{X345 7 B1715 573 o N0vemben1993 NW6 .’ Optimal Breed Choices fer Commerclal Cow-Calf Productlon in the Texas Panhandle: AnApplicatiom Bio-Economic Modellingto Breed Evaluations [Blank Page in Origind Bulletin] “ v1. > ; j I .5! ‘ ‘. hflf’ '5», B-1716 LIBRARY FEB 2 4 1994 TEXAS A&M UNIVERSITY Optimal Breed Choices for Commercial Cow-Calf Production in the Texas Panhandle: An Application of Bio-Economic Modelling to Breed Evaluationsa Bryan E. Melton”, W. Arden Colette‘, and Kenneth I. Smith“ ' A portion of the results reported in this bulletin were extracted from the M.S. Thesis of Kenneth I. Smith, completed at West Texas State University, August 1991. " Formerly a visiting professor and graduate Research Professor in the Division of Agriculture at West Texas State University (1990-91) during which time a portion of the work reported in this study was undertaken. Currently Visiting Professor of Economics and Animal Science, Iowa State University, Ames, lowa 50011. ° Professor of Agricultural Business and Economics, Division of Agriculture, West Texas A&M University, Canyon 79016. w! d Formerly an M.S. candidate at West Texas State University. Currently a Ph.D. candidate in Animal Science at Texas Tech University, Lubbock, Texas. Table of Contents Preface ....................................................................................................................................................... ..Inside Front Cover Abstract ..................................................................................................................................................................................... ..5 Introduction ................................................................................................................................................................... ......... ..5 The Conceptual Basis of Breed Evaluation and Selection ......................................................................... j. ....................... ..5 Nondetenninistic Bio-economic Modelling ......................................................................................................................... ..6 Model Specification for Breed Evaluation ............................................................................................................................ ..7 Breed Differences .............................................................................................................................................................. .. 7 ~ Continuous Differences (Weight, Age, and Lactation) ........................................................................................ ..8 Discrete and Stochastic Elements (Birth, Weaning, and Death Rates) .............................................................. ..9 Product-Resource Inter-relationships ............................................................................................................................ ..9 Cow Daily Maintenance and Growth ..................................................................................................................... ..9 Daily Lactation and Gestation ........................................................ ....................................................................... ..9 Progeny Daily Maintenance and Growth ............................................................................................................ .. 10 Annualizing Daily Nutrient Requirements ......................................................................................................... .. 10 Production Parameters .................................................................................................................................................. .. 1O Breed Group Parameters ........................................................................................................................................ ..1O Crossbred Groups ............................................................................................................................................ ..11 Purebred Groups .............................................................................................................................................. .. 11 The Resource and Market Environment ........................ ... ................................................................................... .. 11 Aggregation to Obtain Expected ”Herd of Breed" Values ....................................................................................... .. 12 Optimization Results ............................................................................................................................................................. .. 12 Economic Values of Purebreds ..................................................... .............................................................................. .. 14 Economic Values of Crossbreds ................................................................................................................................... .. 