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9/7/2010
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Linda Lim, T. Mary Foster, & Lewis Bizo University of Waikato
NZABAUniversity of Canterbury
Christchurch, 3 ‐ 5th Sept, 2010
Own‐Price DemandThis comes from varying the price or amount or work This comes from varying the price or amount or work required to gain access to some event and measuring the way consumption of that event changes
With animals price may be the number of responses required to gain accessWhat is measured the number of accesses obtained (consumption) over a fixed time as price is varied(consumption) over a fixed time as price is varied
A demand function is the log‐log plot of the consumption vs price (with price on the x‐axis)
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(from Hursh, 1980)
Hursh’s equationln (Q) = ln (L) + b ln (P)– a (P) ……………..(1) ln (Q) ln (L) + b ln (P) a (P) ……………..(1)
Q = consumption P = price or FR size L = the consumption at minium price (here at FR 1)b = the slope (elasticity) at minimum price a = the rate of change of elasticity
P i th i f it l ti it d i th i t th Pmax is the price of unit elasticity and is the price at the maximum response rate
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Comparisons of CommoditiesComparisons of the parameters of the demand Comparisons of the parameters of the demand functions are made to compare the ‘values’ of commodities
When consumption of two commodities can be measured on the same scale then can sensibly compare all parameters
Much of the experimental work is with drugs, some id with and different quantities of food
Our Previous DataSix hens who preferred (using concurrent schedules) p ( g )3‐s access wheat to 3‐s access puffed wheatWhen own‐price demand functions for these were generated and compared:
initial level of demand (lnL) was highest for puffed wheat but Pmax was largest for wheat
But number of reinforcers was the measure of consumptionOne question this raised was what would have happened had weight of food consumed been used instead?
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Cross‐Price DemandIn the animal welfare literature a suggested method for In the animal welfare literature a suggested method for comparing the value of two commodities for animals is to allow them to work for access to both concurrently and to vary price of bothUses Concurrent FR FR schedules and varies the FRsTwo ways to do this:
hold one FR constant and increase other from smaller to larger than the constant schedule then reverse or vary both FRs ‐ alternating the smaller FR from one ‘side’ to the other over sessions – is called the alternating‐schedules procedure
Cross‐Price DemandThe consumption of each alternative at each price pair The consumption of each alternative at each price pair is plotted against the price on one of the pair FR schedulesBoth linear and sigmoid functions have been used to describe the data sets and obtain cross pointsThe idea is that the cross point will move to a higher price for one event the more that event is valued over the other To assess the cross point ‘move’ one needs to assess the cross point when the events are the same
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Cross‐Price DemandThe equation for the sigmoid function often used is: The equation for the sigmoid function often used is: Q = C + [(D – C) / (1+ exp (g (log (P) – log (I50) ))] ….2
Q = consumption (normally number of reinforcers)P = FR value or price D & C are the lower and the upper limits of Q (like k in H&S)I i th FR l i i % f i f b t D d C I50 is the FR value giving 50% of reinforcers between D and C, g is the slope of the non‐linear curve at I50 (note that –g is required for the upward trending function)
(Holm et al., 2007)
Cross‐Price DemandConsumption is normally measured as number of p yreinforcersMost studies in this area do not present the data in a way that allows evaluation of what happens for the individual animalsThe aim was:
to examine the use of the cross point method with hens and pwheat and puffed wheatto compare the outcome with number of reinforcer and weight consumedto compare with own‐price demand
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The Aims
1. To compare own‐price demand functions generated from number of reinforcers to those from generated from weight of food eaten with two different foods
2. To do the same for the cross point from cross‐price p pdemand functions
3. To compare the result of the two methods
Method – Own‐Price Demand Subjects j
6 hensApparatus
Two‐key hen chamber with two food magazines on scales that could be read by by the computerby the computer
For own‐price demand one key and one magazine were used
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Method – Own‐Price Demand Procedure Procedure
40‐min ‘key’ time sessionsIn each condition one FR changed each session
Each FR series involved doubling FR each session until no reinforcers obtained over two consecutive sessions
Three series with Wheat Three series with Puffed‐wheatThree series with Puffed wheat
Sessions with FR 20 between series
Results Performance on the FRs replicated earlier data:Performance on the FRs replicated earlier data:
Overall response rates Bitonic for both W and PWLower for W at smaller FRsHigher for W after about FR 64
Running response ratesDecreasing wth increaes in FR for both W and PWLower for W at smaller FRsHigher for W after about FR 64
PRPFlat or increasing with FR for both W and PWLonger for W up to about FR 32
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Overall Response Rates
Running Response Rates
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PRP
ConsumptionNumber of reinforcers obtained decreased with Number of reinforcers obtained decreased with increasing FR for both W and PWMore PW than W reinforcers obtained up to FR 32 or FR 64
Weight consumed decreased with increasing FR for g gboth W and PWWeight of W consumed greater than PW for most FR values (101 the exception)
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Number of Reinforcers Obtained
Weight of Reinforcer Consumed
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DemandHursh’s equation fitted data well
For Number of Reinforcers the differences o u be o e o ce s t e d e e cesfor W and PW were:
Initial level of demand (lnL) > for PW than WPmax > for W than for PWa larger for PW than W
For Weight the differences for W and PW were:were:
Initial level of demand (lnL) > for W than PWPmax > for W than for PW a larger for PW than W
W = filled circles & solid lines PW = open squares and dashed lines
DemandWith number of reinforcers lnL and Pmax replicated max pprevious findings
awas consistently larger for PW i.e., a lower rate of change of elasticity for W than PW. This consistency was not found previously
Weight data showed W had a higher level of demand initially, Pmaxwas larger for W than PW, and showed a consistent lower rate of change of elasticity (a) for W than for PW
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Normalised DemandNormalising these data (Hursh and Winger, 1995) changes l d P
In case someone asks ….
