Premium Essay

Linear Algebra Applied to Economics

In:

Submitted By dm482
Words 1271
Pages 6
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

Similar Documents

Free Essay

Asdw

...Basic algebra: Linear and quadratic equations, Solving linear and quadratic equations, Application of equations: profit, pricing, savings, revenue, sales tax, investment, bond redemption, linear inequalities, applications of inequalities: profit, renting verses purchasing, leasing versus purchasing, revenue, current ratio, investment, Maple session on solving linear, quadratic and higher degree equations, solving inequalities II. Functions and Graphs: Introduction to functions, domain and range of a function, Applications: demand, supply and profit functions, demand and supply schedule, value of business, depreciation, Special functions: polynomial, rational, piecewise defined functions, Absolute value function, and evaluation of such functions. Combination of functions. Applications: cost, investment, sales, profit, business, Graphs of functions: linear, quadratic, piecewise defined functions, graphing of quadratic functions by finding vertex, Applications on graphs: inventory, debt payment, pricing, revenue and profit, demand and supply curves, Maple session on functions and graphs III. Lines and Systems: Equation of a straight line, slope and intercept of a line, parallel and perpendicular lines, Applications: price-quantity relationship, production levels, cost, revenue, demand and supply equations, isocost line, isoprofit line, depreciation, appreciation, systems of linear equations, solution of system of linear equations, nonlinear systems: one linear one...

Words: 846 - Pages: 4

Free Essay

Dr Manger

...Organizational Theory, Design, and Change Jones 6th Edition Test Bank Click here to download the solutions manual / test bank INSTANTLY!!! http://solutionsmanualtestbanks.blogspot.com/2011/10/organizational-theory-d esign-and-change_18.html ----------------------------------------------------------------------Organizational Organizational Organizational Organizational Theory, Theory, Theory, Theory, Design, Design, Design, Design, and and and and Change Change Change Change Jones Jones Jones Jones 6th 6th 6th 6th Edition Edition Edition Edition Test Test Test Test Bank Bank Bank Bank -------------------------------------------------------------------------***THIS IS NOT THE ACTUAL BOOK. YOU ARE BUYING the Test Bank in e-version of the following book*** Name: Organizational Theory, Design, and Change Author: Jones Edition: 6th ISBN-10: 0136087310 Type: Test Bank - The test bank is what most professors use an a reference when making exams for their students, which means there’s a very high chance that you will see a very similar, if not exact the exact, question in the test! - The file is either in .doc, .pdf, excel, or zipped in the package and can easily be read on PCs and Macs. - Delivery is INSTANT. You can download the files IMMEDIATELY once payment is done. If you have any questions, please feel free to contact us. Our response is the fastest. All questions will always be answered in 6 hours. This is the quality of service we are providing and we hope to be your...

Words: 29834 - Pages: 120

Free Essay

Accounting

...Click here to download the solutions manual / test bank INSTANTLY!! http://testbanksolutionsmanual.blogspot.com/2011/02/accounting-information-systems-romney.html ------------------------------------------------------------------------------------------------------------------------ Accounting Information Systems Romney 11th Edition Solutions Manual Accounting Information Systems Romney 11th Edition Solutions Manual Accounting Information Systems Romney 11th Edition Solutions Manual Accounting Information Systems Romney Steinbart 11th Edition Solutions Manual Accounting Information Systems Romney Steinbart 11th Edition Solutions Manual ------------------------------------------------------------------------------------------------------------------------ ***THIS IS NOT THE ACTUAL BOOK. YOU ARE BUYING the Solution Manual in e-version of the following book*** Name: Accounting Information Systems Author: Romney Steinbart Edition: 11th ISBN-10: 0136015182 Type: Solutions Manual - The file contains solutions and questions to all chapters and all questions. All the files are carefully checked and accuracy is ensured. - The file is either in .doc, .pdf, excel, or zipped in the package and can easily be read on PCs and Macs.  - Delivery is INSTANT. You can download the files IMMEDIATELY once payment is done. If you have any questions, please feel free to contact us. Our response is the fastest. All questions will always be answered in 6...

Words: 18533 - Pages: 75

Free Essay

Calculus Mathematics

...[show]Differential calculus [show]Integral calculus [show]Vector calculus [show]Multivariable calculus Calculus (Latin, calculus, a small stone used for counting) is a branch of mathematics focused on limits,functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modernmathematics education. It has two major branches,differential calculus and integral calculus, which are related by the fundamental theorem of calculus. Calculus is the study of change,[1] in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has widespread applications in science,economics, and engineering and can solve many problems for which algebra alone is insufficient. Historically, calculus was called "the calculus of infinitesimals", or "infinitesimal calculus". More generally, calculus (plural calculi) refers to any method or system of calculation guided by the symbolic manipulation of expressions. Some examples of other well-known calculi are propositional calculus, variational calculus, lambda calculus, pi calculus, andjoin calculus. Contents [hide] • 1 History o 1.1 Ancient o 1.2 Modern o 1.3 Significance o 1.4 Foundations • 2 Principles o 2.1 Limits and infinitesimals o 2.2 Differential...