14 Discussion and Implications ................................................................................................................................................ .. 16 Literature Cited ...................................................................................................................................................................... .. 17 Appendix A. Model Parameters .......................................................................................................................................... .. 19 Table A1. Production parameters of alternative crossbred cows ............................................................................ .. 19 Table A2. Production parameters of alternative purebred cows ............................................................................. ..19 Table A3. Per acre forage dry matter production (kg) .......................................................... .. .................................. ..20 Table A4. Base (1980-84) supplemental feed and livestock prices .......................................................................... ..20 Table A5. Optimal average culling age, replacement, and weaning rates ............................................................. ..20 Appendix B. Definite integrals for annual ME and DP requirements assuming a 200 day lactation and an average 287 day gestation period ................................................................................................................................... ..21 Q 7" Optimal Breed Choices for Commercial Cow-Calf Production in the Texas Panhandle: An Application of Bio-Economic Modelling to Breed Evaluations Abstract The applicability of a breed evaluation for commercial producers is enhanced when cast in an economic frame- work recognizing the inherent physical (phenotypic) and genetic capabilities of alternative breed groups in the context of a given production and market environment. This paper presents a multi-stage bio-economic model of breed evaluation, which effectively incorporates differ- ences between breeds and the production environment within a profit-maximizing framework representative of commercial cow-calf producers. The data required to run this model, much of which are readily available, are iden- tified. Modifications to the model to reflect alternative breed groups, new or additional data regarding breed group or crossbred perfomiance, or alternative produc- tion locations are facilitated by the inclusion of the formu- las into which these alternate data may be substituted to provide customized results. Application of this multi-stage bio-economic model is illustrated for a representative West Texas cow-calf producer considering optimal breed choices from among 32 alternative breeds and breed groups. Results-were found to be surprisingly stable across both climatic and market conditions. In each case, a clear and consistent preference is shown for moderately sized, fast gwwing breeds with high reproductive performance and better than average lactation ability. Large breeds are not preferred under even the most liberal of range and climatic conditions or high market prices. This analysis further indicates that a ”wrong” deci- sion, e.g., use of a non-optimal breed, can cost the producer from $150 to $250 per head under the altema- tive prices considered. Furthermore, despite the prefer- ence for purebred Pinzgauer, crossbreeding (in general) is shown to have an average marginal value across breeds of approximately $75 to $100 per head under normal range conditions and base prices. Introduction The choice of breed for a given production environ- ment is one of the most fundamental and critical deci- sions confronting any commercial cow-calf producer. It defines the basic gene pool of the cow herd — which, in turn, determines both the productivity and profitability that the producer may reasonably expect to realize far into the future. 4 As the number of available beef breeds expands, as it has over the past quarter century, the breed selection decision becomes increasingly complex. Producers may now select from an array of breeds representing a much greater range of fundamental performance characteris- tics than has heretofore been available, including ma- ture size, growth potential, milking ability, and repro- ductive performance. When this greatly expanded di- versity of breeds is combined, such as through cross- breeding, the number of choices available to the cow- calf producer expands exponentially. Under such con- ditions, cow-calf producers require an organized method of breed comparison that provides a theoretically sound basis for the determination of a breed's relative value; one which not only recognizes the performance charac- teristics of the breed, but the economic ramifications of its use in a given commercial production environment. While animal scientists have devoted considerable time and resources to quantifying the expected perfor- mance of alternative breeds