This paper explores a new approach to the estimation of a joint production technology. Pseudo data, which are obtained by solving a petrochemical process model for alternative relative prices, are used to estimate a price possibility frontier with 3 inputs and 6 outputs. Unlike traditional data sources, pseudo data are not constrained by historical price variation, technologies, and environmental controls. As an econometric exercise, the approximation of the process model's detailed piecewise linear production surface by a single equation "generalized" functional form, the translog, raises a host of interesting empirical and methodological questions.