An economic analysis of a methionine source comparison response model

Transcription

1 An economic analyi of a methionine ource comparion repone model D. Vedenov and G. M. Peti 1 Department of Agricultural Economic, Texa A&M Univerity, 2124 TAMU, College Station ; and Department of Poultry Science, Univerity of Georgia, Athen ABSTRACT Methionine i the firt-limiting amino acid in corn and oybean meal-baed poultry diet. Therefore, it upplementation level i of primary economic importance to poultry production. The repone to the methionine ource dl-methionine () and methionine-hydroxy analog-free acid (HMTBA) have been compared uing variou methodologie. The o-called common plateau nonlinear model ha been ued to etimate relative bioavailabilitie of the ource. Thi model ha a coefficient that i ued a a ingle value to compare the relative bioavailabilitie of the ource for independent technical parameter like gain and feed efficiency. Thi model wa ued previouly in a metaanalyi of publihed experiment, and 79 and 81% relative biological efficiencie of HMTBA were found for for ADG and feed utilization efficiency, repectively. Becaue different ource would have different optimal feeding level to maximize profit, we demontrate the challenge of calculating a ingle optimal level for the different methionine ource. Further, we apply an economic analyi to reult of the previou meta-analyi to demontrate that the relative value of HMTBA and for BW and ADG are between 81 and 86%, depending on the value of a broiler and the cot of feed and. Key word: methionine, biological efficiency, economic efficiency 2010 Poultry Science 89 : doi: /p INTRODUCTION Noll et al. (1984) propoed a model to etimate the relative bioavailability of nutrient baed on an exponential, common plateau model with a parameter that wa aid to be the relative bioavailability (the ε 1 coefficient). Littell et al. (1997) demontrated how to fit the model to experimental data uing SAS (SAS Intitute, 1989). The Noll et al. (1984) model wa ued by Sauer et al. (2008) in a meta-analyi of experiment on the relative efficiency of 2 potential ource of methionine for broiler. The methionine ource they compared were dl-methionine () and methionine-hydroxy analog-free acid (HMTBA). The meta-analyi included an etimation from a ingle model uing data from 42 experiment in 27 publihed paper. The exponential model ued wa: y = α β exp( γx), [1] where x i the doe in percentage of upplemental methionine ource and α, β, and γ are contant. Sauer et al. (2008) allowed for a difference in plateau from the 2 methionine ource but concluded that the difference 2010 Poultry Science Aociation Inc. Received January 12, Accepted June 6, Correponding author: gpeti@uga.edu wa not tatitically ignificant. Therefore, they ued the model etimated in the meta-analyi experiment to calculate the relative bioavailability of HMTBA to at the plateau level. The latter wa then ued to price HMTBA relative to. However, thi approach i flawed from the economic perpective becaue it implicitly aume that there i a ingle relative value of the ource, regardle of the cot of feed component and the price of live bird. The coefficient ued to compare level of upplement to feed are determined without regard to any price whatoever. In fact, given a nonlinear repone model, it i impoible to have a ingle coefficient that repreent the relative value of methionine ource (or other upplement) under more than one unique et of technical and economic condition at a time. The inadequacy of the Noll et al. (1984) model can bet be illutrated by the following tylized model of economically optimal feeding. Aume that a bird i fed a tandard feed and a upplement. The live weight (w l ) of a bird at laughter i a function of the quantitie of feed (q f ) and upplement (q ) [i.e., w l = w l (q f, q )]. If the per-unit cot of feed and upplement (c f and c, repectively) are contant, and o i the per-pound price of live bird (p), then the net profit per bird i π = pw l (q f, q ) c f q f c q. [2] 2514