lnL, a and PmaxNumber of Reinforcers
lnL still larger for PW than Wa still larger for PW than W for 4 hens (= for 1, smaller for 1)Pmax still larger for W than PW for 5 hens
WeightlnL still larger for W than PW for 4 hens (smaller for 2)
till l f PW th W f ll ha still larger for PW than W for all hensPmax still larger for W than PW for all hens
So same conclusions drawn as with previous analysis
Haven’t done preference adjusted demand as do not know bias yet
Method – Cross‐Price DemandSubjects
Same 6 hensApparatus
Use both keys and both magazinesProcedure
Each condition used a series of nine pairs of CONC FR FR schedulesOne pair per sessionTwo forced‐choice trial at start of session then 40‐min ‘key’ time with CONC FR FR40 min key time with CONC FR FR
Conditions so far are one series each of:Wheat vsWheatPuffed‐wheat vs Puffed‐Wheat vs Puffed‐wheat
Sessions with CONC FR 8 FR 32 alternated with FR 32 FR 8 between series with the food for the next series in the magazines
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Method – Cross‐Price DemandProcedure Procedure
All hens responded up to FR 256 for both foods in the own‐price demandSo the nine FR schedules used were from FR 1 to FR 256They were paired smallest with largest up to largest with smallesth h d l d d hThe pairs were then randomly ordered, giving the series:
Left FR
1 8 128 4 32 2 16 64
Right FR
256 32 64 1 8 128 16 4
ResultsSame foods on both sides sides
left = open circlesright = filled squares
Linear functions fitted
log‐log plots and so no zero reinforcers no zero reinforcers data can be included
Data somewhat ‘noisy’
104 shows bias to right key
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Cross points – LinearSame food on both keysSame food on both keysMany cross near FR 16 vs FR 16 or FR 32 vs FR 8 or FR 8 vs FR 32No consistent difference for W and PW
No .W No. PW WgtW Wgt PW
101 23 18 53 29
102 19 49 16 82
103 20 ‐ 21 ‐
104 5 10 5 3
105 17 13 24 12
106 22 15 25 9
Note: Y axis scales very different and Y not logged
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Cross points – Sigmoid functionSame food on both keys Same food on both keys Many cross near FR 16 vs FR 16 or FR 32 vs FR 8 No consistent difference for W and PW
No. W No. PW WgtW Wgt PW
101 15 32 32 24
102 20 24 16 24
103 20 ‐ 24 ‐
104 12 14 12 16
105 24 16 24 14
106 14 120 14 16
W vs PW
W on left key =open circles
PW on right key = filled squares
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Cross pointsW (left) vs PW (right) W (left) vs PW (right)
No. Linear Wgt Linear No. Sigmoid Wgt Sigmoid
101 14 37 12 18
102 22 253 24 120
103 19 506 30 190
104 24 127 16 128
8 6105 53 283 60 70
106 11 43 14 40
Cross points ‐ Linear60
No of Rfts500 Weight
20
30
40
50
No of Rfts
W vs W
PW vs PW
W vs PW200
300
400
g
0
10
1 2 3 4 5 60
100
1 2 3 4 5 6
Cross points shift right (hens switch to PW at a higher price) for Weight more consistently than for Number of Reinforcers
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Cross points ‐ Sigmoid140
No. of Rfts 180
200
Weight
0
20
40
60
80
100
120
W vs W
Pw cs PW
W vs PW
0
20
40
60
80
100
120
140
160
g
1 2 3 4 5 6 1 2 3 4 5 6
Again cross points shift right more consistently for Weight than for Number of Reinforcers
So …Using the cross‐price procedure and Number of Using the cross price procedure and Number of Reinforcers ‐ we would conclude that the two food could be of similar values as the W vs PW cross points are not shifted consistently from those in the same food conditions
Using Weight ‐ we would conclude that the two food are not of similar values as the W vs PW cross points are shifted consistently right ‐ away from those from the same food conditions (but maybe not so for 101!)
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Also…Very similar conclusions from both linear and the ysigmoid functionsHowever, the sigmoid functions were fitted with all the parameters left free to vary and some of the resulting parameter values are not ‘sensible ’ – given what they are supposed to reflectThe published research so far with these functions pnormally includes all the data sets in one analysis and/or does not show any individual data and often does not report the parameter values anyway ‐ so can’t compare these present values with any others
ConclusionsBoth procedures result in similar conclusions about pthe relative ‘values’ of W and PW to these hens when weight was the measure of consumption
With Weight food eaten both methods suggest W of greater value than PW
With Number of Reinforcers interpretation of the own‐price demand parameters is less clear, while the cross‐price demand cross points suggest the two foods are of equivalent value
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NotesStill have to analyse response rates and pausing in the Still have to analyse response rates and pausing in the CONC FR FR schedules – the hens did respond faster for PW than W at small FRsWe are completing a second series of these cross‐point determinations ‐ the present ones are based on one session only at each FR pair We have yet to assess these hens preferences for these foods (that is next) Then we hope to examine the non‐alternating cross‐price procedure
