Structure of Economics

Economics

Structure of the Science

Science

The invention of deliberately oversimplified theories is one of the major techniques of science, particularly of the “exact” sciences which make extensive use of mathematical analysis.

John Williams The Compleat Strategyst

Underlying Mathematics• Geometry• Algebra• Analytic Geometry• Linear Algebra• Linear vs. Logarithmic• Calculus• Game Theory• Statistics• Computer algorythms

The justification of all mathematical models

is that, oversimplified, unrealistic, and even false as the may be in some respect, they force analysts to confront possibilities that would not have occurred to them otherwise. The history of physics and medicine abounds with wrong or incomplete theories that throw just enough light to allow some other big breakthroughs. The atom bomb, for example, was built before physicists understood the structure of particles.

The Ideal Model

• The effort to put Economics on a rigorous mathematical footing like Newton’s mathematization, using his invention of the calculus, of physics.

GeometryGeometry (Ancient Greek:

γεωμετρία; geo- "earth", -metria "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. Geometry is one of the oldest mathematical sciences. Initially a body of practical knowledge concerning lengths, areas, and volumes, in the 3rd century BC geometry was put into an axiomatic form by Euclid, whose treatment—Euclidean geometry—set a standard for many centuries to follow

Algebra

• Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them.

Algebra• While the word algebra comes

from the Arabic language (al-jabr, literally, restoration) and الجبرmuch of its methods from Arabic/Islamic mathematics, its roots can be traced to earlier traditions, which had a direct influence on Muhammad ibn Mūsā al-Khwārizmī (c. 780–850). He later wrote The Compendious Book on Calculation by Completion and Balancing, which established algebra as a mathematical discipline that is independent of geometry and arithmetic.

Analytic Geometry

In classical mathematics, analytic geometry, also known as coordinate geometry, or Cartesian geometry, is the study of geometry using a coordinate system and the principles of algebra and analysis

Analytic Geometry

Calculus

• Calculus is the study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations.

Calculus

Game Theory

• Game theory is a mathematical method for analyzing calculated circumstances (games) where a person’s success is based upon the choices of others.

• 1944 book Theory of Games and Economic Behavior, with Oskar Morgenstern

Game Theory/Nash Equilibrium

• Stated simply, Amy and Phil are in Nash equilibrium if Amy is making the best decision she can, taking into account Phil's decision, and Phil is making the best decision he can, taking into account Amy's decision.

RAND Corporation

• R and D• Original Think Tank to

come out of WW II• Adopted and advanced

Game Theory and applied it to military, political and economic problems

Econometrics

• Data Collection• Analysis• Statistical techniques• Regression Analysis

– Demand Curves– Supply Functions– Elasticity

• Models

Computers and Super Number Crunching

• Modeling• Big Data• Forecasting• Analysis• Flash Trading

Managerial Economics

• Mathematics are tools that provide a structure for analysis.

• Economics is the science of making decisions in the presence of scarce resources.

• Managerial Economics is the study of how to direct scarce resources in the way that most efficiently achieves a managerial goal.

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