A linear programming study of the supply of store beef cattle from hill country farms

Abstract

Within the general area of aggregate New Zealand beef supply, the supply of store cattle and associated beef products from beef breeding farms on a certain class of North Island hill country was chosen as the object of immediate study and the scope of this thesis. The desirability of concentrating on one section of the farming industry in isolation is discussed in Chapter III. It is argued, in the same chapter, that the establishment of one or several store beef cattle supply functions is an essential prerequisite to the normative derivation of a prime beef supply function. This choice appeared to be a logical one in a field in which all aspects are yet to be investigated in detail.

It was intended to quantify as far as possible the relationships between this particular supply variable and certain product prices, namely export beef schedule prices, mutton and lamb schedule prices, and auction wool price. Ceteris paribus assumptions were made about all other determining variables.

Linear programming of individual producer units, with subsequent weighted summation to obtain the aggregate supply/price relationships for the area of study, was selected as the most appropriate technique. This choice is discussed in Chapter III in the light of previous supply studies in this general area. The theoretical and practical advantages and disadvantages of this technique will be taken as already well documented and will not be reiterated here.

Specific Aims The specific aims of this study were determined in the light of the general considerations outlined above. It is appropriate and useful at this stage to enumerate these as succinctly as possible. They were as follows: (1) To specify a linear programming model which would realistically represent the management problem of choice of enterprise on North Island hill country of the type defined in Chapter III. The scope of applicability of such a model is discussed in Chapter IV, but it should be noted here that it is concluded that it embraces the producers of approximately half of New Zealand's store beef cattle, at the present time. (2) On the basis of the degree of success achieved in stage (1), to reach conclusions as to the practicability of applying linear programming to this pattern of farming, both for the present purposes of supply analysis, and, if possible, as a farm management planning tool. (3) Dependent on the successful completion of stage (1), to compute the optimum (maximum profit) solutions for a representative range of farm fixed resource situations from within the regional population. This was to be done over a range of beef, wool, and sheep-meat prices, with corresponding store stock prices in each case. A prerequisite for this step was to be the investigation of the relationships between store prices and final product prices, and the construction of a regime of store livestock prices to correspond to each level of final product prices adopted (4) The weighted summation of the results from stage (3) to obtain aggregate beef supply curves for the region, over the range of beef prices, and for each of the different levels of sheep product prices assumed. (5) To present results from stages (3) and (4) together with any relevant 'by-product' information, e.g., marginal productivities of resources, which may arise as the result of the use of the linear programming technique. (6) An interpretation of these results, together with an evaluation of the meaningfulness of such normatively derived relationships, and their significance and implications from the national point of view, was envisaged to conclude the study.

At all stages certain details as to the direction and extent of specific areas of investigation within the general framework of the study were to be modified as progress suggested. However the proposed plan of the study, as presented above, was in fact followed fairly closely, and subsequent discussion of results and conclusions appear in the final chapters of this thesis. Earlier chapters aim to present a background to the problem, together with a logical development, and a description, of the particular method of analysis.