and crosses, a comparable degree of attention has not been devoted to rigorous economic evaluations. As a result, producers have ac- cess to a significant body of data regarding production potential, but limited information relating this potential to the economic considerations on which commercial decisions are largely based. As such, commercial breed choices have often been based on criteria more closely related to physical output maximization than profit maximization- frequently to the long-term detriment of the producer. This paper presents a breed evaluation and com- parison for commercial cow-calf producers through the development of a mathematical model (set of 16 equa- tions) that integrates animal breeding and economic principles to provide an economic evaluation of 16 different breeds, both singly and in F1 crosses with Hereford and Angus cows, under alternative produc- tion and price conditions typical of the Texas Panhandle production and economic environment. Furthermore, the model developed in this study may be viewed as a general model of breed evaluation in that it facilitates, through changes in a limited number of parameters, economic evaluations representative of alternative pro- duction environments and economic conditions de- fined by different geographic areas, market conditions, or producer objectives. The Conceptual Basis of Breed Evaluation and Selection The underlying premise of any evaluation is that a set of alternatives may be ranked or evaluated in terms of their ability to satisfy some specified criteria or objec- tive. That criteria may be one of two basic types: physical or economic. A physical evaluation is one which reports observed production levels under a specific production environment. As such, its breed evaluation is based upon observed means of physical measures of perfor- mance. An economic evaluation, on the other hand, bases the evaluation in terms of a breed’s potential ability to satisfy an economic criteria, such as profit maximization. Hence, an economic breed evaluation would differ from a physical evaluation in that (1) rather than being cast in physical terms, results are expressed in economic terms (dollars) that more closely reflect the concerns and criteria of commercial producers and (2) results appropriatly cast in economic terms facilitate aggregation of the multiple physical measurements so that a breed superior in one physical characteristic but inferior in another can still be correctly ranked on the basis of aggregate economic values. Most breed evaluations have taken one of two ap- proaches to breed evaluation, both of which are physical in nature. These alternatives are 1) gross evaluations reporting the means of all characteristics observed such as those reported by Cundiff et al. (1982 and 1986) and Jenkins et al. (1991) or 2) efficiency evaluations report- ing the mean ratios of output (product) to input use such as those reported by Green et al. (1991a and 1991b). The predominance of these two methods of breed evaluation should not be taken to imply that animal scientists are unaware of their deficiencies or have not considered alternatives to improve the method s of breed evaluation. Nearly a half-century ago Hazel (1943) ar- gued that in multi-trait selection each characteristic should be appropriately weighted by its relative eco- nomic value. Unfortunately, from the viewpoint of eco- nomic theory, much of the subsequent work involving animal economics misinterpreted ”economic value" at the average rather than the margin or otherwise misap- plied economic theories. More recent studies, some more directly involving economists in the evaluation, have remedied a portion of these early deficiencies and expanded the role of economics in breed and animal evaluation (Moav and Moav, 1966; Moav and Hill,1966; McClintock and Cunningham, 1974; Melton et al., 1979; Ladd and Melton,1979; Melton, 1980; Doren et al., 1985; Smith et al., 1986; Stokes et al.,1986; and McArthur and Del Bosque Gonzalez, 1990). Some of these studies have even made use of com- puter simulation models in an attempt to simultaneously consider the multitude of characteristics, production practices, and economic events effecting beef produc- tion and its profitability in deterministic analyses (Long et al., 1975). In most cases, however, the evaluation has remained deterministic in nature, reflecting the eco- nomic outcome of prespecified breed and management choices. A significant question regarding the perfor- mance of each breed under optimal (by breed) variable input use in a given environment remains unanswered in such analyses. Nondeterministic Bio-economic Modelling The standard criteria of an economic analysis is profit maximization (Henderson and Quandt, 1980). A profit-maxirnizingcommercial cow-calf producer would wish to select the breed or breed combination which maximizes the value of the firm, recognizing the multi- year, multi-product nature of the cow asset. On this basis, one might argue that the commercial cow-calf