This book provides a systematic exposition of mathematical economics, presenting and surveying existing theories and showing ways in which they can be extended. One of its strongest features is that it emphasises the unifying structure of economic theory in such a way as to provide the reader with the technical tools and methodological approaches necessary for undertaking original research. The author offers explanations and discussion at an accessible and intuitive level providing illustrative examples. He begins the work at an elementary level and progessively takes the reader to the frontier of current research. This second edition brings the reader fully up to date with recent research in the field.
Preface to second edition; Preface to first edition; Introduction; 1. Preliminaries; 2. Developments of nonlinear programming; 3. The theory of competitive markets; 4. The stability of competitive equilibrium; 5. Frobenius theorems, dominant diagonal matrices and applications; 6. The calculus of variations and the optimal growth of an aggregate economy; 7. Multisector models of economic growth; 8. Multisector optimal growth models; 9. Developments of optimal control theory and its applications; Indexes.