Minimum Cost Nutrient Requirements from a Growth Response Function

Abstract

The objectives of this study were: 1) to show the applicability of energy-protein substitution in the growth of cattle, 2) to quantify this into four different functional forms and 3) to analyze the results from a biological and an economics point of view. Data from previous studies were used to evaluate energy-protein substitution in the growth of cattle. Thirty-eight pairs of identical twins that were purebred, crossbred or grade beef-type cattle (Aberdeen Angus, Guernsey, Hereford, Jersey and Shorthorn) were used. Diets were composed of corn and corn by-products, linseed meal, supplemental minerals and vitamins and a variable amount of alfalfa hay. Means and standard deviations were: crude protein intake (P), .457 (.257) kg/d; metabolizable energy intake (E), 7.136 (3.200) Mcal/d; body weight (W), 162.2 (52.5) kg and daily gain (G), .310 (.272) kg/d. Four different functional forms of G = f(E,P,W) were fitted: a polynomial, a nonlinear model, a translog and a Cobb-Douglas function. The four models fit the data well with R2 higher than .90 and sy less than .085 kg/d. National prices for corn and soybean meal (1949 to 1981) were used as estimators of energy and protein prices. Minimum cost requirements for each model and for each set of prices were computed at three rates of gain and were compared with the 1976 National Research Council requirements. Daily savings of .54 to 5.93 cents/head were found by using minimum cost requirements compared with fixed requirements, depending on which model was assumed to be “true.”