This section makes use of three different methodologies to determine the farm size-efficiency relationship in commercial agriculture: first, total factor productivity differences between small and large farms are determined; second, non-parametric Data Envelope Analysis (DEA) is used to estimate scale efficiencies; and third, following the suggestions of Binswanger, _et. al_ (1993), regression analysis is used to test the farm size-productivity relationship.

# _Data_

The data used in these analyses come from farm surveys conducted by the Department of Agriculture's Directorate of Agricultural Economics over the period 1974/75 to 1990/91. Farm surveys, covering a representative sample of between 65 and 85 individual farmers, were conducted in each of the six major grain production areas of South Africa. Two regions were surveyed per annum, implying that each region was surveyed every three years. These six areas involve rain-fed agriculture; subsequently, an irrigation area was also included in the analysis. The regions included in the analysis are representative of the relatively medium and high potential agricultural areas of South Africa, excluding perennial crops. More than 80 percent of all maize, wheat and other grain are produced in these areas, while livestock (dairying, beef cattle and woollen sheep) is also important in most areas. Table 5 provides more information on the surveys included in the analyses. They were selected to represent all the regions; poor, normal and good rainfall years; thus, selected years during the period 1974 to 1991.

The data from these surveys specifically allow for the elimination of the problems with previous studies. In particular, farm size is adjusted for differences in land quality within regions by using land value to normalize areas; differences in operational holding size and ownership holding size are incorporated into the analysis; and family labor is considered. Another important point is that, within a specific region, all farmers essentially face the same prices because they buy from the same input suppliers and output markets for most commodities were controlled. This implies that monetary values of outputs and inputs (revenues and costs in the relevant categories) can be treated as quality adjusted quantities,'<sup>6</sup> which greatly enhances the reliability of the analysis as it also normalizes input and output quantities by

> **16** This amounts to assuming that the corresponding implicit price indexes are unity. This approach has the advantage of being empirically tractable. Although it allows for price variation across years and areas, it has the disadvantage of neglecting price variations across farms within any particular survey. While the intuition is that these variations are small or even negligible, they cannot be ruled out. The "rule of one price" (Chavas and Aliber (1992) does, for example, not take into account different transaction costs or market failures. However, the assumption that all farmers within a survey face the same prices seem to reasonable given the nature of the farm support system in these areas. An additional, but related point is that the "rule of one price" implicitly accounts for commodities which are not of homogeneous quality. Different farmers may face different prices because they purchase inputs or sell outputs of different quality. By using the monetary values of input and output as quantities, there is an adjustment for these quality differences, with an implicit assumption that the markets work fairly well.

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