Words: 5650 - Pages: 23

Premium Essay

Keanu Reeves: Video Analysis

...because these numbers could represent the color intensity at a certain point. They could represent whether an object is there at a certain point. And as we develop an algebra around matrices, and when we talk about developing an algebra around matrices, we're going to talk about operations that we're going to perform on matrices that we would normally perform with numbers. So we're going to essentially define how to multiply matrices, how to add matrices. We'll learn about taking an inverse of a matrix. And by coming up with an algebra of how we manipulate these things, it'll become very useful in the future when you're trying to write a computer graphics program or you're trying to do an economic simulation or a probability simulation, to say, oh, I have this matrix that represents where different particles are in space. Or I have this matrix that represents the state of some type of a game. And I know the algebra of matrices. And I know ways of doing it very efficiently so that I can multiply a bunch of them. Or I could come run a simulation, and I can actually come up with useful results. So that's all matrices are. But as you'll see through this, we can define operations on them. And then later on, when you take a linear algebra course in college, you'll learn a lot more of the depth of how they can be applied and what you can use them to represent. ...

Words: 797 - Pages: 4

Free Essay

Subjects Information

...Academic assistance is the defined as an activity for teaching available for students in all subjects including science, mathematics, management, business studies, business and law and information technology. In the academic assistance, all subject related helps is being provided to the students to meet specific subject related queries. It is defined as a tutoring practice, which provides support to the students in solving particular subject related queries. Apart from this, this makes the learning process easy for the students through providing ready to learn or tailor made notes and helps in solving specific subject problems. Basically, academic assistance is the new method of tutoring by a large number of institutions to facilitate the students in their studies. Academic assistance encompasses all types of subjects from English to Management. In the academic content development, a number of subjects such as business studies, marketing, accounting and financial management, operations management, qualitative techniques, history, science, statistics, dissertation and its proposal development, human resources and organizational behaviour are covered. In pertinent to the given subjects, academic assistance is a kind of help provided to the students in developing particular topic related subjects content. Academic assistance is not only limited to provide a notes specific to subjects, but also it covers a full helps in completing the project steps such as authentic data collection...

Words: 5329 - Pages: 22

Premium Essay

Micrpeconomics

...The main goals of the course are to develop technical skills allowing the analysis of real life problems, to provide the tools necessary to formulate, analyse and implement a simple quantitative model to support a business decision, and to understand articles and books on business analysis Starting with preliminaries to calculus, and limits, we follow with derivatives and its applications to real life problems, and integration. This course covers also functions with more than one variable, differential equations, and optimization. Basic requirement. Students must have a good background on algebra and arithmetic, as well as a good understanding of mathematical functions and their applications to practical problems. Course Objectives * To builds skills and proficiency in methods of calculus * To understand concepts, formulas and techniques of calculus through exercises and applied examples * To be able to translate real-world problems to mathematical language and models * To acquire ease in identifying the different kind of problem and the appropriated rule to solve it * To interpret results of calculus * To apply analytical methods of calculus that are relevant to managerial and business sciences. Course Outcomes * To work with functions represented in a variety of ways, including graphical, numerical, analytical, or verbal * To understand the meaning of limit graphically and numerically and be able to compute limits involving infinite ...

Words: 1257 - Pages: 6

Free Essay

A4 Paper

...interaction with each one of you during the term. This will however depend on your active participation and attention during the class sessions and an active follow up afterwards. Course Description: The course will stress mainly on developing basics concepts of mathematics. It will include basic mathematical operations, factorization, solving first and second-degree equations, solving first and second-degree inequalities, analytical geometry (graph, linear equation – slope-intercept form), solving simultaneous equations, mathematical functions (concept of domain and range), quadratic functions, mathematics of finance and matrices. All topics will be discussed along with their applications. Some features of Microsoft Excel on graph and matrices are also included in the course. Course Objective: This is the first course in mathematics and the main objective of this course is to improve the level of quantitative abilities possessed by students and prepare them for the applications of mathematics in the courses like finance, economics, operations research, etc. Teaching Methodology & Requirements: Please arrive and leave on time. Class will begin promptly five minutes after the hour and will end exactly on the hour. Late arrivals and early departures disrupt class and ruin the presentations of others. They are unprofessional. Do your own work. Plagiarism and cheating will lead to dismissal. Do not copy the work of others. Do not use others to do your work. Do not pass...

