|
The term mathematical economics
is employed in two main senses:
(1) As a specialized area of study,
mathematical economics is a distinct
sub-field within the discipline of economics
concerned with the application and development
of mathematical techniques to shed light
on economic problems;
Paul Samuelson is generally considered
to be the father of mathematical economics
(see, for instance,
Foundations of Economic Analysis,
1947).
(2) As a general set of analytical methods,
mathematical economics -- or, to distinguish
it from the first sense employed above,
the mathematical method of economics
-- represents a widely though by no
means universally adopted approach to
the presentation and interpretation
of economic problems.
While the field of mathematical economics
is widely acclaimed (due in large part
to the success of its progeny, mathematical
finance), the widespread use of mathematical
methods in economics is controversial.
Opponents of the mathematical method,
notably the
Austrian School, argue that the
use of formal techniques lends to the
field an impression of scientific exactness
that, by nature of the eccentricities
of its human subject matter, is unfeasible,
even in principle. By contrast, proponents
argue that the validity of the mathematical
method derives from economists' distinctive
assumptions about the internal mechanics
of economic decision-making: economic
agents are generally (and, to many social
scientists, strangely) assumed to be
(i) rational and (ii) self-interested,
from which it follows that an economic
agent's deductions and behaviour may
be compared against the calculations
reached using formal logical and analytical
techniques, including optimization and
other advanced mathematical procedures.
The rational-actor framework has been
disputed as a valid characterization
of human decision-making, but it remains
the primary framework in mainstream
economics.
Although the mathematical method of
economics has evolved through geometric,
algebraic and higher forms, a solid
grasp of modern algebraic methods is
a prerequisite for formal study, not
only in mathematical economics, but
in economics generally. For instance,
the
Journal of Economic Theory, one
of the most prominent academic references
in the field, is the apotheosis of the
mathematical approach -- though surprisingly,
according to the Editors, it is a
non-specialist journal.
|
