Returns to Scale and Efficiency in Production: A Distance Function Approach to Southern Illinois Hog Farms
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In this paper, we introduce a parametric specification of a ray-homothetic input distance function. We choose to parametrice our distance function in such a manner that it becomes log-linear in the parameters. This choice enables us to utilize a generalized version of Aigner and Chu (1968) to compute the parameters of the function as solutions to a linear programming problem. The purpose of these theoretical developments are to formulate a framework for the measurements of scale elasticity and input efficiency. The analysis follows ideas introduced by Farrell (1957) and it is applied to the U.S. agricultural sector. The approach followed in this paper allows for a multiple output technology and does not require knowledge of prices. In addition, our methodology allows us to explicitly study the notion of scale elasticity and technical efficiency with respect to output size (in a multi-output setting) and output mix.
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