Technology Asymmetries, Group Algebra and Multi-Plant Cost Minimization

For a homogeneous good, this article studies firm-level production activities when the firm controls a plural number of plants. Through careful construction of cost function technology asymmetries, we inquire into the ordinal structure of the production vector for multiplant cost minimizers. When Schur-convexity of a reference pseudo-cost technology is the principal functional assumption, then ordinal concepts of technical asymmetries map into rank order on the equilibrium production vector. Under a more generalized characterization of the technical asymmetries a multiplant firm encounters, group theory is used to map a cardinal concept of asymmetries into cardinal bounds on the optimum allocation.