An algebraic theory of multi-product decisions

We exploit the existence of matrix group symmetries on a production possibility set to identify group symmetries on the profit function. The groups are isomorphic, and provide a pre-ordering on firm preferences over prices. Together with additional structure on the technology, symmetries generate comparative statics on price responses. Linear and other invariances place bounds on firm choice vectors. Reflection group asymmetries on the feasible choice set also support welfare rankings over prices. The methods are adapted to study consumer decisions. Copyright Springer-Verlag Berlin/Heidelberg 2005