NECESSITY, it has been said, is the mother of invention. In this paper we present a dynamic recursive model for the livestock-feed sector designed for the specific purpose of making long-run projections. The commodities analyzed are cattle and calves, hogs, sheep and lambs, chickens, turkeys, eggs, milk, and feed grains and other concentrates. While this model is not an invention in the theoretical sense [see, for example, 9, pp. 12-15] it may qualify in the practical sense. Numerous questions are asked that require an integrated supply-and-demand model for adequate solutions or answers. This is especially true in macro and long-run analysis where the ceteris paribus assumption is inappropriate. For example, such questions as What will happen to farm income if beef production expands 20 percent?, If exports of wheat are cut 50 percent, what kind of impact will this have on the price of feed?, and How much beef will be consumed in the U.S. in 1970? require an integrated supply-and-demand analysis to provide satisfactory answers. It is not very realistic to assume that production of beef does not affect the price of pork, that wheat supply does not affect the price of feed grains, or that we can estimate the consumption of beef in the future by assuming that prices will be the same then as they are today. Of course, economists know that these interdependences exist and they have theoretical ideas of how to deal with them. But the real problem, as demonstrated in earlier studies by Hildreth and Jarrett [6], Cromarty [3], Hasseler [5], and Brandow [2], lies in estimating or developing a supply-anddemand structure of the agricultural sector or agricultural subsectors that is adequate for answering such questions as those posed above. 5l Since most economists are more familiar with short-run predictions work, it is useful to point out where research methods applicable to long-run projections differ. Here, we define the long run as being a period of inore than one year. This is quite arbitrary, of course. It is often convenient and reasonably sufficient to base short-run forecasts on a single equation. That is, one may assume that a given variable,
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