Economic models as an application of Linear Algebra
In this blog we will discuss about what is Economic model it’s applications in Linear Algebra and also discuss it’s applications in Eigenvalues and Eigenvectors and talk about what makes good in economic model and How to construct this model and also discuss about why Economic models Fail
What is Economic Model?
Economic model a hypothetical construct that embodies economic procedures using a set of variables in logical and quantitative correlations.
Economic models are simplified representations of Economic Phenomena.
They allow the design of Economic policies.
They allow the diagnosis of Economic Phenomena and the forecast of future behavior of variables.
Economic model as an application of Linear Algebra :
Linear Regression:
Linear regression is a statistical method used to study the relationship between two or more variables. It is commonly used to predict a numerical value (dependent variable) based on one or more other variables (independent variables). The goal of linear regression is to find the equation of a straight line that best fits the data points, in such a way that the sum of the squared errors (the difference between the predicted value and the actual value) is minimized.
Linear regression has many applications in various fields, including finance, economics, biology, engineering, and social sciences. For example, it can be used to predict stock prices based on historical data, to analyze the effect of advertising on sales, or to study the relationship between a person's age, weight, and blood pressure.
Linear algebra plays an important role in linear regression, as it provides the mathematical framework for solving the equations involved. The basic idea is to represent the data as a matrix, where each row corresponds to a data point, and each column corresponds to a variable. The equation of the straight line can then be expressed as a linear combination of the variables, where the coefficients are the unknown parameters to be estimated. By using linear algebra techniques such as matrix multiplication and inversion, it is possible to solve for these parameters and obtain the best fit line. Additionally, linear algebra can be used to perform various operations on the data, such as scaling, rotation, and projection, which can help to improve the accuracy of the model.
Input-output models:
Game Theory:
Economists use 'Game Theory' as a tool to analyze economic competition, economic phenomena such as bargaining, mechanism design, auctions, voting theory; experimental economics, political economy, behavioral economics etc. Game theory is applied for determining different strategies in the business world.
Linear programming:
Programming is the process of creating software or applications using programming languages. It involves writing instructions in a language that a computer can understand, so that it can perform specific tasks or solve problems.
Linear algebra is a branch of mathematics that deals with linear equations, matrices, vectors, and their properties. Programming is frequently used in linear algebra to perform numerical computations, data analysis, and machine learning tasks.
Some common programming languages used in linear algebra include Python, MATLAB, and R. These languages have powerful libraries and modules for linear algebra computations, such as NumPy and SciPy in Python, and the linear algebra toolbox in MATLAB.
Programs can be written to perform a wide range of linear algebra tasks, including matrix multiplication, matrix inversion, eigenvalue and eigenvector calculations, singular value decomposition, and linear regression. These tasks are essential in many scientific and engineering fields, including physics, chemistry, computer science, and machine learning.
Economic model as an application of Eigenvalues and Eigenvectors :
- Input-output models
- Factor analysis
- Portfolio Analysis
- Game Theory
- Social Network Analysis
What makes a good Economic Model?
The seven key properties of useful economic models:
Parsimony, tractability, conceptual insightfulness, generalizability, falsifiability, empirical consistency, and predictive precision. of these properties, although almost no economic models have them all.
How to Build an Economic Model?
Consider an architect who is looking to build a major office building somewhere in a city. To get the right plan and follow to the latter, they may consider building a physical model that sits on top of the table to show how the entire block will appear at the end of the project. This model is drawn to scale and can be opened up to show both the interior and the exterior. Apart from this, companies often build models of their new products, which are generally rougher and less finished to demonstrate how the new product will look like and work once out on the market. These models are important because they help people visualize what a product or a building will look like once complete. It works better in finding the right aspects of the projects than it would without them.
This is the same way economic models work. They let economists and policymakers get a complete view or picture of economic phenomena. Models show how different factors fit together, affecting the entire system. As you may have already learned in the previous courses, consumers and manufacturers are the main players in an economy. Firms produce goods, which households acquire by paying set amounts of money for them. One the other hand, households define the labor market, which they sell to firms to gain wages, salaries, and benefits. These mutual relationships must happen for economic growth, development, and stability.
Why Model’s Fail?
Conclusion:
Economic models are often expressed as systems of equations that relate different economic variables, such as prices, quantities, and production levels. Linear algebra provides a powerful tool for solving these systems of equations, which can help economists understand how different economic factors are related and predict how changes in one variable will affect others.
Linear algebra is particularly useful for solving large systems of equations, which can be difficult or impossible to solve by hand. By using matrix algebra and other techniques from linear algebra, economists can quickly and efficiently analyze complex economic models.
In addition to solving systems of equations, linear algebra can also be used to perform other types of economic analysis, such as optimization, regression analysis, and factor analysis. These techniques can help economists identify important economic trends, forecast future economic outcomes, and develop more accurate economic models.
Overall, linear algebra is an essential tool for economists, enabling them to model and analyze complex economic systems with speed and accuracy. By using linear algebra techniques to analyze economic data, economists can gain new insights into how the economy works, helping to inform policy decisions and drive economic growth.
