A production function in which one or more resources are fixed in amount is termed SHORT-RUN production function. In the production process, some factors are held constant while others are varied in amount and stages. SHORT-RUN AND LONG-RUN PRODUCTION FUNCTION Similarly, the output must refer to the same type of product. To be meaningful, the additional amount of labour employed must be that of an adult as this will enable us make assumption about their output. the initial input of labour refers to the labour of an adult and the additional input of labour refers to that of a child, it does not make any meaning because, it will be difficult to refer to the amount of labour used. Production and resource relationships are meaningful if they refer to input and output that are homogenous.

This mean that for every one unit change in X, Y changes by b, it is important to know that both input and output must be homogenous. b is the coefficient of elasticity, and it is 4 by substitution, which is also the slope of the line.Įxplicit Production function (unsubstituted) (substituted) a is the value of Y when there is no change in X and it is 25. For simplicity, the general formula, for explicit function is Y = a + bx, where a = constant, and b = elasticity of response of Y to a unit change in X. If we put a bar between x1 and X2, X3….Xn it shows that X1 is variable while the other factors are assumed constant or fixed. Hence an algebraic expression is more accurately represented as Y = f(x1, x2, x3….xn). However, the product output is not dependent upon only one factor. In the implicit function, x is the independent or the explanatory variable while Y is the dependent or the explained variable. If the second and third columns are shown on a graph, the result would be the factor product pair, a relationship.Īlgebraic Expression of the Production Function Graphical Expression of the Production Function The values in the forth column are derived by dividing total product by the corresponding labour values, while the marginal products are the differences between successive total products. The second and third columns whose values are given represents the production function. Total Production Live weight of Animals (kg) Table 1:Arithmetic Representation of Production Function (3) It can be expressed algebraically by means of nations. (2) It can be expressed graphically by means of two-dimensional graphs (1) It can be expressed arithmetically by means of tables There are three ways of expressing a production function.

They may be a piece of land, number of animals to which variable inputs are introduced or added to produce a given level of output. It is a technical relationship in the sense that technical units are involved in the production process. The relationship shows that total output depends on the quality and quantity of the inputs used in the production process. The production function is a technical relationship between resource (factor) inputs and production (commodity) output. This decision brings us to the production function. One of the production decisions farmers have to make is the decision on how much of the commodity to produce. Its differentiability enables us to establish the rates of return. In mathematical terms, this function is assumed to be continuous and differentiable. The production function stipulates the technical relationship between input and output in any production scheme or process. These resources are scarce and, therefore a choice has to be made in their use with the ultimate objectives may be profit maximization, output maximization, cost minimization, or the maximization of satisfaction or the combination of these motives of enterprise. Agricultural production decisions are, in effect decision making in the allocation of scarce resources. Agricultural Production Function AnalysisĪgricultural production is the process of transforming agricultural resources into a form that will give us maximum satisfaction.