| Abstract |
Economists are often called upon to analyse experimental data in order to formulate appropriate recommendations for farmers. The data may be analysed as a set of discrete points or it may be possible to represent the data by a continuous response function. Some types of experiments, comparing different production processes, can only be analysed as a set of discrete points. An example is the comparison of chemical weed control with farmers' hand weed control methods. In this case we want to compare two discrete technologies for which there are no reasonable intermediate points. The analysis can usually be efficiently nade by partial budgeting in which changes in revenues are compared with change in costs; considering only changes brought about by using chemical weed control. In more complex farming systems it may be useful sometimes to extend this analysis to a linear programming approach in which the changes in resources of labor and cash are evaluated in relation to farmers resource constraints and opportunities in other fam and non farm enterprises (e.g, Lynam and Sanders, 1980). However, the choice is still made among a discrete number of alternatives. Fertilizer experiments and other experiments comparing different levels of a factor present the opportunity to use regression analysis to fit a continuous response function to the data and then by setting the marginal value(s) product of the input(s) equal to the input price(s), the profit maximizing level of the input(s) can be determined. By this method the optimum fertilizer level may be chosen from any one of an infinite number of points on the response curve and will not usually be one of the points represented by the treatments in the fertilizer experiments. On the other hand, partial budgeting methods may be used to select among a discrete number of treatments represented in the experiment, that which gives highest profits. The purpose of this note is to discuss the advantages and disadvantages of continuous versus discrete analysis of fertilizer experimental data and in particular to relate one form of discrete analysis used by Perrin et. al to the commonly employed production economics theory. We begin then with the analysis of a fertilizer experimental data set using a conventional response function. We extend this analysis to examine the sensitivity of the optimum fertilizer level and associated profits to changes in the level and cost of capital. We then turn to discrete analysis using partial budgeting and show how this approach can also be extended to examine the sensitivity of the optimal fertilizer levels and profits to changes in the cost and availability of capital. |
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