
Figure 2-1. Sample of an FR 2 (FR 50) token-reinforcement schedule
All data analyses are based on the last five sessions from each condition. Figure 3-
1 shows responses per min from Part 1 conditions, plotted as a function of token-
production ratio value (small, medium, and large), and as a function of exchange-ratio
value within a given token-production ratio. Response rates tended to decrease as the
token-production schedule increased. Under higher token-production ratios response rates
also tended to decrease as the exchange schedule increased. For two pigeons, 732 and
774, replications of conditions were consistent with original exposures. For the other two
pigeons, however, some subsequent exposures to conditions failed to replicate the initial
findings. Replications occurred after an intervening history on unconstrained
consumption conditions. In most of these instances, response rates increased when
compared to initial exposures.
Figure 3-2 shows responses per min across successive token-production segments
for Part 1 conditions under all combinations of token-production and exchange schedules.
A token segment is defined as the portion of an exchange cycle that occurs during the
production of a given token. Graphs in the left, center, and right columns show response
rates under FR 2, 4, and 8 exchange schedules, respectively. For all subjects, response
rates were bi-valued, with lower initial-link rates giving way to higher, relatively constant
rates in subsequent links. Under the FR 2 and FR 4 exchange ratios, the initial-link
response rates were generally lowest in conditions with higher token-production ratios
(FR 50 and FR 100). Under the FR 4 exchange ratio, rates under the highest token-
production schedules tended to increase more gradually than under the smaller token-
Figure 3-3 shows for each token-production schedule, from Part 1 conditions, the
pre-ratio pause across successive token-production segments under each exchange
schedule. The data in this figure are organized as in Figure 3-2, with the graphs in each
column showing data for a given exchange schedule and graphs in each row specific to
an individual pigeon. For all pigeons pre-ratio pausing was longest in the initial link of
the exchange ratio, and relatively short and undifferentiated thereafter. Within a given
exchange ratio, initial-link pausing was directly related to the requirements of the token-
production schedules. Increases in the exchange-schedule value from 2 to 4 also tended
to produce increased initial-link pauses, but generally only when comparing conditions
under the highest token-production value. For lower token-production FR values,
increases in the exchange schedule either had no effect on initial-link pausing or
produced small increases.
Figures 3-4 and 3-5 show total response output and total consumption,
respectively, for Part 2 conditions plotted as a function of unit price on log coordinates.
For all subjects total response output tended to increase as unit price increased. Total
consumption, however, decreased very little, if at all, with increases in unit price.
200 702 small medium large
2 4 8 2 2 4 4 2 2 4
240 732 small medium rge
200 732 large
0- 2 2 4 8 2 2 4 2 4
) 240 -
LU 772 small medium large
(0 200 774
O 160 Initial exposure
2 2 4 4 8 8 2 2 4 4 2 2 4 4
240 small medium large
2 2 4 4 8 8 2 2 4 4 2 2 2 4 4
Figure 3-1. Mean responses per minute and standard deviations for each pigeon under
constrained consumption conditions plotted as a function of small, medium,
and large token-production ratios, and as a function of exchange ratio.
1 2 1 2 3 4
S --- small
2 4 6 8
Figure 3-2. Mean responses per minute plotted as a function of token-production
segment for each pigeon under constrained consumption conditions. Open
symbols represent initial exposures to a condition, filled symbols represent
1 2 3 4
2 4 6 8
Figure 3-3. Mean latency plotted as a function of token-production segment for each
pigeon under constrained consumption conditions. Open symbols represent
initial exposures to a condition, filled symbols replications.
CO 1000 1000
LU 10 40 10 40
10 40 5 20
Figure 3-4. Mean total responses for each pigeon under unconstrained consumption
conditions plotted as a function of unit price.
conditions plotted as a function of unit price.
10 10 4
Figure 3-5. Mean consumption (total seconds access to food) for each pigeon under
unconstrained consumption conditions plotted as a function of unit price.
