The production function expresses a functional relationship between quantities of inputs and outputs in agriculture, illustrating how and to what extent output changes with variations in inputs during a specified period of time.
Basically, the production function is a schedule or table showing the amount of output obtained from various combinations of inputs given the state of technology. Algebraically, it can be expressed as Y = ƒ(X₁, X₂, X₃, X₄), where:
Y = farm output per unit of time
X₁, X₂, X₃, X₄ = inputs such as land, labour, capital, and entrepreneurial ability.
The production function is determined by technical conditions of production and may be rigid or flexible. In the short run, the technical conditions are rigid so that the various input resources used to produce a given output are fixed.
This situation is rare in production theory. Even in the short run, increasing the quantity of one input while keeping the others constant can result in more output. It should be noted that production is a flow; therefore, the transformation of factor inputs into output must be expressed in many units per period of time.
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Uses of the Production Function in Agriculture
The production function was first developed by physical and biological scientists in experimental laboratories to determine the quantity of a variable required to produce the maximum output level, thereby transforming resources into output. In the case of these scientists, a simple linear relationship was sufficient to express the discrete relationship between input and output. For example, in artificial insemination, only a small quantity is needed to fertilize the ovum.
Physical and biological scientists also needed to understand the basis for the profitability of their products—that is, the economic effects. Determining the optimum level of dosage to achieve the desired goal led economists to adopt the production function as a useful analytical tool, establishing it as it is known today.
Olayide and Heady (1982) itemize some of the usefulness of the production function as follows:
- It enables derivation of how the national product is produced from various resources, expressing the relationship between national product and the available resources used in its production.
- It is used to assess inter-regional or international trade balances. Coefficients derived from the production function serve as the basis for determining optimum patterns of intra-state, inter-state, inter-regional, and international trade. This optimization is a natural consequence of achieving optimum output at minimum cost based on comparative advantage for maximum net revenue and regional specialization.
- It is equally useful in the allocation of total output or national income, serving as a tool in the marginal production theory of distribution.
- It serves as a tool in maximizing farm profit by providing the major data needed to determine or specify the use of resources and the pattern of outputs that maximize farm-firm profits.
- It is useful in the algebraic formulation of the theory of supply, as the nature of supply functions rests in large part on the production function.
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For the production function to achieve these uses, production economists obtain experimental, cross-sectional, time series, and engineering data to determine the following:
- The point of maximum output and input relationships
- The point of economic optimum
- The quantity of resources needed to produce a given maximum—either a physical or economic maximum.
This article explains the meaning of the production function and highlights some of its usefulness, particularly in the agricultural sector. It can be concluded that the production function is valuable in all sectors of the economy, including agriculture.
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