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.
Quirino Paris is Professor of Agricultural and Resource Economics at the University of California, Davis, where he has taught since 1969. He received his Ph.D. from the University of California, Berkeley, in 1966 and then served on the university staff of the Advanced Training Center for Economic Research at the University of Naples, Italy. Professor Paris's research has concentrated on investigations of producer and consumer behavior, of which the present text is the most recent example. He is the author of more than 100 journal articles in economics and research methodology and of the textbook An Economic Interpretation of Linear Programming (1991). Professor Paris is also a Fellow of the European Association of Agricultural Economists. He has served as a visiting professor at universities around the world.
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.