Economic Foundations of Symmetric Programming

ISBN-13: 9780521194723 / Angielski / Twarda / 2010 / 568 str.

Quirino Paris

Opis

The search for symmetry is part of the fundamental scientific paradigm in mathematics and physics. Can this be valid also for economics? This textbook 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.

Recenzje

'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

Spis treści

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.