Pseudoproduction, Pseudocost and Profit Functions in Monopoly from the Dual Perspective

Ilko Vrankić,Mira Krpan

doi:10.1515/bsrj-2016-0012

Abstract

Abstract Background: Duality in the microeconomic theory enables us to represent consumers’ preferences and production technology with various dual functions satisfying certain regularity conditions. Objectives: Since the basis for the application of duality in the microeconomic theory is the price taking behaviour, this paper takes the challenge of applying principles of duality to a monopolistic case where a single producer has an influence on the price which it charges for its product. Methods/Approach: The standard approach of deriving the profit function for the monopolist from the production function and the defined pseudoproduction function is accompanied by an alternative approach in which the starting point is the pseudocost function. Starting from the derived profit function, the pseudoproduction function and the pseudocost functions are recovered and a version of Hotelling’s lemma is given. Results: The structure of the profit maximization problem in a monopolistic case was made similar to the structure of the profit maximization problem in the perfectly competitive case and it is shown that all starting functions can be recovered back from derived functions. A version of Hotelling’s lemma is illustrated, which brings us indirectly from the profit function to the supply function. Conclusions: By introducing the pseudoproduction function in the profit maximization model of a monopolist, the structure of the problem becomes similar to the perfectly competitive case and duality results can be applied. The profit function is derived from the pseudoproduction and the pseudocost function, and all starting functions are recovered back from the derived profit function.

Highlights

Since the introduction of duality in microeconomic theory and acknowledgments of its advantages from a theoretical and empirical standpoint, many applications followed and are still widespread (Diewert, 1982; Briec, Kerstens, Eeckaut, 2004; Kuosmanen, 2003; Taylor, 1989)
The basis for the application of duality in microeconomic theory is the price taking assumption, and the question is how can the principles of duality be applied in the case of a monopolistic firm where the single producer has an influence on the price which he charges for the product (Appelbaum,1975; Diewert, 1982; Lau, 1978)
In this paper we applied principles of duality in a monopolistic case where the single producer has an influence on the price which he charges for the product

Summary

Introduction

Since the introduction of duality in microeconomic theory and acknowledgments of its advantages from a theoretical and empirical standpoint, many applications followed and are still widespread (Diewert, 1982; Briec, Kerstens, Eeckaut, 2004; Kuosmanen, 2003; Taylor, 1989). Duality in microeconomic theory includes derivation and recovering of the alternative representations of the consumer preferences and the production technology (Blume, 2008; Shepard, 1970). The most important result in duality theory from an empirical standpoint is Hotelling's lemma (Mas – Colell, Whinston, Green, 1995), which enables us to obtain the supply function and the input demand functions by simple differentiation of the profit function satisfying certain regularity conditions. We discuss it in the case of monopolist and illustrate a version of it

From the production function to the profit function

From the pseudocost function to the profit function

From the profit function to the pseudoproduction function

From the profit function to the pseudocost function

Conclusion