An original contribution to economics, this book demonstrates how convex optimization via duality provides a unified methodology for discovering and developing economic and econometric theory. It presents diverse applications in microeconomics, econometrics, finance, and mathematical programming. A central theme is that conjugate duality enables the discovery of new economic relationships. One sets up a minimization problem (the "primal") to embody an economic condition. From the primal, one derives an equivalent but different problem (the "dual"). By solving the dual, one both discovers and proves a new economic result. The primal and the dual are solved simultaneously by setting them equal and factoring. The requirement that each factor must be zero at the solution yields necessary and sufficient conditions for the solution. Taking a subtle and sophisticated approach to optimization, this book will interest academic economists in many fields-microeconomics, international trade, finance, econometrics, and mathematical economics-as well as scholars in other disciplines such as operations research, statistics, mathematics, and electrical engineering.