Economic Foundations of Symmetric Programming

This book on symmetric programming is for graduate students who have already taken a graduate course in microeconomic theory.

Quirino Paris (Author)

9780521123020, Cambridge University Press

Paperback, published 1 November 2010

568 pages, 33 b/w illus. 27 tables
22.9 x 15.3 x 3 cm, 0.76 kg

'Mathematical programming approaches applied to a broad range of economic problems are experiencing resurgence, and Quirino Paris's Economic Foundations of Symmetric Programming is a major contribution in this direction. This book sets itself apart as it interweaves economic theory with mathematical programming frameworks. It will serve also as a useful reference for the foundations of optimization (Lagrangean and Karash–Kuhn–Tucker approaches) and for perspectives on primal-dual problems in economics, all the while emphasizing the computational implementation of the theory with the addition of GAMS and other numerical routines. Overall, this book offers an uncommon (and innovative) approach from the perspective of the conventional literature, even though the themes covered are mainstream economic notions and theories.' Spiro E. Stefanou, Pennsylvania State University

The search for symmetry is part of the fundamental scientific paradigm in mathematics and physics. Can this be valid also for economics? This book represents an attempt to explore this possibility. The behavior of price-taking producers, monopolists, monopsonists, sectoral market equilibria, behavior under risk and uncertainty, and two-person zero- and non-zero-sum games are analyzed and discussed under the unifying structure called the linear complementarity problem. Furthermore, the equilibrium problem allows for the relaxation of often-stated but unnecessary assumptions. This unifying approach offers the advantage of a better understanding of the structure of economic models. It also introduces the simplest and most elegant algorithm for solving a wide class of problems.

1. Introduction
2. Lagrangean theory
3. Karush–Kuhn–Tucker theory
4. Solving systems of linear equations
5. Asymmetric and symmetric quadratic programming
6. Linear complementarity problem
7. The price taker
8. The monopolist
9. The monopsonist
10. Risk programming
11. Comparative statics and parametric programming
12. General market equilibrium
13. Two-person zero- and non-zero-sum games
14. Positive mathematical programming
15. Multiple optimal solutions
16. Lemke complementary pivot algorithm - user manual
17. Lemke Fortran 77 program.

Subject Areas: Software Engineering [UMZ], Optimization [PBU], Economic statistics [KCHS], Econometrics [KCH], Economic theory & philosophy [KCA], Research methods: general [GPS]