On 'Non-substitution' in Production Models

The Author of this article analyses professor Samuelson’s ‘Non-substitution Theorem’ and concludes that in fact it is composed of two different theorems: the PAS (Paul A. Samuelson) theorem, asserting that prices remain unchanged as demand changes; and the Supplementary Substitution Theorem (implicitly taken for granted), asserting that a variation in prices induces substitution. The Author concludes that the PAS Theorem is correct but the Supplementary Theorem is false. He continues to prove that to refer to the PAS Theorem as the ‘Non-substitution Theorem” is misleading and induces logical error. The misleading feature of the statement consists in conveying information in a negative way (by negation) and thereby implying logically that, if the conditions postulated by the theorem were not satisfied, then that something (i.e. substitution) would happen. This statement according to the Author is false. The Author concludes that in a production context with a given technology, with or without joint products, the traditional concept of substitution makes no sense.