2 ECONOMIC ANALYSIS OF METHIONINE SOURCE COMPARISON RESPONSE MODEL 2515 The economically optimal level of the upplement i then determined by taking a derivative of [2] with repect to q and etting it to zero o that p = p w q q l - c = 0 (ee, for example Ma-Colell et al., 1995, p. 137). An economic interpretation of thi condition i that the upplement i fed up to the level when the additional revenue of the live weight gained from one additional unit of upplement i equal to the cot of that additional unit. A imilar reult would be obtained even if part of the carca were priced differently, a long a the weight of the part remained in a contant proportion to the live weight. The condition can be rewritten a an equation on the optimal quantity of the upplement: w ( q, q ) l f c =. q p [3] Graphically, the rule in [3] implie that, at the optimum, the lope of the tangent to the nutrient repone curve i equal to the ratio of the nutrient cot and the price of live bird per unit of weight. Generally peaking, different nutrient ource would reult both in different repone function w l = w l (q f, q ) and the ratio of the nutrient cot to the price of live bird. A a conequence, economically optimal level of variou nutrient a determined by [3] might be incomparable. Figure 1 demontrate thi point by a typified example of feed repone curve for 2 ource of a upplement (or a nutrient). The example how 2 different combination of repone curve and price of upplement that reult in 2 different economically optimal quantitie of the upplement. Here, c and 1 c are perunit cot of 2 upplement, p i the per-unit price of 2 live bird, and q 1 and q 2 are economically optimal quantitie of 2 upplement implied by the condition in [3]. Thi example demontrate the challenge of calculating a ingle optimal level of upplement ource or the degree of relative ubtitutability between 2 ource becaue thee different ource would have different optimal level. However, a direct comparion of the upplement ource in thi context i till poible (e.g., by electing the ource that provide the highet profit at the optimum repone). One poible approach to uch a comparion i to find the cot of one ource which, at optimum, reult in the ame live weight a another ource. Thi approach i illutrated in a tylized example hown in Figure 2. In Figure 2, the price of upplement 1 ( c 1 eq ) i choen o that the correponding optimal level of the upplement ( q 1 ) determined according to [3] reult in the ame live weight w a the optimal level of upplement 2. In thi context, the price of the firt ource ( c 1 eq ) i ( ) indeed equivalent to the price of the econd ource c 2. However, thi equivalence would only hold at the optimum and only a long a all of the other parameter are Figure 1. Economically optimal upplement level for different combination of repone function and upplement price. c 1 and c are perunit cot of 2 upplement, p i the per-unit price of live bird, and q 1 2 and q 2 are economically optimal quantitie of 2 upplement implied by the condition in [3].

3 2516 Vedenov and Peti Figure 2. An equivalent price of a upplement determined o a to produce the ame optimal live weight. = dl-methionine; HMTBA = methionine-hydroxy analog-free acid. fixed. In other word, if, for example, the price of a live bird were to change, the lope of tangent in Figure 2 would change and the equivalence would diappear becaue each ource of nutrient would now have optimal quantitie reulting in different optimal weight. Similarly, a change in other component of the diet might change the curvature of the repone function and once again break the equivalence. Finally, a choice of the live weight for comparion i completely arbitrary (i.e., different objective function would reult in different implied relative cot of the nutrient ource). In fact, although the optimal quantitie in the example hown in Figure 2 yield the ame weight, they would mot likely reult in different net profit. Depite that the ε 1 coefficient of Noll et al. (1984) and Sauer et al. (2008) i inadequate for determining the relative economic value of and HMTBA, an economic interpretation of the regreion model i till valuable in demontrating how the relative value of and HMTBA change with changing price of input (feed) and output (live weight). MATERIALS AND METHODS Note that there are error in the publihed