ÿþ <HTML> <head> <TITLE>Demand equations for qualitatively different foods under fixed&#45;ratio schedules&#58; A comparison of three data conversions. </TITLE> <meta name="Title" content="Demand equations for qualitatively different foods under fixed&#45;ratio schedules&#58; A comparison of three data conversions."> <meta name="Author" content="Foster, T.M., Sumpter, C.E., Temple, W., Flevill, A. &AMP; Poling, A."> <meta name="Volume" content="92"> <meta name="Number" content="03"> <meta name="StartPage" content="0305"> <meta name="Pages" content="305-326"> <meta name="Year" content="2009"> <meta name="JournalNameShort" content="JEAB"> <meta name="JournalName" content="Journal of Experimental Analysis of Behavior"> </head> <body> <A HREF="/jeab/articles/2009/jeab-92-03-0305.pdf"> <IMG SRC="/pics/viewFullArticle.gif" BORDER="0"> </A> <H2> Foster, T.M., Sumpter, C.E., Temple, W., Flevill, A. &AMP; Poling, A. (2009). Demand equations for qualitatively different foods under fixed&#45;ratio schedules&#58; A comparison of three data conversions. <i> Journal of the Experimental Analysis of Behavior, </i> <B>92</B>, 305-326.</H2> Concurrent schedules were used to establish 6 hens&#146; preferences for three foods. The resulting biases suggested wheat was preferred over honey&#45;puffed and puffed wheat, and puffed wheat was the least preferred food. The hens then responded under fixed&#45;ratio schedules for each food in 40&#45;min &#40;excluding reinforcer time&#41; sessions, with the response requirement doubling each session until no reinforcers were received. At the smaller ratios, the less preferred the food, the faster the hens&#146; overall response rates &#40;mainly as a result of shorter postreinforcement pauses&#41; and the more reinforcers they received. The relations between the logarithms of the number of reinforcers obtained &#40;consumption&#41; and the response ratio &#40;price&#41; were well fitted by curvilinear demand functions. Wheat produced the smallest initial consumption &#40;ln L&#41;, followed by honey&#45;puffed and puffed wheat, respectively. The response requirement at which the demand functions predicted maximal responding &#40;Pmax&#41; were larger for wheat than for the other foods. Normalizing consumption and price, as suggested by Hursh and Winger &#40;1995&#41;, moved the data for the three foods towards a single demand function; however, the Pmax values were generally largest for puffed wheat. The results of normalization, as suggested by Hursh and Silberberg &#40;2008&#41;, depended on the k value used. The parameter k is related to the range of the data, and the same k value needs to be used for all data sets that are compared. A k value of 8.0 gave significantly higher essential values &#40;smaller ± values&#41; for puffed wheat as compared to honey&#45;puffed wheat and wheat, and the Pmax values, in normalized standard price units, were largest for puffed wheat. Normalizing demand by converting the puffed and honey&#45;puffed wheat reinforcers to wheat equivalents &#40;by applying the bias parameter from the concurrent&#45;schedules procedure&#41; maintained separate demand functions for the foods. Those for wheat had the smallest rates of change in elasticity &#40;a&#41; and, in contrast to the other analyses, the largest Pmax values. Normalizing demand in terms of concurrent&#45;schedule preference appears to have some advantages and to merit further investigation. <P> Key words: fixed&#45;ratio schedules, reinforcer quality, concurrent schedules, behavioral economics, demand functions, normalization, magnitude&#45;of&#45;reinforcer, key peck, domestic hens</body> </HTML>