Words: 876 - Pages: 4

Free Essay

Fdfglkd

...Studies N-7 HUM-Huma Ijaz N-1 Math-Imran Zulfiqar Chem-Amjad Riaz Cheema Chemical Process Principles I N-11 Calculus I 2 Chemical Process Principles I 2 English Comprehension and Composition 2 Islamic Studies 2 Lab-Engineering Drawing 2 Lab-Physics for Chemical Engineers 2 Physics for Chemical Engineers 2 Tuesday Monday English Comprehension and Composition Calculus I N-7 N-12 Chem-Amjad Riaz N-11 Wednesday Phy-Dr. Saif Ur Rehman Physics for Chemical Chemical Process Engineers Principles I N-18 HUM-Dr. Musferah Mehfooz N-19 Math-Imran Zulfiqar Cheema Dr. Saif Ur Rehman / Dr. Ishrat Sultana Thursday Islamic Studies Calculus I Lab-Physics for Chemical Engineers N-15 N-3 Applied Physics Lab Chem-Muhammad Imran Rafiq Friday Lab-Engineering Drawing PC Lab-C Lessons/week 14 Timetable generated:11/13/2014 aSc Timetables Final Time Table - Fall 2014 ( v 20141113-1130 ) CIIT_Lahore FA14-BEC-B (Semester 1) (DDP) 2 10:00 - 11:30 Math-Syed Tahir Raza Rizvi 1 8:30 - 10:00 HUM-Huma Ijaz 3 11:30 - 1:00 4 1:30 - 3:00 5 3:00 - 4:30 6 4:30 - 6:00 7 6:00 - 7:30 Subjects Count English Comprehension and Composition Calculus I N-10 Phy-Dr. Ayesha Anjum N-4 HUM-Huma Ijaz Calculus I 2 Chemical Process Principles I 2 English Comprehension and Composition 2 Islamic Studies 2 Lab-Engineering Drawing 2 Lab-Physics for Chemical Engineers 2 Physics for...

Words: 31997 - Pages: 128

Premium Essay

Applied Mathematics for Business

...Applied mathematics for business, economics, life sciences, and social sciences, 1997, 1175 pages, Raymond A. Barnett, Michael R. Ziegler, Karl Byleen, 0135745756, 9780135745755, Prentice Hall, 1997 Published: 14th July 2010 DOWNLOAD http://bit.ly/1RspljW Applied mathematics for business, economics, life sciences, and social sciences This book prepares readers to understand finite mathematics and calculus used in a wide range of disciplines. Covering relevant topics from finance, linear algebra, programming, and probability, the Seventh Edition places emphasis on computational skills, ideas, and problem solving. Other highlights include a rich variety of applications and integration of graphing calculators. Provides optional regression analysis, containing optional examples and exercises illustrating the use of regression techniques to analyze real data. Both graphing calculator and spreadsheet output are included. Offers more optional technology examples and exercises using actual data. Implements use of graphing calculators in optional examples, exercises in technology, illustrations of applications of spreadsheets and sample computer output. DOWNLOAD http://bit.ly/1qC8Dk0 http://www.jstor.org/stable/2483933 Solutions manual to accompany Raymond A. Barnett and Michael R. Ziegler's finite mathematics for business, economics, life sciences, and social sciences , R. Michael Ziegler, Raymond A. Barnett, 1990, Science, 476 pages. . Precalculus functions and graphs...

Words: 3090 - Pages: 13

Free Essay

Jon Von Nomann

...December 28, 1903 Budapest, Austria-Hungary | Died | February 8, 1957 (aged 53) Walter Reed General Hospital Washington, D.C. | Residence | United States | Nationality | Hungarian and American | Fields | Mathematics, physics, statistics, economics | Institutions | University of Berlin Princeton University Institute for Advanced Study Site Y, Los Alamos | Alma mater | University of Pázmány Péter ETH Zürich | Doctoral advisor | Lipót Fejér | Other academic advisors | László Rátz | Doctoral students | Donald B. Gillies Israel Halperin | Other notable students | Paul Halmos Clifford Hugh Dowker Benoit Mandelbrot[1] | Known for |  [show] | Notable awards | Bôcher Memorial Prize (1938) Enrico Fermi Award (1956) | Signature | John von Neumann (/vɒn ˈnɔɪmən/; December 28, 1903 – February 8, 1957) was a Hungarian and American pure and applied mathematician, physicist, inventor and polymath. He made major contributions to a number of fields,[2] including mathematics (foundations of mathematics, functional analysis, ergodic theory, geometry, topology, and numerical analysis), physics (quantum mechanics, hydrodynamics, and fluid dynamics), economics (game theory), computing (Von Neumann architecture, linear programming, self-replicating machines, stochastic computing), and statistics.[3] He was a pioneer of the application of operator theory to quantum mechanics, in the development of functional analysis, a principal member of the Manhattan Project and...

