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2014 | Book

Household Expenditure Read chapter Read first chapter

Principles of Mathematical Economics

Author: Shapoor Vali

Publisher: Atlantis Press

Book Series : Mathematics Textbooks for Science and Engineering

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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About this book

Under the assumption of a basic knowledge of algebra and analysis, micro and macro economics, this self-contained and self-sufficient textbook is targeted towards upper undergraduate audiences in economics and related fields such as business, management and the applied social sciences. The basic economics core ideas and theories are exposed and developed, together with the corresponding mathematical formulations. From the basics, progress is rapidly made to sophisticated nonlinear, economic modelling and real-world problem solving. Extensive exercises are included, and the textbook is particularly well-suited for computer-assisted learning.

Table of Contents

Frontmatter
Chapter 1. Household Expenditure
Abstract
A household allocates its income to variety of goods and services. A collection of goods and services that a household purchases and consumes over a specific time period or horizon (a week, a month, or a year) is called a consumption bundle (bundle for short), or a basket.
Shapoor Vali
Chapter 2. Variables, a Short Taxonomy
Abstract
A phenomenon that changes over time, space, objects, or living things is called a variable. If a variable’s changes could be measured, that is, expressed by numbers or quantities, then we have a quantitative variable; otherwise, we have a qualitative variable. Blood pressure is an example of a quantitative variable—because it takes different values from individual (living thing) to individual. It can be measured, and has its own scale of measurement.
Shapoor Vali
Chapter 3. Sets and Functions
Abstract
A set is a collection of distinct objects with a precise description or mechanism for determining whether a given object belongs to the collection. If an object belongs to the collection it is called an element or a member of the set.
Shapoor Vali
Chapter 4. Market Equilibrium Model
Abstract
A household’s demand for a good or service expresses the quantities of that good or service that the household is willing and able to purchase as a function of a number of variables.
Shapoor Vali
Chapter 5. Rates of Change and the Derivative
Abstract
A function of the form is called a linear function because the graph of the function is a straight line.
Shapoor Vali
Chapter 6. Optimal Level of Output and Long Run Price
Abstract
The cost structure of a firm is reflected in its costs functions: total cost TC; average cost AC; and marginal cost MC. Total cost, the sum of total variable and total fixed costs, is generally expressed as a function of the level of output Q. While a firm’s production function is often a bivariate or multivariate function relating its output to various inputs, the cost functions are usually univariate functions relating different costs to only one variable, output. It is therefore much easier to specify and estimate various cost functions for a firm than specify and estimate its production function.
Shapoor Vali
Chapter 7. Nonlinear Models
Abstract
There is a host of economic models—related to firms, markets, sectors, and the whole economy—that are extensively, but only graphically, presented in various levels of micro-macro-economics studies and mathematical economics.
Shapoor Vali
Chapter 8. Additional Topics in Perfect and Imperfect Competition
Abstract
A major step in completing a market model is deriving the supply function of a typical firm and the whole market supply function.
Shapoor Vali
Chapter 9. Logarithmic and Exponential Functions
Abstract
The entire algebra of logarithm is based on the following definition: The logarithm of a number a to the base b is a number c such that a can be expressed as b to the power c.
Shapoor Vali
Chapter 10. Production Function, Least-Cost Combination of Resources, and Profit Maximizing Level of Output
Abstract
The fundamental concept related to the supply side of an economy is the production function. A production function relates the maximum quantity of output that can be produced from given quantities of inputs.
Shapoor Vali
Chapter 11. Economic Dynamics
Abstract
Most macro- and micro-economic variables are time series variables. We can track changes of time series variables over time in two ways, continuously or discretely. In continuous case values of a variable are measured at every moment of time.
Shapoor Vali
Chapter 12. Mathematics of Interest Rates and Finance
Abstract
A sequence is an ordered set of numbers. Consider the sequence of real numbers expressed as
Shapoor Vali
Chapter 13. Matrices and Their Applications
Abstract
A matrix is a rectangular array of numbers. These numbers are arranged in rows and columns enclosed by parentheses, square brackets, single vertical lines, or double vertical lines (I will use the square brackets).
Shapoor Vali
Backmatter
Metadata
Title
Principles of Mathematical Economics
Author
Shapoor Vali
Copyright Year
2014
Publisher
Atlantis Press
Electronic ISBN
978-94-6239-036-2
Print ISBN
978-94-6239-035-5
DOI
https://doi.org/10.2991/978-94-6239-036-2