THE DUALITY BETWEEN COST AND PRODUCTION FUNCTIONS WITH APPLICATIONS TO THE AGRICULTURAL LABOR MARKETS IN THE UNITED STATES, WASHINGTON STATE AND CALIFORNIA

The transformation of the United States Agriculture caused a secular shift of labor out of agriculture which has continued to this day. Contemporary with this secular labor shift, the combination of inputs has turned toward a more machine-intensive technology. Although the number of farm workers shows a distinguishable reduction, there still exists a wage difference between the nonagricultural and agricultural sector. The minimum wage law and the labor organizations in agriculture are partially credited with attempting to bring about higher wage rates and better working conditions for agricultural laborers and possibly for reducing or closing the wage gap between the agricultural and nonagricultural sector.In deriving and estimating the constant output-input demand equations, also referred to as the short-run demand functions, special attention was given to Shephard's duality theorem between cost function and production function. Using Shephard's duality theorem a translog cost function with the four inputs, capital, land, labor, and fertilizer, was applied to agriculture for the United States, Washington state, and California. The four factor shares were derived from the given cost function. Three out of four of these factor share equations, capital share, labor share, and fertilizer share, were estimated by the Joint Restricted Generalized Least Squares method using time series data for the period 1960 to 1977. Utilizing the estimated factor share parameters the Allen partial elasticity of substitution and the price elasticity of the four factor demands were calculated for each year between 1960 and 1977.The results of this study showed that the demand for labor was inelastic for the United States, Washington state, and California. This means the percentage reduction in employment will be less than the percentage increase in wages due to the effects of the minimum wage law or unionization. In other words, attempts to raise agricultural wages, ceteris paribus, will result in an increase in labor's share of agricultural income. Additionally, the results indicated that the labor demands are moving smoothly toward the elastic portion for the United States and the state of Washington. However, in the state of California this smooth trend towards the elastic portion is not apparent.In regard to factor substitution, the Allen partial elasticity of substitution between capital and labor was higher than one for the United States and for California. The partial elasticity of substitution between capital and labor was slightly less than one for Washington state.The purpose of this study was to increase the body of knowledge regarding possible effects of the minimum wage law and unionization on agriculture in the United States, Washington state, and California by employing the estimated elasticity of substitution and the factor price elasticity from a translog cost function. Special attention was given to the direction of change regarding the labor demand elasticities.