Linda Lim, T. Mary Foster, & Lewis Bizo University of Waikato

Transcription

1 Linda Lim, T. Mary Foster, & Lewis Bizo University of Waikato NZABA University of Canterbury Christchurch, 3 5 th Sept, 2010 Own Price Demand 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 access What is measured the number of accesses obtained (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) 1

2 (from Hursh, 1980) Hursh s equation 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 P max is the price of unit elasticity and is the price at the maximum response rate 2

3 Comparisons of Commodities 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 Data Six hens who preferred (using concurrent schedules) p ( g ) 3 s access wheat to 3 s access puffed wheat When own price demand functions for these were generated and compared: initial level of demand (lnl) was highest for puffed wheat but P max was largest for wheat But number of reinforcers was the measure of consumption One question this raised was what would have happened had weight of food consumed been used instead? 3

4 Cross Price Demand 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 both Uses Concurrent FR FR schedules and varies the FRs Two 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 Demand The 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 schedules Both linear and sigmoid functions have been used to describe the data sets and obtain cross points The 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 4

5 Cross Price Demand The equation for the sigmoid function often used is: Q = C + [(D C) / (1+ exp (g (log (P) log (I 50 ) ))].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 50 is the FR value giving ii 50% of reinforcers between D and C, g is the slope of the non linear curve at I 50 (note that g is required for the upward trending function) (Holm et al., 2007) Cross Price Demand Consumption is normally measured as number of reinforcers Most studies in this area do not present the data in a way that allows evaluation of what happens for the individual animals The aim was: to examine the use of the cross point method with hens and wheat and puffed wheat to compare the outcome with number of reinforcer and weight consumed to compare with own price demand 5

6 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 demand functions 3. To compare the result of the two methods Method Own Price Demand Subjects 6 hens Apparatus Two key hen chamber with two food magazines on scales that could be read by by the computer For own price demand one key and one magazine were used 6

7 Method Own Price Demand Procedure 40 min key time sessions In 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 wheat Sessions with FR 20 between series Results Performance on the FRs replicated earlier data: Overall response rates Bitonic for both W and PW Lower for W at smaller FRs Higher for W after about FR 64 Running response rates PRP Decreasing wth increaes in FR for both W and PW Lower for W at smaller FRs Higher for W after about FR 64 Flat or increasing with FR for both W and PW Longer for W up to about FR 32 7

8 Overall Response Rates Running Response Rates 8

9 PRP Consumption Number of reinforcers obtained decreased with increasing FR for both W and PW More PW than W reinforcers obtained up to FR 32 or FR 64 Weight consumed decreased with increasing FR for both W and PW Weight of W consumed greater than PW for most FR values (101 the exception) 9

10 Number of Reinforcers Obtained Weight of Reinforcer Consumed 10

11 Demand Hursh s equation fitted data well For Number of Reinforcers sthe edifferences e for W and PW were: Initial level of demand (lnl) > for PW than W P max > for W than for PW a larger for PW than W For Weight the differences for W and PW were: Initial level of demand (lnl) > for W than PW P max > for W than for PW a larger for PW than W W = filled circles & solid lines PW = open squares and dashed lines Demand With number of reinforcers lnl and Pmax replicated previous findings a was 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, P max was larger for W than PW, and showed a consistent lower rate of change of elasticity (a) for W than for PW 11

12 In case someone asks. Normalised Demand Normalising these data (Hursh and Winger, 1995) changes lnl, a and P max Number of Reinforcers lnl still larger for PW than W a still larger for PW than W for 4 hens (= for 1, smaller for 1) P max still larger for W than PW for 5 hens Weight lnl still larger for W than PW for 4 hens (smaller for 2) a still larger for PW than W for all hens P max 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 Demand Subjects Same 6 hens Apparatus Use both keys and both magazines Procedure Each condition used a series of nine pairs of CONC FR FR schedules One pair per session Two forced choice trial at start of session then 40 min key time with CONC FR FR Conditions so far are one series each of: Wheat vs Wheat Puffed 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 12

13 Method Cross Price Demand Procedure All hens responded up to FR 256 for both foods in the own price demand So the nine FR schedules used were from FR 1 to FR 256 They were paired smallest with largest up to largest with smallest The pairs were then randomly ordered, d giving the series: Left FR Right FR Results Same foods on both sides left = open circles right = filled squares Linear functions fitted log log plots and so no zero reinforcers data can be included Data somewhat noisy 104 shows bias to right key 13

14 Cross points Linear Same food on both keys Many cross near FR 16 vs FR 16 or FR 32 vs FR 8 or FR 8 vs FR 32 No consistent difference for W and PW No.W No. PW Wgt W Wgt PW Note: Y axis scales very different and Y not logged 14

15 Cross points Sigmoid function 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 Wgt W Wgt PW W vs PW W on left key = open circles PW on right key = filled squares 15

16 Cross points W (left) vs PW (right) No. Linear Wgt Linear No. Sigmoid Wgt Sigmoid Cross points Linear 60 No of Rfts 500 Weight W vs W PW vs PW W vs PW Cross points shift right (hens switch to PW at a higher price) for Weight more consistently than for Number of Reinforcers 16

17 Cross points Sigmoid No. of Rfts 180 W vs W Pw cs PW W vs PW Weight Again cross points shift right more consistently for Weight than for Number of Reinforcers So 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!) 17

18 Also Very similar conclusions from both linear and the sigmoid functions However, 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 reflect The published research so far with these functions normally 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 Conclusions Both procedures result in similar conclusions about the 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 18

19 Notes 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 FRs We 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 crossprice procedure 19