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Public Interest and Private Enterprize: New Developments

Theoretical Results and Numerical Algorithms

Authors: Prof. José Guadalupe Flores Muñiz, Prof. Dr. Nataliya Kalashnykova, Prof. Dr. Viacheslav V. Kalashnikov, Prof. Vladik Kreinovich

Publisher: Springer International Publishing

Book Series : Lecture Notes in Networks and Systems

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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About this book

This book deals with the effect of public and semi-public companies on economy. In traditional economic models, several private companies – interested in maximizing their profit – interact (e.g., compete) with each other. Such models help to avoid wild oscillation in production and prices (typical for uncontrolled competition), and to come up with a stable equilibrium solution. The problems become very complex if we take into account the presence of public and semi-public companies – that are interested in public good as well as in the profit. The book contains theoretical results and numerical techniques for computing resulting equilibria. As a case study, it considers the problem of selecting optimal tolls for the public roads – tolls that best balance the public good and the need to recover the cost of building the roads. It is recommended to specialists in economics as well as to students interested in learning the corresponding economic models.

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Table of Contents

Frontmatter

Chapter 1. Introduction

Abstract

Researchers in the field of mathematical economics have extensively and intensively studied mixed oligopoly models. In contrast to the classical oligopoly, a mixed oligopoly, apart from standard producers who seek to maximize their net profit, usually includes at least one public company trying to optimize another objective function involving indicators of the firm’s social responsibility.

José Guadalupe Flores Muñiz, Nataliya Kalashnykova, Viacheslav V. Kalashnikov, Vladik Kreinovich

Chapter 2. Consistent Conjectural Variations Equilibrium in a Semi-mixed Duopoly

Abstract

Consider a semi-mixed duopoly with two producers where \(i=0\) is a semi-public company and \(i=1\) is a private firm. The companies supply a homogeneous produce under the expenditure estimated by the cost functions \(f_i (q_i )\), \(i=0,1\), where \(q_i\ge 0\) is the output volume by producer i. The market-clearing supply is specified by a demand (inverse price) function \(G=G(p)\), whose argument p is the price suggested by the suppliers.

José Guadalupe Flores Muñiz, Nataliya Kalashnykova, Viacheslav V. Kalashnikov, Vladik Kreinovich

Chapter 3. Consistent Conjectural Variations Coincide with the Nash Solution in the Meta-Model

Abstract

Consider an oligopoly of at least two producers of a homogeneous good with cost functions \(f_i=f_i(q_i)\), \(i=1,\dots ,n\), \(n\ge 2\), where \(q_i\ge 0\) is the supply by producer i. Consumers’ demand is described by a demand function \(G=G(p)\), whose argument p is the market price established by a cleared market.

José Guadalupe Flores Muñiz, Nataliya Kalashnykova, Viacheslav V. Kalashnikov, Vladik Kreinovich

Chapter 4. Bilevel Tolls Optimization Problem with Quadratic Costs

Abstract

As usual, we formulate the Tolls Optimization Problem (TOP) as a single-leader-multi-follower game that occurs in a multi-commodity highway network. The usual parameters for this formulation are the following.

José Guadalupe Flores Muñiz, Nataliya Kalashnykova, Viacheslav V. Kalashnikov, Vladik Kreinovich

Chapter 5. Conclusions and Future Research

Abstract

In Chap. 2 we presented mathematically rigorous proofs of the conjectures (cf., [1]) concerning the behavior of the semi-public company and private firm of a semi-mixed duopoly of a homogeneous good. The main difference of this work from the classical duopoly models is in the presence of one producer who maximizes not its net profit, but the convex combination of the latter with the domestic social surplus.

José Guadalupe Flores Muñiz, Nataliya Kalashnykova, Viacheslav V. Kalashnikov, Vladik Kreinovich

Backmatter

Title: Public Interest and Private Enterprize: New Developments
Authors: Prof. José Guadalupe Flores Muñiz
Prof. Dr. Nataliya Kalashnykova
Prof. Dr. Viacheslav V. Kalashnikov
Prof. Vladik Kreinovich
Copyright Year: 2021
Publisher: Springer International Publishing
Electronic ISBN: 978-3-030-58349-1
Print ISBN: 978-3-030-58348-4
DOI: https://doi.org/10.1007/978-3-030-58349-1

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