U.S. livestock production and factor demand: a multiproduct dynamic dual approach

There is a need for modeling livestock production and factor use incorporating the interlinked dynamics of breeding herd adjustments in a theoretically consistent manner. Therefore, a multiple input-multiple output theoretical model is developed based on the adjustment cost hypothesis of production relationship involving sluggish adjustments of quasi-fixed inputs. Employing the results of intertemporal analogue of Hotelling's lemma, a system of equations of optimal output supply, variable input demand, and quasi-fixed inputs (livestock breeding herds) investment is derived. Various issues like aggregation, expectation formation, and nonjointness in implementing this theoretical model are appraised.;A normalized quadratic value function is used to implement the proposed theoretical model. Beef, milk, pork, chicken, turkey, eggs, sheep and lambs, and wool (including mohair) are the eight outputs considered. The five variable inputs included in the empirical model are labor (numeraire), operating capital, grain feed, high protein feed, and hay. Various stocks of breeding herds like beef cows, dairy cows, sows, chicken layers, turkey breeder hens, and ewes (including Angora goats) are treated as appropriate nonallocatable quasi-fixed inputs. Stock of durable capital used in livestock production is also included in the list of quasi-fixed inputs studied. Sector-level aggregate data for the sample period 1950-1987 are used in the estimation. All parametric restrictions implied by the underlying theory of producer behavior (homogeneity, symmetry, and convexity) are maintained throughout the analysis.;The estimated model is subjected to a series of tests of hypotheses on the structure of dynamics of the livestock breeding herds. Nonjointness in production of some outputs is also tested. Results indicate the validity of the present approach in capturing the interlinkages that exist among the dynamics of these breeding herds. The nature and magnitude of such linkages are assessed by means of the coefficients of dynamic adjustments matrix. The important distinction of short run versus long run in responses for simulated external economic stimuli like changes in relative prices is accounted for in the elasticities calculation. In general, the reported elasticities compare favorably with similar estimates from other studies.;The present modeling effort does have few restrictive assumptions like static price expectation formation and a simple linear first order differential equation for approximating the dynamics of herd building. Nevertheless, it amply demonstrates that the theoretical requirements of economic modeling can be fully and meaningfully incorporated in practical applications for realistic results.