This study is an application of production-cost duality theory. Duality theory is reviewed for the competitive and rate-of-return regulated firm. The cost function is developed for the nuclear electric power generating industry of the United States using capital, fuel and labor factor inputs. A comparison is made between the Generalized Box-Cox (GBC) and Fourier Flexible (FF) functional forms. The GBC functional form nests the Generalized Leontief, Generalized Square Root Quadratic and Translog functional forms, and is based upon a second-order Taylor-series expansion. The FF form follows from a Fourier-series expansion in sine and cosine terms using the Sobolev norm as the goodness of fit measure. The Sobolev norm takes into account first and second derivatives. The cost function and two factor shares are estimated as a system of equations using maximum likehood techniques, with Additive Standard Normal and Logistic Normal error distributions. In summary, none of the special cases of the GBC function form are accepted. Homotheticity of the underlying production technology can be rejected for both the GBC and FF forms, leaving only the unrestricted versions supported by the data. Residual analysis indicates a slight improvement in skewness and kurtosis for univariate and multivariate cases when the Logistic Normal distribution is used.
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