ign of the β coefficient in the equation in Sauer et al. (2008). Therefore, the actual equation ued in the preent analyi were a follow: ADG = ( ASE) exp( doe) [4a] and ADG HMTBA = ( ASE) exp( doehmtba) [4b] G:F = ( ASE) 0.12 exp( 8.41 doe) [5a] G:F HMTBA = ( ASE) 0.12 exp( 6.67 doehmtba), [5b] where ASE i age at tart of experiment and doe and doehmtba are the amount of the repective methionine ource (Figure 3 and 4). For a given choice of the methionine ource, the model in [2] can now be written either a or max p = p N ADG ( ASE, doe ) - éc ( 1- doe ) + c doe ù ëê f û ú ADG ( ASE, doe) N GF : ( ASE, doe) max p = p N ADG ( ASE, doegmtba) GMTBA - éc ( 1- doegmtba) + c doegmtbaù ëê f ûú ADG ( ASE, doegmtba) GMTBA N GF : ( ASE, doegmtba), GMTBA [6a] [6b]

4 ECONOMIC ANALYSIS OF METHIONINE SOURCE COMPARISON RESPONSE MODEL 2517 Figure 3. Mean value of the doe-repone relationhip between dl-methionine () and methionine-hydroxy analog-free acid (HMTBA) with ADG on an equimolar bai baed on the common plateau covariate model of Noll et al. (1984). Age at the tart of the experiment wa 10 d. where N i the number of day the bird i fed; p, c, and c f are the ame a in [2]; doe, ADG, and G:F are a defined in [4a] and [5a], repectively; and doehmtba, ADG HMTBA, and G:F HMTBA are a defined in [4b] and [5b], repectively. The maximization problem in [6a] and [6b] were olved for everal combination of upplement and live bird price (cenario) lited in Table 1. Scenario 1 contain average price for the very volatile autumn of 2008, wherea other cenario repreent a range of hitorical high and low for the baal diet cot, live broiler value, and cot to illutrate extreme combination of thee factor. The profit-maximizing doe of wa determined uing the Solver module in Figure 4. Mean value of the doe-repone relationhip between dl-methionine () and methionine-hydroxy analog-free acid (HMTBA) with G:F on an equimolar bai baed on the common plateau covariate model of Noll et al. (1984). Age at the tart of the experiment wa 10 d.

5 2518 Microoft Excel (Microoft Corp., Redmond, WA). The optimal level of for each cenario are reported in Table 1. After the procedure illutrated in Figure 2, the price of HMTBA wa then varied o a to et the maximum profit baed on the HMTBA repone function equal (within $ ) to the maximum profit obtained in the cae of. The ratio of the cot of HMTBA to that yielded identical profit were then calculated and alo reported in Table 1. RESULTS The profit-maximizing doe of and HMTBA computed in thi paper were outide of the range of methionine ource fed in 38 of the 42 experiment that provided data to analyi by Sauer et al. (2008). A expected, when the cot of increaed, it ue decreaed and the relative value of HMTBA increaed. Furthermore, when the cot of either the baal diet or live broiler increaed, and HMTBA uage on an abolute bai increaed. The ratio of the value of to HMTBA ranged from 80.5% with low feed and broiler price and high price to 85.6% with high feed and live broiler price and low price. DISCUSSION The model of Noll et al. (1984) ha become known a the nonlinear common plateau regreion model (Kratzer and Littell, 2006). Thi i urpriing becaue the model ha no plateau, and the only common point i where the value of the upplement are both equal to zero. With the model of Noll et al. (1984) and Littell et al. (1997), the ource with the lower initial repone will necearily alway approach the plateau from below and never actually equal the repone from the other ource that ha the higher initial repone. Thu, although the data and theory upport the common plateau idea, in the practical application of thi exponential model, the repone never reach equality at any common plateau. The difference in approache i not trivial, a evidenced by the different economic reult in Table 1. The only reference to the model ued by Noll et al. (1984) are to general reference article on nonlinear regreion, o we aume that the model hould be attributed to them. In the Noll et al. (1984) model, the relative potency wa the parameter they called the ratio of teepne coefficient. Noll et al. (1984) correctly tate Thee are the factor that, when multiplied by