PLANNING HORIZONS AND THE MONOPOLIST: A NOTE ON A GENERALIZED SAMUELSON‐LE CHATELIER PRINCIPLE

Abstract

Time is an important determinant of factor demand and supply elasticities in producer theory. The typical textbook distinction between the short‐run and the long‐run focuses upon the ability of the decision‐maker to adjust fixed factors. Indeed, the length of the firm's planning horizon may be identified with the degrees of freedom available to the firm; i.e. the number of factors that can optimally be adjusted to a changing economic environment. The purpose of this note is to illustrate use of the envelope theorem to recover a generalized Samuelson‐Le Chatelier principle in a simple and elegant manner. In particular, we will show how a monopolist's derived factor demand elasticities may be ordered by the length of the planning horizon. Thus the economically appealing and intuitive notion that the monopolist's factor demand decisions will be more responsive to price changes, the greater the flexibility in utilizing fixed factors will be given an analytically rigorous, though quite simple, demonstration utilizing duality theory and the well‐known envelope theorem.