The results of the present experiment are consistent with those previously reported
on extended chain and second-order schedules with ratio components. Similar to
Kelleher (1958), increases in the token-production ratio at a given exchange ratio
decreased response rates. Similar to Foster et al. (2001), increases in the exchange
schedule produced lower overall response rates, but generally only under the larger
token-production ratios. In the context of the lowest token-production value, response
rates varied less, if at all, with the exchange ratio. Further, for both token-production and
exchange-schedule manipulations, decreases in response rates were primarily a result of
longer pre-ratio pausing and weak behavior early in the ratio (see Figures 3-2 and 3-3), a
finding also consistent with previous research (Foster et al., 2001; Kelleher, 1958; Webbe
et al., 1978). Also similar to these previous findings, response rates were low, and pauses
high, in early links of all exchange cycles. The present results also correspond to those
reported by with extended chain and token schedules in regard to the gradually increasing
rates seen under combinations of higher token-production and exchange-schedule values
(Foster et al., 2001; and Jwaidah, 1973). The present results then both replicate and
extend previous investigations with token-reinforcement procedures, manipulating the
token-production and exchange schedules across a wider range of values than previously
The results also have implications for the unit price concept. Researchers have
typically examined unit price with a closed economy, defined as one in which the total
consumption of a reinforcer is limited by a subject's interaction with the contingencies.
By contrast, an open economy is one in which total consumption is controlled by the
experimenter. The majority of conditions in the present experiment involved an open
economy in that the total consumption for a session was kept constant at 48 reinforcers.
However, for 3 of 4 subjects, daily consumption within a session was sufficient to
preclude post-session feedings, a feature generally consistent with closed economies. In
that the majority of subjects' consumption of food occurred solely via contact with the
experimental contingencies, the economic conditions might be considered a functional
closed economy, suggesting the potential applicability of a unit price analysis.
The main dependent measures in unit price experiments are total consumption and
response output (Hursh et. al, 1988; Hursh, 1980, 1984; Madden, Bickel, and Jacobs,
2000). Madden et. al (2000) noted two predictions of unit price. First, when the unit
price of a reinforcer increases, one can expect decreases consumption of that reinforcer.
Second, as unit price of a reinforcer is increased, overall responding increases to some
peak, with further price increases decreasing responding. Stated differently, the functions
relating total consumption and responding to unit price are negatively accelerated and
Data from Part 2 conditions were generally in accord with these predictions.
Total response output varied directly with unit price in all cases. As Figures 3-4 and 3-5
show, total responding generally increased, while consumption remained constant or
decreased, as unit price increased. The number of unconstrained consumption conditions
included in this analysis is insufficient for an examination of the shape of the full
function for these two measures.
Because both consumption and responding were restricted in constrained
consumption conditions, analysis of total consumption and responding as a function of
unit price is not feasible. However, as Sumpter, Temple, and Foster (1999) point out, for
contingencies where absolute consumption is restricted, consumption rate is still free to
vary and may also be sensitive to unit price manipulations. In Sumpter et al. (1999),
consumption rate was examined in sessions that ended after either 30 reinforcers had
been delivered or 40 minutes had passed. Consumption rate proved an orderly measure
and was found to vary as a function of unit price, similar to total consumption in other
contexts. Similarly, response rates are also free to vary in conditions with restricted
response output. In light of the successful use of unit price as an account of consumption
rate in Sumpter et al. (1999), consumption rates were used in the analysis of constrained
consumption conditions. Additionally, because total responding was restricted in the
constrained consumption conditions, response rate was investigated as another measure
potentially sensitive to unit price manipulations.
Figure 4-1 shows consumption rate (s access to food per min) from Part 1
conditions plotted on log coordinates as a function unit price. Consumption rate
decreased as unit price increased, a finding consistent with unit price predictions. As in
Sumpter et al. (1999) consumption rate in this case therefore serves as a suitable proxy
for total consumption with regard to unit price predictions. Under all exchange ratios,
consumption rate generally decreased with increases in unit price. However, under
higher exchange ratios, sharper decreases in consumption rate tended to occur with
increases in the token-production schedule. For Part 1 conditions with higher exchange
values, the function relating consumption rate to unit price has a steeply decreasing slope.
However, for conditions with the same unit price, consumption rates sometimes varied
inversely with token exchange-schedule value. This mirrors the variation in response
rates mentioned earlier for these same conditions, and is not in strict accord with unit
As mentioned earlier, a literal version of the unit price concept predicts that two
schedules of reinforcement with the same response-reinforcer ratios should engender
equivalent response output, regardless of the particular response requirements or
reinforcer amounts that comprise the ratio. In the present study, decreases in responses
rates that occurred as a function of increasing the token-production schedule is consistent
with the unit price formulation. Further, the lack of consistent exchange-schedule effects
(where unit price is held constant) at lower token-production values is also in accord with
the unit price equation. The rate decreases which occurred as a function of increases in
the exchange schedule at higher token-production schedule values (where the cost benefit
ratio remains the same), however, are not predicted by unit price.
