Data for production function analysis

The production standards discussed in the last chapter are useful for comparing average products of specific resources on different farms or in different enterprises. However, in theory we would expect marginal products to be more important in determining the economic optimum level of production, combination of resources and of enterprises. If we are to use the marginal approach to decision-making we must first establish the production function relating output to different levels of inputs. Hence we need a series of observations at different levels of input.

Several observations are needed even in the simplest case where there is one single variable input and one single product and the relationship is assumed to be linear (a straight line). This is illustrated graphically in Figure 13.1 showing hypothetical data relating nitrogen fertilizer input to maize yield. In Figure 13.1 (a) we have only one single observation of input and output; there is only a single point on the graph. Obviously, any number of straight lines, all with different slopes, could be made to pass through this single point. The marginal product cannot be estimated. It should be noted, however, that the average product is easily obtained by dividing output by input.

In Figure 13.1(b), where there are two observations and hence two points, there is only one straight line which will pass through both. The slope and hence the marginal product per unit of nitrogen fertilizer on maize can be estimated.