Introduction to optimization for economists

This book reviews a range of standard mathematical tools used to solve optimization problems. It discusses the conditions under which function optima exist, considering both single-variable and multi-variable functions. Because resources are often limited, special attention is given to constrained optimization problems, where the domain of the function is restricted. Convex and linear programming problems are examined in greater detail due to their favorable numerical properties. Finally, the book addresses a number of concepts related to optimization problems involving multiple agents or multiple objectives. Each chapter ends with a collection of exercises divided into three categories. The first category contains exercises designed to help students assess their understanding of the material presented. The second category promotes a deeper engagement with mathematical rigor, including proofs of theorems discussed in the main text as well as related topics. The third category demonstrates how the theoretical tools can be applied in economics to enhance understanding of real-world phenomena. In this accompanying volume, we provide solutions to all exercises included in the book.