Control Theory for Agricultural Policy: Methods and Problems in Operational Models

Abstract

IN VIEW of the large amount of research by agricultural economists that leans heavily for justification on its contribution to policy decisions, it is surprising that so little effort has been devoted to systematic utilization of such research. Or considered from the other side, we might have expected more research devoted explicitly to utilization of objective information for policy purposes, and that work could exert its influence on the research that purports to be policy oriented. We have apparently conceived policy decisions as being of such a subjective nature that researchers should stop short of anything like an optimization model for policy purposes. An exception to this point of view is that expressed in the recent book by Fox, Sengupta, and Thorbecke [5]. Recently, there has been an inclination to move further in the direction of trying to quantify social costs asssociated with various policy actions [11, 12, 16, 17], but we need to go another step by using these quantitative measures in the objective function of an intertemporal optimization model. Gustafson's pioneering work in models for optimal grain storage is an example of the direction that we should be moving [7], as is also the general theory of economic policy set out in [5]. Such models take us into the realm of modern control theory. Control theory encompasses not only recent extensions of the calculus of variations, including Pontryagin's work [13], but also discrete time optimization models such as Rosen's convex programming formulations [14] and Bellman's dynamic programming [3]. The latter encompasses the methodology used by Gustafson in his storage control models. Although the classical continuous time models are most applicable to physical phenomena, the discrete time models are usually better adapted to economics. Most decision problems in economics are periodic, and in agriculture, the period is often a year. Of course, economic problems can be approximated by continuous variational models, but numerical solution of these models usually requires discrete approximation methods. Therefore, it would seem advantageous to use a discrete model at the start since it is more realistic and can be solved directly. One advantage of a continuous model is the ability to treat end points of the time horizon analytically through the transversality conditions. For numerical analysis, the discrete model is satisfactory on this point, too, because the time horizon can be arbitrarily extended until the solution values