producer’ s objective is to maximize the net present value of the cow herd or, alternatively, of the average cow in the herd. This objective is satisfied by the producer's selection of the breed or breed combination, from among the finite number of choices available, which has the greatest net present value per head through infinity, defined as follows: C (b,s,1,j) (1) C(b,s,<><>,j)= ——--—-— 141M945)»; (1 +g)(s-b) where, following Melton’s (1980) adaptation of Perrin’s (1972) notation with the addition of a subscript denot- ing breed (j ): ‘ NR (y,j ) c (b,s,1,j > = 2 y=b +1 M (s,j ) _b+ sgb-M(b,j) (1+r)Y (1+r) = the net present value of the first animal (or herd mean) of the j"' breed acquired at age b and opti- mally culled at age s ; y = cow age in years; r = the appropriate annual discount rate; g = the annual rate of genetic progress associated with culling the cow at s years of age; NR (y,j ) = R (y,j ) — C (y,j ) = the residual earnings, defined as the difference between current rev- enues, R (y,j ), and costs, C (y,j ), attributable to a cow at y years of age; M (b,j ) = the market value of the cow at acquisition; and M (s,j ) = the market value of the cow at culling. While the determination of optimal culling and replacement strategies requires a representation of the producer's objective in this form (Melton, 1980), it does not fully address the issue of optimal breed selection decisions.‘ Specifically, the selection of a breed or breed combi- nation with the greatest value of equation (1) implies that the firm’s aggregate net present value is maximized ‘ Breed evaluations which reflect commercial production conditions based upon the net present value method would be possible if estimates of the non-linear relationship between breed production parameters and costs were obtained. By then constraining (1) t0 the mean levels of production parameters, by breed, and differentiat- ing with respect to both culling age and breed parameters would allow for simultaneous determination of optimal culling age and the value of the breed parameters as the Lagrangian of the con- straint, as shown by Ladd and Melton. The sum of these values, by breed, would then allow for between breed comparisons and evaluations of value. However, the alternative presented in this paper is judged to be more easily performed by producers, as well as professional and practicing animal scientists, utilizing the ca- pacity of modern personal computers. by maximizing the net present value (per head) of the 5Q cow herd. However, this is true only when all inputs may be varied at a constant price in response to changes in herd size or resource use (i.e., C (y, j ) is a constant per head). In most commercial cow-calf operations, how- ever, land area is a fixed resource. As a result, increases in herd size beyond the capacity of the land to supply supporting nutrients can be accomplished only at a higher per unit nutrient cost (purchase of supplemental feed). Similarly, unused forage nutrients, arising from reductions in stocking rate and herd size, have essen- tially no alternative use — implying a zero opportunity cost. Short- or intermediate-run analyses of cow-calf pro- duction decision-making are, therefore, more correctly stated in terms of maximizing values per unit of fixed resources, such as land area, rather than maximizing values per head or the net present value of the cow herd. Accordingly, from a set of available breeds and breed values, it is more appropriately assumed that the pro- ducer selects the combination of one or more breeds which maximizes economic returns per unit of land area, subject to any other resource constraints, such as operating capital. For cows of a given condition, the set of available breeds represents a one-to-one mapping of the set of animal nutrient requirements and productivity values. The optimization problem for n available breeds may, therefore, be stated mathematically as follows: (2) maxZ=2wjXj i=1 subjectto: EaUXisdi i=1t0m j=l XjZO Vj where: X . = the level of use or number of head of the j"' breed; w. = the net annual return per head of the average (aggregate) animal of the j"' breed when optimally culled according to the criterion implied by equa- tion (1); a‘. = the technical coefficient relating the requirement of one head of the j“ breed for the i“ nutrient (or other resource); and d l. = the available level of the i“ nutrient (or other resource) associated with the fixed land area. It is obvious that with only minor changes in nota- tion to avoid possible confusion, equation (2) is simply a representation of the traditional, profit-maximizing, mathematical programming model. Further assuming that w I. is constant with respect to the levels of X i, the model easily reduces to a traditional problem of linear programming. The advantages of linear programming in analyses such as breed evaluation include: 1) The availability of numerous, highly effective, com- puter algorithms for the solution of linear program- ming problems, thereby simplifying the mechanics of the analysis. 