A regional analysis of future sheep production in New Zealand; an application of spatial linear programming

Abstract

The study of supply has always interested agricultural economists. A complete understanding of the supply behaviour of farmers under different price situations is the basis of most teaching in agricultural economics and a necessity for all policy making in this area. And yet this textbook view of agricultural supply has always been difficult to quantify and apply to actual situations or in practice. The application of linear programming techniques to this problem has now altered the measurement situation completely. Not only can the representative farm be analysed in a large number of price and factor supply situations but groups of different representative farms can be handled just as competently to obtain the correctly specified national response to a given change in prices and so on. A national industry can be divided into homogeneous regions, and regions can be further divided into numbers of farms, different types of farm and so on. In fact, linear programming is completely flexible as a tool of research in this field, as the appropriate specification of the firm, region or industry can be made for any number of different policy studies. One word of caution should be added to temper this enthusiasm for linear programming as a tool of research. The results of such a study as this do not purport to be a prognosis of what ought to be; this study is purely normative in nature and states what may happen if certain assumptions are made about resources available, price levels, and farmers’ responses to changing price levels at the margin. In short, it is a study of normative supply from which policy makers and others will be able to draw certain broad conclusions about the effects of different export outcomes and national policies. This report sets out the details of the linear programming model that has been developed in the Research Unit for the New Zealand sheep industry. The research work was started in response to a request from the International Wool Secretariat for estimates of New Zealand wool supplies in 1980. Preliminary study showed that the problem was amenable to the linear programming approach, and that the regional basis of an aggregate model could be readily identified. In the event, the New Zealand sheep industry was divided into eight fairly homogeneous producing regions based on the classification of farm regions used by the Economic Service of the New Zealand Meat and Wool Boards. Within the regions a total of 33 separate enterprises were identified as having a possible influence on the national output of wool. The information on these enterprises and regions was assembled in the usual linear programming tableau and then used to predict wool supplies in 1980. In the following pages, the details of the model used are set out with appropriate discussion of the more agricultural aspects of each stage of formulation. The formal properties of the model are stated briefly for those interested, but the main purpose of this report is to set out the Unit's thinking on how to best take advantage of the potentialities of linear programming in the construction of normative supply models for New Zealand agriculture. Further work is continuing in this area in the Research Unit.