Quantitative Methods for Business and Economics

Adil H. Mouhammed

• Verlag: Routledge
• Jahr: 2015
• ISBN:
  9781317461531
• Auflage: 1
• Thema: Business
• Thema: Business General

This book provides a brief yet rigorous introduction to various quantitative methods used in economic decision-making. It has no prerequisites other than high school algebra. The book begins with matrix algebra and calculus, which are then used in the book's core modes. Once the reader grasps matrix theory and calculus, the quantitative models can be understood easily, and for each model there are many solved examples related to business and economic applications.

CHAPTER ONE

Vectors and Matrices

Vectors and matrices are very important tools in economic analysis. This chapter outlines the algebra of vectors. Students will not only be able to add and subtract vectors but also to multiply vectors. For economic modeling, linear independence is indispensable in that economic models must have unique solutions, and linear independence provides these solutions. Similarly, linear and convex combinations are also important for economics.

An extension of vector analysis is matrix algebra. The types of matrices and matrix operations are outlined in this chapter. A system of equations is solved by using matrix methods such as the inverse method, Cramer’s rule and the Gauss-Jordan method. Eigenvalues and vectors are explained and used for diagonalizing matrices. Finally, various economic applications of matrices are provided.

Vectors

A vector is a symbol used to refer to a set of variables or coefficients. For example,

Y = (y₁, y₂, y₃, ..., y_n),

where Y is used to represent n-variables. Vector A can be represented by

A = (a₁, a₂, a₃,..., a_n),

where A contains a set of coefficients denoted by a’s. Also, vector Y can also be a set of real integer numbers such as Y = (3, 4, 6, 8).

Vector Y has a dimension as well. The dimension of a vector is the total number of elements (components) in that vector. For example, the above vector, Y, has four components and hence it is said to be of dimension four. Very compactly, a vector such as Y, where Y = (5, 6, 7), has one row and three columns. Accordingly, it is said to be a vector of dimension 1 by 3 or Y_{1 × 3} or Y_{1 3}, where 1 and 3 indicate number of rows and columns, respectively. In general, Y_{m x n} is said to be a vector of dimension m x n: with m rows and n columns.

Example:

All these vectors have different dimensions: A is 1 × 2, B is 1 × 3, and A is 3 × 1. Vectors A and B are called row vectors, whereas vector C is a column vector.

The Transpose of a Vector

The transpo...