the correponding level, make the dl-methionine growth curve coincide with that of the other ource. That tatement i true. However, it doe not follow that the ratio of teepne coefficient can be ued to determine appropriate relative price of the nutrient ource without regard to cot of input (baal diet and upplement) and output (body or carca weight) a i typically done. Vedenov and Peti Table 1. Combination of price parameter ued in determining optimal level of dl-methionine () and the methionine-hydroxy analog-free acid (HMTBA) Item Scenario 1 Scenario 2 Scenario 3 Scenario 4 Scenario 5 Scenario 6 Scenario 7 Scenario 8 Scenario 9 Scenario 10 Baal diet cot ($/kg) Live broiler value ($/kg) Cot ($/kg) Optimal doe (%) ADG (g) G:F Final weight (kg) Feed intake (kg) Net profit ($) HMTBA Cot to match profit ($/kg) Optimal doe (%) ADG (g) G:F Final weight (kg) Feed intake (kg) Net profit ($) Cot ratio (HMTBA:)

6 ECONOMIC ANALYSIS OF METHIONINE SOURCE COMPARISON RESPONSE MODEL 2519 Figure 5. Mean value of 28-d BW gain (g) in broiler chicken a reported by Schutte and de Jong (1996). A t-tet revealed that the predicted plateau for methionine-hydroxy analog-free acid (HMTBA) wa ignificantly higher than that for dl-methionine () (P = ), which demontrate that the doe repone of the 2 product are different (Kratzer and Littell, 2006). Two eparate obervation trongly ugget that the exponential model i inadequate. Firt, mot of the profit-maximizing and HMTBA optimal doe upplemental level were above 0.32%; the only exception wa when both baal diet cot ($/kg) and live broiler value ($/kg) were at very low value and the value wa high (Table 1). However, only 4 of the 42 reearch trial included in the analyi of Sauer et al. (2008) fed or HMTBA level thi high. Of the 38 experiment in which le than 0.32% wa fed, the average highet doe fed wa 0.19% (Table 1 of Sauer et al., 2008). Second, none of the individual experiment included by Sauer et al. (2008) in their analyi howed ignificant difference between methionine ource when they were fed at the highet level. Therefore, the plateau were reached at an average of 0.19% upplement level in the majority of experiment included in the analyi. The maximum repone (plateau) were clearly reached at 0.28% in 38 of the 42 experiment in the analye of Sauer et al. (2008). The optimal doe Figure 6. Mean value of 28-d BW gain (g) in broiler chicken a reported by Schutte and de Jong (1996). Ue of the nonlinear common plateau aymptotic regreion model force a common plateau for the 2 ource of methionine at 1,714 g (Kratzer and Littell, 2006). HMTBA = methionine-hydroxy analog-free acid; = dl-methionine; b4 = ratio of rate etimate, the relative efficiency; CL = confidence limit.

7 2520 (Table 1) wa coniderably (0.04 to 0.34%) above the upplement level, where the plateau hould have been reached, except when both baal diet cot ($/kg) and live broiler value ($/kg) were at very low value and the value wa high (Table 1). But even with very low diet and broiler value and high upplement value, the optimal doe of 0.26% and 0.32% HMTBA were coniderably above where the maximum repone wa reached in many of the experiment (0.19% or HMTBA). The proce of determining relative ingredient price i very important for animal nutrition and critical to economically producing food. Any propoed mathematical model hould undergo careful crutiny from the biological, tatitical, and economic perpective. Kratzer and Littell (2006) teted the hypothei that the ame maxima are approached by 2 methionine ource uing the model of Noll et al. (1984). They concluded that, from a tatitical perpective, the maxima (plateau) for the 2 ource were different and, therefore, the biological principle involved hould be reevaluated. The biological principle, of coure, eem to indicate a common plateau for ource of the ame nutrient. If there i no common plateau, it would eem that baic aumption of the experiment, that methionine wa the limiting nutrient in the diet and that the upplement were olely ource of methionine, were fale. Mathematical model hould necearily decribe the oberved biological procee. Extrapolation outide the oberved point are by definition