When attempting to account for departures from unit price predictions in his data
set, Madden et al. (2000) found that a modification of the unit price concept made better
ordinal predictions than a traditional unit price account. The modified unit price equation
is given by
P = (FR + H)/ V (4-1)
where P is modified unit price, FR is total number of responses prior to reinforcement, H
is handling costs (in the present study, the number of responses to exchange each token,
equal to the exchange-schedule value), and V is the reinforcer value (Mazur, 1987). The
equation for reinforcer value is written
V = A/ 1 +kD (4-2)
where A is the reinforcer amount, D is the reinforcer delay, and k is a scaling constant
(set to 1s-1 for the present analysis). A modified unit price analysis was conducted on
response rates generated in the present experiment, with s of food access used for
reinforcer amount and the average time from the illumination of the token-production key
to exchange used for reinforcer delay.
Figure 4-2 shows modified unit price and the reciprocal of responses per minute for
each condition as a function of unit price. As with the traditional unit price formulation,
response rates are expected to vary inversely with modified unit price. The reciprocal of
responses per minute was thus used to allow ease of inspection, as the reciprocal
measures would be expected to vary directly with modified unit price. Figure 4-2 is
organized similar to Figure 2-1 in that conditions are plotted with respect to increasing
unit price (Figure 2-1 is organized with respect to token-production value) and within
unit price, as a function of increasing exchange-schedule values. The gray bars situated
directly over each condition label represent the modified unit price for that condition.
The black bar directly to the left of a given gray bar represents the reciprocal of responses
per minute for that condition.
The modified unit price equation allows for better ordinal predictions than a
standard unit price account with respect to exchange-schedule manipulations. That is,
within a given unit price, this formulation correctly predicts the direction of the variations
in responding in the majority of cases. A standard unit price account, based on nominal
programmed values, is silent with respect to such variations. Additional research is
needed to determine the full extent to which unit price, and modified unit price, are useful
metrics for token-reinforcement schedules.
In summary, the present research replicated the results of token-production and
exchange-schedule manipulations of previous token-reinforcement studies (Foster et. al.,
2001; Kelleher, 1958) in showing that response rates vary systematically as a function of
FR token-production and exchange schedules. Unit price does a reasonably good job in
accounting for the effects of token-production manipulations in both constrained and Part
2 conditions. The modified unit price formulation, however, provides better ordinal
predictions of the effects of exchange-schedule manipulations than a traditional unit price
0 FR 2 exchange
A FR 8 exchange
E FR 8 exchange
Figure 4-1. Mean consumption rate as a function of unit price for each pigeon under
constrained consumption conditions plotted on log-log coordinates. Open
symbols represent initial exposures to a condition, filled symbols replications.
2 2ce 4 8 2 2 2ce 4 4 2 2 4
10 20 40
I lIllI ll I
2 22ce4 4 8 8 2 22ce4 4 2 22ce4 4
0 10106 -
2 2 2ce 4 8 2 2 2ce 4 2 2ce 4
2 22ce4 4 8 8 2 22ce4 4 2 2 22ce4 4
I MODIFIED UNIT PRICE
I RECIPROCAL RESPONSES PER MINUTE
Figure 4-2. Mean reciprocal responses per minute and modified unit price for each
pigeon plotted as a function of unit price and exchange schedule. Conditions
denoted with the letters ce were run under a closed economy with
IinIllIHI I II
'' "* *' *
,n ,nl, ,H ll ,
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Christopher Bullock graduated from J. F. Webb High school in the spring of 1994.
He then enrolled at the University of North Carolina at Wilmington (UNCW) in the Fall
of 1994. He graduated from UNCW in the spring of 1999 with a Bachelor of Arts in
psychology with honors. The next fall he enrolled in the Behavior Analysis graduate
studies program in the Department of Psychology at the University of Florida. He is
presently continuing his education and conducting research in Behavior Analysis.