2) The opportunity cost values of constrained re- sources, such as grazing nutrient production, are reflected by the shadow prices of the constraints. 3) Only a finite number of alternative breeds are con- sidered in any one evaluation, thereby simplifying the development of the model. 4) Only a few breed alternatives will be optimal in any solution, thereby simplifying the interpretation of results. 5) The shadow prices of the breed activities may be interpreted as the relative economic values of the breed alternatives. The last of these is based upon the fact that the shadow price of an excluded activity, often termed its income penalty, reflects the reduction in the value of the objective function (Z) which would arise from a mar- ginal increase (from zero) in the use of the activity. As such, it provides a theoretically sound basis for the determination of relative economic values for evaluat- ing breed selection alternatives (Heady and Candler, 1958). Model Specification for Breed Evaluation Several elements are required to complete the speci- fication of a bio-economic breed evaluation model. These include: 1) the production parameters of each breed under consideration; 2) the relationships between the breeds and the envi- ronment including both production levels (output) and resource requirements (inputs) necessary to achieve the output; and ‘ 3) the production environment for which the evalua- tion is applicable, including resources available as well as economic and market conditions. In the following sections, the model is specified by first specifying the nature of the inter-relationships be- tween breeds and their production environment, com- mencing with the specification of the nature of breed differences. We then specify the parameters of the model with respect to breeds and resources available, as well as prevailing economic conditions. Breed Differences To appreciate the differences which exist between alternative breeds of beef cows, one must first appreci- ate the multifaceted nature of the productive services provided by these animals. Specifically, the beef cow not only provides a flow of services resulting in the production of marketable products in the form of her own progeny, she also produces her own replacement asset and is, herself, a marketable product upon culling from the herd. As such, in each year of her life, the beef cow must achieve normal weight maintenance and growth while conceiving, nurturing the embryo, giving birth, and nursing her progeny to achieve its own ge- netic potential (weight) at weaning. The possibility of economically significant differences between breeds, with respect to genetic potential, reproductive life, re- sources required, the product produced, or a combina- tion, clearly exists in each of these facets of the cow-calf production process. Continuous Differences (Weight, Age, and Lactation) For the model under development, it is critical that continuous breed differences (those reflecting continu- ous variables) be expressed in a continuous mathemati- cal function. These continuous variables include weight, weight gain or growth, and daily lactation over the span of a lactation cycle to reflect within year changes. Repro- ductive performance (such as percent weaning rate), on the other hand, may be adequately expressed as an annual, average, productivity measure reflecting the static nature of the variable. To accomplish this a "Brody-type" (1945) growth function of the form (3) W‘=A-Be"“ is chosen where A — B is the expected birth weight expressed as the difference between the asymptotic mature weight (A) and total weight gain (B), k is the rate of growth parameter and t is days of age after birth. Two aspects of this growth curve are critical to its use in a bioeconornic model of breed evaluation. First, the expected weaning weight (heifer basis) of the animal may be obtained by solving the growth curve at an age standardized weight, such as t = 200 days. Second, the animal's expected rate of growth on any day, measured in terms of daily weight gain (G j), may also be obtained by differentiating the growth curve with respect to time, dW (4) c,=_T‘=/1) - A tanh‘ i-n/q - B e t) —tan '1 ———i-——(A - B e t) y‘ ' 214.25 A15 A25 (A _ B e4“ ) _75 k t=365(y+1)+200 - - 6.3 B e 4+ C 3 k t=365y+200 .164 A (A_Be~k(365(y+1)+t1))"25 ME l(yz2) = "—- tanhJ 5 k A25 ‘l (A _ B e-k(365(y+1)+t1) >15 -tan A25 -k(365( n+t > ~75 (A-Be y+ I -k(365(y+1)+t1) - -1.9Be 3 t e-klrl e-klz, ‘Fzoo +.7443AA(y) ' - +c - -k A —k2A 1 1 l z “=0 -ME5(;V21)=.03259AA,(A-Be"“3°5’+78))'75e'017f“*+C +_O3259AAH1(A_Be-kcses'25 + P’ tanh -1 P’ P k 2A.25 A15 p P P _ .25 4‘, .75 (A -B @"P'P) (A -B e PP) _t -1 P P _ r r an < A35 3 t e-xpp e-Iqtp ‘P=2°° -.546 p - 2 1.06 AA y + C -klAl klAl lp=0 B e DP (y 2 0) = 00056 At + kBzeak‘ t=365(y+1)+200 --- +c l=365y+200 + .000275 (A B e PP - t e kl‘! t|=200 DP,(y22)= AAy.0335 ' - +c ekstg l8=287 DP (y 2 1) = .0023 AA + C 8 y ekgtg ¢8=121 +0023 AAyH +c 41¢ BePP DP (y22)= 1.06AA {.OO056