### ESTIMATION OF THE PRODUCTION OF MATIARI SUGAR MILL SINDH USING SPSS THROUGH COBB-DOUGLAS MODEL

#### Abstract

The production function is the combination of the Labor and Capital. It is really a business concept that defines the maximum rate of output approaching from specified input rates of capital and labor. The least cost capital-labor combination for the production or the output rate would yield maximum profit, and are not the objectives of this function. This function only shows that the maximum output should be obtained from any input combination. Economists use variety of functional form to describe the function, but the most frequently used function is Cobb-Douglas production function. It was proposed by Charles Cobb and Paul Douglas in 1928. It is widely used in economics because it has good properties and is representative of much production process. Almost every production manager is interested in maximizing his production. He attempts to minimize the cost or maximize production, subject to producing a specified output rate. In this sense estimation of production plays the crucial role for planning maximum production but the main problem is which procedure of estimation should be used for the forecasting of production. This problem seriously depends on the behavior of production curve while Cobb-Douglas is a non-linear model and, therefore, the behavior of this model is curvilinear. In this paper, our objective is to estimate the sugar production for the next two years (i.e., 2010, 2011). Due to the fixed capital1 the production is mainly dependent on labor. That is why this paper also provides the optimal labor input as appendix information. All these analyses are carried by using the Statistical Package for Social Science (SPSS). This is widely used statistical package for the linear and non-linear regression analysis. The behavior of production is normally non-linear and can be analyzed through Cobb-Douglas function. This function consists of two independent variables i.e., labor and capital. In this software linear and non-linear regression analysis can be performed via Curve Estimation procedure, but Cobb-Douglas model is analyzed trough Nonlinear regression menu. During the model building of Cobb-Douglas, starting values of parameters are essential to be given. In production function Return to Scale refers to a technical property of production that examines the changes in output following proportional changes in all inputs. Usually many functions have a property called constant return to scale which means an increase of an equal percentage in all factors of production causes an increase in output of the same percentage. In the SPSS during the modeling of production function the assumption of the constant return to scale is followed which is that the sum of parameters are exponents (i.e., α and β) on capital and labor variables must be equal to one. Estimation procedure makes iterations1, and due to these iterations the model select the best parameters values for estimation. In this study, estimated model for sugar production of Matiari Sugar Mill of Sindh for the collected data was found to be satisfactory with some diagnostic checks such as standard deviation of regression and coefficient of determination (R-square); all these practices followed by SPSS.

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