Constrained Optimization

Abstract

In a scene in The Godfather, the late Marlon Brando, playing Don Vito Corleone, tells his son, “Well, this wasn’t enough time, Michael. It wasn’t enough time.” There is never enough time, nor is there ever enough money. In personal life, in the affairs of a company or university, and in the government budget, there are never enough resources, be it time, money, or energy. Economics has always been concerned with optimal allocation of scarce resources to competing and unbounded wants. We can imagine that if resources were infinite or wants were limited, there would be no economic problems. Thus, in deciding the family consumption, the hiring for a university, the number and types of courses to offer in a discipline, the amount of R&D expenditures in the company, the allocation of the federal budget among national defense, education, and welfare programs, we face the same problem of allocating scarce resources to achieve the best result possible. But if the behavior of economic decision makers is determined by choosing the best allocation subject to budget constraints, then the starting point of economic theory of households and firms ought to be constrained optimization.