Book: Economic Foundations of Symmetric Programming
Publisher: Cambridge University Press
This book formulates and discusses models of producers’ economic behavior
using the framework of mathematical programming. Furthermore, it
introduces the Symmetry Principle in economics and demonstrates its analytical
power in dealing with problems hitherto considered either difficult
or intractable. It assumes that its readers have a beginner’s knowledge of
calculus and linear algebra and that, at least, they have taken an intermediate
course in microeconomics.
The treatment of economic behavior expounded in this book acquires
an operational character that, in general, is not present in a theory course.
In a microeconomics course, for example – even at the graduate level –
the treatment of a monopolist’s behavior considers only one commodity.
Often, however, a monopolist owns demand functions for three or more
commodities (think of Microsoft) and her firm’s equilibrium requires a
careful analysis, especially in the case of perfectly discriminating behavior.
Another example regards the analysis of risk and uncertainty in the
presence of nonzero covariances between risky output market prices and
input supplies. These and many other “realistic” economic scenarios require
the introduction of a structure called the Equilibrium Problem. Although
this specification is the logical representation of quantity and price equilibrium
conditions for any commodity, economic theory courses privilege
statements of economic models that involve a dual pair of maximizing and
minimizing objective functions. This book makes it clear that these optimizing
structures are only special cases of the class of Equilibrium Problems
and that, often, they impose unnecessary restrictions on the specification
of economic models.