This paper demonstrates that the result proposed in Barelli and Pessoa (2003) yields contradictions, making their main conclusion unproven and inconsistent. First, we correct the error of the authors. Second, we prove that imposing the Inada conditions on a production function inevitably transforms that function into the Cobb-Douglas production function whose parameters are endogenously determined by the original production function. Accordingly, we demonstrate that our results invalidate the interpretation of Litina and Palivos (2008), and we correct the erroneous conclusion of Litina and Palivos (2008). (c) 2021 Elsevier B.V. All rights reserved.