Computational Approach for the Firm's Cost Minimization Problem Using the Selective Infimal Convolution Operator

摘要

The Infimal Convolution operator is well known in the context of convex analysis. This operator admits a very precise micro-economic interpretation: if several production units produce the same output, the Infimal Convolution of their cost functions represents the joint cost function distributing the production among all of them in the most efficient possible way. The drawback of this operator is that it does not discriminate whether one of some of the production units is not profitable (in the sense that it would be preferable to do without it). This is the motivating idea for the present work, in which we introduce a new operator: the Selective Infimal Convolution. We give not just its definition and basic properties but also an algorithm for its exact computation. Using this, we avoid the combinatorial blowing-up of other classical methods used for solving similar problems. Even more, our approach solves a one-parameter family of problems, not just a single one. We provide an application to the Firm's Cost Minimization Problem, one of the most important problems in Microeconomics.