Words: 9454 - Pages: 38

Premium Essay

Linear Programming and Simplex Method

...LINEAR PROGRAMING AND SIMPLEX METHOD Devharajan Rangarajan Department of Electronic Engineering National University of Ireland, Maynooth devharajan.rangarajan.2016@mumail.ie Abstract— An optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. This pays way to a new world of constrained optimization. This paper focuses on one such optimization technique known as Linear programming and one of its method known as Simplex method in detail with examples. cTx = c1x1 + · · · + cnxn The subject of linear programming can be defined quite concisely. It is concerned with the problem of maximizing or minimizing a linear function whose variables are required to satisfy a system of linear constraints, a constraint being a linear equation or inequality. The subject might more appropriately be called linear optimization. Problems of this sort come up in a natural and quite elementary way in many contexts but especially in problems of economic planning. (or Ax ≤ b) I. INTRODUCTION Linear programming is the process of taking various linear inequalities relating to some situation, and finding the "best" value obtainable under those conditions. A typical example would be taking the limitations of materials and labour, and then determining the "best" production levels for maximal profits under those conditions. In "real life", linear...

Words: 1927 - Pages: 8

Premium Essay

Lf Cv

...Fang Li Donghuwan 14-1-801, Wangjing West Rd, Chaoyang Dist., Beijing 100102, China Cell: (86)-18601018786, Email: lifang9304@163.com EDUCATION Central University of Finance and Economics Beijing, China Major: B.Sc. in Applied Accounting 09/2011-06/2015  Cumulative GPA: 3.64/4.0, Rank 2/40  Coursework: Math: Advanced Mathematics I & II, Linear Algebra, Statistics, Probability & Statistics Accounting: Intro to Accounting, Accounting Principles, Analysis for Financial Accounting, Intermediate Financial Accounting, Cost Accounting, Accounting of Financial Enterprises, Accounting Information System, Tax Law, Auditing, Management Accounting, Financial Accounting, Financial Analysis Eco. & MGMT: Principles of Management, Information Management and Database Technology, Microeconomics, Macroeconomics, Management Information System, Management of Intangible Assets PROFESSIONAL EXPERIECNE Beijing Xinhong Certified Public Accountants Co. Ltd. Beijing, China Accountant Assistant 07/2014-09/2014  Acquired practical knowledge of mergers and acquisitions (M&A), private equity, and merchant banking  Utilized financial accounting software to prepare various kinds of journal entries and status reports to analyze company’s current financial condition.  Utilized the internet, online databases, industry association company lists, and company’s own proprietary database to identify and profile target companies, private equity group, and corporates. Beijing Yingzhibao...

Words: 434 - Pages: 2

Premium Essay

Gate

...ate Aptitude Test in Engineering GATE 2014 Brochure Table of Contents 1. Introduction .............................................................................................................1 2. About GATE 2014 ......................................................................................................1 2.1. Financial Assistance ............................................................................................................................ 1 2.2 Employment ............................................................................................................................................ 2 2.3 Administration ....................................................................................................................................... 2 3.1 Changes Introduced in GATE 2013 that will continue to remain in force for GATE 2014 .......................................................................................................................................................... 3 4.1 Eligibility for GATE 2014 ................................................................................................................... 4 4.2 GATE Papers ............................................................................................................................................ 5 4.3 Zone-Wise List of Cities in which GATE 2014 will be Held ................................................... 6 4.4 Zone-Wise List of Cities for 3rd...

Words: 32784 - Pages: 132

Premium Essay

Personal Statement

...long way to go. I plan to further improve my programming ability, especially the options and programming techniques I didn’t know before, like the combination of C++ and R will make the loop in R run faster. With the huge amounts of data collected in the worldwide everywhere in every second, the marriage of theories, the effective methodology of numerical analysis and computer science becomes more urgent and important than ever. I believe a good statistician need also be a good programmer. So a university that emphasize statistical methodology and statistical programming is perfect fit my goal. And I found the Master of Science with a Major in Applied Statistics in MSU is the one. I have built up a sufficient foundation in statistics knowledge during my undergrad study. The courses Calculus I&II, Probability, Linear Algebra,...

Words: 557 - Pages: 3