A procedure is developed for representing competitive and noncompetitive market structures in linear programming models. Arbitrarily close approximations to nonlinear forms—in both the objective function and constraint set—can be made without much loss of the computational efficiency of the simplex algorithm. The noncompetitive market structure may be used for measuring income at endogenous prices in a competitive model and may serve as a constraint on that measure of income to represent certain classes of economic policies. Product substitution effects in demand can be approximated by a linear program. The demand structure can be transformed to take account of any shift in demand which can be represented by a rotation of the demand function.
This paper demonstrates a procedure for determining economically optimal rations which avoids problems that arise in conventional analysis of experimental results. It consists of maximising a suitably constrained profit per unit time objective function, itself formed from functions obtained from pig fattening experiments under special Australian conditions. The relevant functions‐for consumption of milk and wheat, time to slaughter and percentage lean meatare first demonstrated, followed by a brief discussion of results obtained. Specifcally, it is noted that optimal diets differ according to whether the criterion adopted is profit per pig or profit per pig per week, that dairy farmers fattening pigs should feed substantial quantities of grain, and that the optimal diets are very stable to changing prices. More generally, the procedure avoids the statistical difficulties of conventional analysis of experiments arising from the estimation of weight‐gain functions based on actual quantities of food consumed.
In livestock feeding experiments the problem of recursiveness arises because the quantity of feed consumed by an animal is a function of its past history of Feeding. The problem is most acute where experiments are designed to analyse sub ad lib feeding. The analysis of such experiments encounters two important problems. The first is that the actual quantity of feed consumed is an endogenous variable and is not directly under the control of the experimenter or the livestock producer. The second problem is the mathematical complexity of the relationships involved. A solution is suggested as a quasi reduced-form model.Livestock production processes are essentially of two types : the first is the factory type, such as milk and wool production, where inputs are processed by a relatively fixed livestock unit to yield a flow of outputs (which may or may not be harvested continuously); the second is that Df meat production, where the livestock increase in weight, and it is this growth which constitutes the product. We are here concerned with the second type of process, although it is apparent that the analysis has relevance to the f0rrner.lIn experiments aimed at estimating the production functions associated with meat production and hence at determining the optimal use of resources, two particular problems are noted. First, for physiological reasons, it is likely to make sense to feed an animal rations of different composition as it matures and grows, Second, an animal is fed at different levels of feeding over time. We abstract from the first problem of ration composition by assuming that animals are brought into the experiment at a constant weight and age, and that the composition of the ration is held constant for the further duration of its life. However, it is clear that the methodology proposed at the end of the paper can be extended to account for changing the ration composition throughout the production period.Consideration of the second problem of differing feed levels over time reveals important differences between livestock and crop experiments. In a crop experiment designed to explore response to fertilizers, no special difficulties arise in fixing the levels of fertilizer inputs, given the experimental design. Also, with most annual crops, only one crop is possible each year, with the time to harvesting largely being determined by the plant's physiological response to various environmental stimuli: thus, time is not a relevant instrumental variable. However, in livestock ex-:I. The authors are indebted, with the usual caveats, for comments and suggestions to a number of colleagues, foremost amongst these being John L. Dillon.1 The design and analysis of agricultural experiments has generated an extensive literature. Excellent bibliographies are to be found in Heady and Dillon (1961) and Dillon (1967).
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.