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MATH 342-01, Mathematical Economics, Spring 2011
Hamrick, Jeff
Hamrick, Jeff
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Syllabus, Curriculum, Academic departments, Text, Mathematics and Computer Science, Department of, 2011 Spring
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Abstract
Mathematics has been used by economists since its inception,
though mathematics did not become the mainstream tool for communicating economic theory until the 19th
century. Early economists who incorporated mathematics into their work included Gottfriend Achenwall
(who used data to justify his analysis of various issues related to public policy), Sir William Petty (who
used mathematics to develop theories of taxation and the velocity of money), and John Graunt (who again
insisted on the use of data to analyze public policy problems).
The field of mathematical economics became much more defined when Augustin Cournot and Leon Walras
recast the field of economics axiomatically around the concept of a utility function. They believed
that individuals maximize their personal utility functions (with units of “utils”). From this perspective,
Cournot developed a mathematical model for duopolies and Walras developed a mathematical model of
general competitive equilibrium.
Later, Vilfredo Pareto analyzed issues in microeconomics by assuming that economic actors attempt to
change a given allotment of goods to another more preferred allotment of goods. His work resulted in the
concept of a Pareto efficient allocation: an allocation in which no exchanges occur that make at least
one individual better off without making any other individual worse off. Later, John von Neumann showed
that every equilibria in Walras’ model is Pareto efficient.
Towards the middle part of the 20th century, economists came to see the usefulness of other mathematical
areas like convex analysis, graph theory, and functional analysis. A Soviet economist named Wassily
Leontief built a famous model of economic inputs and outputs from data taken by central economic planners
in the former U.S.S.R. Linear programming became a powerful tool in microeconomics, even though its
initial applications were related to the shipment of men, weapons, and other materials during the Second
World War. Shortly after the end of the war, John Nash developed the notion of a Nash equilibrium
in a 28-page dissertation on non-cooperative games he wrote at Princeton. This particular mathematical
achievement was (somewhat ridiculously) depicted in the movie A Beautiful Mind.
Later, the calculus of variations and optimal control theory were applied to economic problems to permit
models to have dynamic solutions (typically through time) rather than static solutions. Paul Samuelson
generalized the concept of individual utility-maximizing economic actors with aggregate groups of actors
by developing the field of comparative statics. His son, Paul Samuelson, Jr., would later prove that in
a properly constituted stochastic model, prices fluctuate randomly around a general equilibrium.
Today, the field of economics is utterly dominated by mathematical and statistical methodologies. It
is increasingly difficult to find an academic paper in a reputable economic journal that does not use
mathematics or econometrics in a meaningful fashion. Nonetheless, the “mathematization” of economics
has been criticized by many economists. Friedrich Hayek, a notable member of the anti-mathematical (and
really, anti-data) “Austrian” school of economic thought, argued that mathematical formalism could never
properly account for informational limitations faced by real-world economic actors. Karl Popper despised
the invasion of economics by mathematics, arguing that axioms, theorems, and proofs do not really subject
themselves to empirical refutation—turning the entire field of economics into a wobbling tautology. J.M.
Keynes himself said that many concepts in mathematical economics are “merely concoctions which are
as imprecise as the initial assumptions upon which they rest...[mathematical economics is] a maze of
pretentious and unhelpful symbols.”
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This syllabus was submitted to the Office of Academic Affairs by the course instructor. Uploaded by Archives RSA Josephine Hill.