1. Basic Concepts and their economic applications
Ingredients of a Mathematical model: Variables, Constants, Parameters, Equations and Identities.
Linear Equations, Straight Lines, Determining the equation of a straight line
Economic Applications: Demand, Supply, Cost, Revenue, Cost Constraints, Budget Constraints, Changes in prices and income.
Solving Simultaneous Linear Equation system of 2 equations with 2 variables and 3 equations with 3 variables.
Equilibrium and break-even analysis: taxes, subsidies and their distribution, The National Income Model and IS-LM model.
Linear inequalities: Definition, Properties and their solution.
2. Functions and Relations
The Concepts of Sets: Set Notation, Relationship between sets, Operations on sets.
Relations and Functions: Ordered Pairs, Relations and Functions.
Types of Functions: Constant function, Polynomial functions, Rational functions, Non-algebraic functions.
3. Differentiation Techniques and their applications
Limits and Continuity of a function; Limit theorems.
Derivatives; Rate of change and the derivative; Difference quotient
Average and instantaneous rate of change, the slope of a secant line and a tangent line.
Differentiability of a function; Rules of differentiation, Higher order derivatives, Derivative of exponential and logarithmic functions
Partial differentiation, the second order derivatives, higher-order derivatives
Economic Applications: Marginal analysis in business and economics.
4. Optimization: Techniques
Increasing and Decreasing Functions, Concavity and Convexity, Relative Extrema, Inflection Point
Optimization of Functions, Successive Derivative Test for Optimization.
5. Optimization: Applications
Marginal, Average and Total Concepts.
Optimization of economic functions including Revenue, Cost, Utility and Profit functions.
The Marginal Rate of Technical Substitution
Relationship Between Functions and Graphs
The main objective of the course is to introduce the students to the most fundamental and basic aspects of mathematical methods that have become indispensable for the proper understanding of the current economic literature.
These basic concepts include ingredients of mathematical model, introduction, solution and applications of linear equations, linear inequalities, set theory and functions and relation.
Emphasis is on the differentiation techniques and their applications in understanding marginal analysis in business and economics and optimization problems.
The aim is to give students the knowledge of mathematical tools they need to understand underlying economic theories. Therefore, this course is designed to provide strong mathematical foundations.
Course Learning Outcomes
By the end of the course, successful students will be in a position to understand all the basic tools of mathematical methods that have become indispensable for the proper understanding of the current economic literature.
Students will be comfortable in understanding and solving problems related to marginal analysis in economics.
Optimization techniques will enable students to solve the problems related to the optimization of economic functions including cost, revenue and profit functions.
The course will focus on presenting common micro, and macro topics in a more rigorous mathematical way than standard core economics courses.
Limits and Continuity
Derivative as a Concept
Derivative as a Rate of Change
Differentiability of a function
Slope of a Secant Line and a Tangent Line
Rules of Differentiation
Higher Order Derivatives
Derivatives of Exponential Functions
Derivative of Logarithmic Functions
Partial Derivatives - Multivariable Calculus
Marginal Revenue, Average Cost, Profit, Price & Demand Function
Optimization: profit | Applications of derivatives
Optimization: cost of materials | Applications of derivatives
Optimization Techniques - Concavity, Inflection Points, Increasing Decreasing, First & Second Derivative
Book Title : Introduction to mathematical economics
Author : Edward T. Dowling
Edition : 3rd
Publisher : McGraw Hill