Estimating Agricultural Production Functions from Experimental Data for Different Crops in Relation to Irrigation, Fertilization and Soil Management in Northern Utah

Estimates of agricultural production functions from experimental data for four different crops in relation to six variable inputs are calculated by this study. There are four basic sections in the study. The first section covers the review of production function concepts and the procedures and problems that specifically pertain to this study. Also the importance of joint economic-agronomic research efforts, methodologies and applications of agricultural production functions are cited. The second section includes the presentation data and postulated functional relationships in estimating production functions. Model building programs are used in developing three dimensional figures, which aid in the selection of the appropriate model. A multiple regression model using linear, non-linear and interaction terms is employed in deriving three production function for each crop. The problem of selecting a best model from the above three models is solved on the basis of economic theory, observed biologic physical production process, projected three dimensional production surfaces and statistical analyses. The polynomial form was selected as the best model for each crop. The third section of this study analyzes the results and the economic implications. Optimal rates of input use are determined. Qualification of these results are required because of the non significant statistical relationships including the F values of the regression coefficients and relatively low coefficient of determination (R2), and, also, because some optimal inputs values did not seem reasonable relative to observed rates. Further statistical analyses are carried out to determine the confidence interval for each input\u27s marginal productivity and this results in unbounded solutions. As an alternative, the above confidence interval problem is rephrased as a system of equalities and solved simultaneously to obtain optimal input levels at the marginal productivities maximum and minimum values and these estimates are shown not to be confidence intervals. Finally, in the fourth section of this study, summary and conclusions are given. Also, limitation and recommendations to the study are discussed