On the technical (in)efficiency of a profit maximum

In general, production-theoretical analysis aims at identifying an enterprise's (technically) efficient production alternatives. According to the principles of economy, achieving technical efficiency is considered as a prerequisite for a producer's further optimization behaviour and, therefore, as a matter of rationality. We will show in our article, however, that it might be economically unfounded to focus only on technically efficient production alternatives. Using a nonlinear inequality-constrained optimization framework, we demonstrate that a profit-maximizing production may imply technical inefficiency, i.e., in graphical terms, depending on the topology of the profit function the optimal input-output combination may be located in the interior of the producer's production possibilities set. In order to show this, we establish mathematical (and economic) conditions for the profit-maximization approach to yield a technically efficient or inefficient solution, respectively. In fact, inefficient solutions emerge when input or output prices are not strictly positive over the entire domain and/or the objective function is non-monotonic. We highlight some non-pathological economic situations that are likely to set the stage for technically inefficient profit maxima and provide an example that illustrates how an enterprise can make use of this approach in order to improve profits by choosing technically inefficient production points. In spite of those optimal inefficiencies, economic environments with positive prices and technical efficiency of the optimum shall remain the normal case.