Determination of Economic Optima from Crop-Rotation Experiments

Abstract

The practice of rotating the crops grown on a particular piece of land is rooted in antiquity. The principal reasons for rotation cropping have been control of weeds, insects, diseases, and soil erosion and the improvement of soil fertility. The statistical analysis of long-term crop-rotation experiments is discussed in a number of important papers such as Cochran [1939], Yates [1949; 1954], Patterson [1953; 1959; 1964], and Patterson and Lowe [1970]. These papers basically deal with the specification of error structures for long-term experiments and the estimation of variance components. Particular attention is given to the correlations in yields arising from observing the same plots over several years. There is considerable literature on the economic aspects of rotation cropping but the literature on the economic analysis of crop-rotation experiments per se is limited. In Heady et al. [1956], a linear programing approach is used to examine the effect of different factors in determining optimal rotation and fertilizer schemes. Abraham and Agarwal [1967] and Agarwal [1968] employed the statistical principles outlined by Patterson [1953] and Yates [1954] to analyze rotation experiments in India and compared the net-return for the different rotations for several combinations of product prices. In a practical farm situation, crop-rotation practices are considered in an economic framework. The farmer's problem is to determine the 'optimal' crop-rotation and the 'optimal' level of the treatments applied to the crops in that rotation. We assume that the choice of a rotation from a set of alternative crop-rotations depends primarily on two characteristics, namely, average annual net-return and variance of annual net-return. Given