Optimization in economic theory

The analysis of optimum choice from among a set of alternatives is a feature of most economic problems. Models of command economies naturally introduce an overall criterion function to be maximized bearing in mind the resource availability and technological possibilities. Models of market economies find it useful to formulate the behaviour of individual agents in an optimum choice framework, with each consumer maximizing utility constrained by his budget and each producer maximizing the net worth of his enterprise given its production possibilities. Between the polar cases we have mixed economies in which the government can manipulate some policy instruments but cannot achieve complete command over resource allocation. Such economies involve two stages of optimization: given each set of government policies, the other agents make their own best choices, and in considering its optimum policy choice the government has to bear in mind the responses of private agents. well as the overall resource and technology constraints.

Even in an age where most economists of recent vintage have some knowledge of mathematics, the techniques used for optimization subject to constraints are often thought to be very esoteric. This is particularly true of decisions involving time, where the choice at one point in time affects the alternatives available at later points. The problem usually arises because students meet this type of mathematics suddenly and in its full glory, and never quite recover from the experience. It is really quite feasible to begin in a much simpler way, relating the mathematics to the economics from the beginning, and progress in manageable steps to an understanding of the more advanced methods. This short book is an attempt at this programme. S

Naturally, I have emphasized understanding rather than rigour. Proofs are given only when they help further understanding, and illustrative examples and applications are chosen for their economic interest and usefulness.