| Sumario: | A system of derived input demand functions with the property of zero elasticity of substitution between any pair of inputs is investigated. It is shown that such a system can be derived from cost minimization subject to a production function constraint. The underlying production function is explicitly derived and is named the "nonhomothedc Leontief production function," it being the most general production function with zero elasticities of substitution between all pairs of inputs. This production function allows differential returns to scale to inputs. It is applied to a sample of Japanese petrochemical plants. The results indicate that homotheticity must be rejected; that there are substantial though different economies of scale with respect t.o capital and labor, but that energy and raw materials are used in constant proportions to output, even over time; that technical progress, to the extent that it is present, is embodied in scale. In this study we are interested in analyzing the structure of production of the Japanese petrochemical processing industry, which is believed to be characterized by ex ante limited substitutability between inputs for a given level of output but also at the same time by substantial economies of scale, possibly to different degrees for different inputs. Maintaining the hypothesis of zero elasticities of substitution,[11] we conclude that, on the bases of the F-tests; homotheticity of the production function must be rejected for the Japanese petrochemical processing industry. Hence it 'will be inappropriate to analyze this industry using a conventional homothetic or a homogeneous production functions. [12] Sincehomotheticity is rejected, constant returns is also automatically rejected.
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