Linear Algebra Applied to Economics

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Linear Algebra Applied to Economics
Input-Output Analysis

Introduction:
There are several non-mathematical subjects that linear algebra can be applicable too. Economics is a topic that linear algebra can be used to make a formal application, for example in Input-Output Analysis, econometrics, Game theory, and break-even point analysis. As a group we are going to be focusing on the Input-Output analysis, a type of analysis created for the purpose of describing and making predictions of complicated mathematical models using systems of linear equations. It was established by “W. Leontief, who won the 1973 Nobel Prize in Economics” (Hefferon, p.60). In this paper, mathematical and linear algebra formulas, calculations, graphs, diagrams, pictures, etc., will be clearly shown as to further understand the applicability of linear algebra in economics. Calculations and mathematical examples used in economics will be provided in the context of this paper for better understanding. Also, terms and notations used will be explained, derivation and origin of mathematical results will be shown.

Definitions:

Economics is a branch of knowledge concerned with the production, distributions, and consumption of goods and services.

Linear algebra is a branch of mathematics with the properties of finite dimensional vector spaces and linear mapping between the spaces. The equations are represented using matrices and vectors and consist of several unknowns.

Econometrics is branch of economics that aims to give the definitions of application of mathematics and statistical methods to economic data.

Game theory is a method of studying strategic decision-making, that is, the study of mathematical models of conflict and cooperation between decision makers (Levine).

Input-output Analysis Application:

The economy is a complicated network of sectors that interact with each…...

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