unupported. Therefore, it i intereting to note that even for the example data that Kratzer and Littell (2006) choe to illutrate their point, the maximum (plateau) i clearly outide the range of the oberved data (Figure 3); t-tet comparing repone to methionine ource at the highet level of ubtitution would have been much more convincing than t-tet comparing predicted plateau. When a tatitical model ugget problem with biological theory, it may correctly ugget that the biological interpretation i inappropriate. In the cae of methionine ource tudied by Kratzer and Littell (2006), one poibility i that ome property of HMTBA, other than it methionine activity, i increaing growth repone from it ue (Figure 5). Methionine-hydroxy analog-free acid i known to have activity a an organic acid and may increae phytate phophoru and trace mineral aborption (Liem et al., 2008). For appropriate comparion of HMTBA and, experimental diet need to be formulated to only compare methionine activity. Any poitive influence from any organic acid effect or other propertie hould be accounted for eparately. If the difference in plateau wa due to d- methionine toxicity, there hould be no plateau in the repone to. Sauer et al. (2008) ued the common plateau model to find 79 and 81% relative efficiencie ( v. HMTBA) for ADG and feed utilization efficiency, repectively. It Vedenov and Peti i difficult to interpret model with eparate efficiencie for whatever parameter happen to be meaured. The efficiency etimate for individual parameter may be intereting from a technical perpective. However, from an economic perpective, it i more important to find the relative value of the upplement in a model that include the value of gain produced and cot of feed conumed (net profit, a in Table 1). In thi cae, the relative economic value (cot ratio, HMTBA:) are between 81 and 86%. But again, becaue the profit-maximizing level of and HMTBA are o far above the level tudied in mot of the experiment, the validity of any concluion i highly upect. Thi comparion wa only made to illutrate how the data hould be interpreted. It doe not eem reaonable that one nutrient ource hould alway approach the maximum from an inferior poition becaue of lack of repone at very low level (Figure 6) any more than there hould be different maxima (plateau; Figure 5). A mathematical expreion capable of modeling a igmoidal approach to a true plateau need to be applied that biologit, tatitician, and economit can all conider adequate. The real relative value of nutrient ource need to be evaluated in term of the complete feed that are to be ued to determine fair value. In that way, all poitive and negative attribute and interaction can be accounted for. A illutrated in Table 1, relative economic value are dependent on the technical repone and cot of the input (like feed) and value of the output (like broiler meat). Therefore, model with only technical data hould not be ued to determine relative biological value that are to be ued for determining relative price. REFERENCES Kratzer, D. D., and R. C. Littell Appropriate tatitical method to compare doe repone of methionine ource. Poult. Sci. 85: Liem, A., G. M. Peti, and H. M. Edward Jr The effect of everal organic acid on phytate phophoru hydrolyi in broiler chick. Poult. Sci. 87: Littell, R. C., P. R. Henry, A. J. Lewi, and C. B. Ammerman Etimation of relative bioavailability of nutrient uing SAS procedure. J. Anim. Sci. 75: Ma-Colell, A., M. D. Whinton, and J. R. Green Microeconomic Theory. Oxford Univerity Pre, New York, NY. Noll, S. L., P. E. Waibel, R. D. Cook, and J. A. Witmer Biopotency of methionine ource for young turkey. Poult. Sci. 63: SAS Intitute SAS Uer Guide: Statitic. SAS Intitute Inc., Cary, NC. Sauer, N., K. Emrich, H.-P. Piepho, A. Lemme, M. S. Redhaw, and R. Moenthin Meta-analyi of the relative efficiency of methionine-hydroxy analogue-free-acid compared with dl-methionine in broiler uing nonlinear mixed model. Poult. Sci. 87: Schutte, J. B., and J. de Jong Biological efficacy of dl-methionine hydroxy analog free acid compared to dl-methionine in broiler chick a determined by performance and breat meat yield. Agribiol. Re. 49:74 82.