A Production Function Analysis of the South African Sugar Industry

• DOI: http://doi.org/10.1111/j.1813-6982.1985.tb01019.x
• Date: 01 December 1985
• Published date: 01 December 1985
• Author: G. F. ORTMANN*

A Production Function Analysis of the South African Sugar Industry

G. F. ORTMANN*(1)

THE SOUTH AFRICAN SUGAR INDUSTRY comprises approximately 22 000 individual farmers and 17 sugar mills spread along the

Natal coast, the Midlands of Natal and extending into the Eastern Transvaal (South African Sugar Association, 1983/84, p. 119).

The Industry forms a cornerstone of the Natal economy and is a direct employer of about 150 000 workers (Smeaton,1984, p. 236).

In this article production functions for various sugar-cane areas are presented. The objective is to ascertain the major factors

affecting sugar-cane production and the extent to which resources are misallocated in six areas of the Sugar Industry and across

the Industry as a whole. The analysis is based on cross-sectional and time-series data over four years, namely 1976177 through

1979/80. In total more than 1700 farm units are involved. Before the production functions are presented and analysed,

developments in the use of production functions are sketched.

1. Developments in the Use of Production Functions

When Heady and Dillon (1961) published their book Agricultural Production Functions the application of formal production

function concepts in agricultural research was considered as 'a relatively recent development' (p.v.). Since then developments in

production function analysis have been slow. In 1979 Upton published an article entitled 'The Unproductive Production Function'.

In that article he reviewed some major problems of farm survey data. These problems, which include treatment of capital,

aggregation of, inputs and outputs, aggregation of functional relationships, specification of'the function and statistical estimation,

have not yet been resolved, even though one of the first major attempts to fit production functions to farm data was made by

Tolley, Black and Ezekiel in 1924. Upton (1979) has his doubts regarding the validity of many farm-level production function

analyses.

Production function analyses of farm data are generally aimed at deriving estimates of input coefficients. These are used to guide

the future allocation of resources, to investigate the economic rationality of farmers, to investigate

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returns to scale and to study technology change where time series data are available (Upton, 1979, pp. 184-81). Heady and Dillon

(1961, ch. 17) studied the efficiency of resource use in various parts of the world while Hopper (1966) investigated the economic

rationality of farmers in traditional Indian agriculture with the use of production functions of farm data. Griliches (1963) attempted to

quantify the sources of productivity changes in the USA using cross-sectional data, while Binswanger (1974) used time series data

to investigate technology change. Alcantara and Prato (1973) used standard and generalized Cobb-Douglas production functions

to estimate the returns to scale and the elasticities of production of various inputs on sugar-cane farms in Brazil. A vast number of

articles on the use of production functions have been written. Heady and Dillon (1961) provide a long list of publications in their

bibliography while Upton (1979) also has a useful reference section.

Of the numerous alternative functional forms available, the Cobb-Douglas function has been the most popular in farm analyses

(Heady and Dillon, 1961, p. 228). The main reasons for its popularity have been its convenience in interpreting elasticities of

production; because estimation of parameters involves fewer degrees of freedom than other algebraic forms which allow increasing

or decreasing returns to scale; and because its use involves simple computations (ibid. p. 25). Griliches (1963), for example, used the

Cobb-Douglas form 'partly for its ease of manipulation and interpretation, but mainly for its good fit to the data' (p. 420). Upton

(1979, p. 186) ascribes the popularity of the Cobb-Douglas or quadratic forms 'to the relative ease of their estimation using ordinary

least squares regression methods'. However, he considers this reason alone poor justification for choosing a particular form of

function. Although some objective assessment criteria such as economic theory or statistical tests of goodness of fit should be

considered, Upton (1979) comes to the conclusion that 'neither of these types of criteria provides clear and unambiguous

guidelines, so choice of functional form is inevitably somewhat arbitrary' (p.186).

Each algebraic form has its advantages and disadvantages. With the standard Cobb-Douglas function a major disadvantage is the

constant production elasticity assumption over the input-output curve and unitary elasticity of factor substitution. These

limitations have given rise to the development of more flexible algebraic functions. For example, Ulveling and Fletcher (1970)

developed a modified Cobb-Douglas function with variable production elasticities and returns to scale. 'The method permits

pooling of all observations to preserve degrees of freedom and test systematically for productive differences among production

techniques' (p. 326). (The transcendental production function of

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Halter, Carter and Hocking (1957) also yields variable elasticities of production but does not systematically relate returns to scale to

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