Foundations of Mathematical EconomicsThis book provides a comprehensive introduction to the mathematical foundations of economics, from basic set theory to fixed point theorems and constrained optimization. Rather than simply offer a collection of problem-solving techniques, the book emphasizes the unifying mathematical principles that underlie economics. Features include an extended presentation of separation theorems and their applications, an account of constraint qualification in constrained optimization, and an introduction to monotone comparative statics. These topics are developed by way of more than 800 exercises. The book is designed to be used as a graduate text, a resource for self-study, and a reference for the professional economist. |
Contents
Linear Functions | 263 |
Smooth Functions | 417 |
7 | 474 |
Optimization | 497 |
Comparative Statics | 601 |
Functions | 604 |
| 635 | |
Index of Symbols | 641 |
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Common terms and phrases
affine approximation Assume bounded called coalition compact concave concave functions cone constraint qualification continuous contour converges convex cone convex function convex set corollary correspondence defined denote differentiable function economic elements equations example exists f(xo Farkas lemma feasible figure finite finite-dimensional first-order conditions fixed point following exercise function f Hint homogeneous functions homogeneous of degree implies inequalities input inverse Kuhn-Tucker conditions Lagrange multipliers Lagrangean Let f linear functional local optimum matrix maximization maximum theorem metric space mixed strategy monotone neighborhood nonempty nonnegative normed linear space objective function optimal solution optimum output partial derivatives payoff player power function preference relation production function profit proof proposition quadratic quasiconcave requires satisfies separating hyperplane theorem sequence Show subject to g(x subset subspace supermodular Suppose tion TP-coalitional game unique utility function value function variables vector x₁