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Course Syllabus

Bachelor 2020/2021

Mathematics for Economics and Business

Type: Compulsory course (HSE University and Kyung Hee University Double Degree Programme in Economics and Politics in Asia)
Area of studies: Foreign Regional Studies
Delivered by: Faculty of World Economy and International Affairs
Where: Faculty of World Economy and International Affairs
When: 1 year, 1, 2 module
Mode of studies: distance learning
Instructors: Ivan Deseatnicov
Language: English
ECTS credits: 3
Contact hours: 60

Course Syllabus

Full SyllabusAsk Question

Abstract

No Pre-requisites required but familiarity with basic algebra and calculus is assumed. Anyone who interested in basic mathematics is always welcome. The course consists of three parts. In the first, we introduce some concepts from linear algebra. The second part is devoted to multivariate calculus constrained static optimization. The last section provides an introduction to differential equations and dynamic systems. This course covers the basic mathematical tools that are used in classical and modern economics analysis and econometrics. By the end of this course, students are expected to master a number of derivations techniques, and this mastering comes only at the price of doing a sizable number of exercise. The instructor is there to help you through the learning process.
Learning Objectives

Learning Objectives

  • To introduce the key mathematical theories that are applied in economic analysis such as equilibrium analysis, linear algebra, and calculus
  • To develop the mathematical maturity so that students are not intimidated by mathematical notations and abstractions
  • To develop intuition, creativity, critical thinking and problem-solving skills of students
Expected Learning Outcomes

Expected Learning Outcomes

  • Lessons learned by students: a. Students can distinguish the ingredients of a mathematical model b. Students understand the real-number system c. Students understand the concept of sets d. Students can identify relations and functions
  • Lessons learned by students: a. Student understands the meaning of market equilibrium b. Student can solve one and two-commodity market equilibrium models
  • Lessons learned by students: Students can perform various matrix and vector operations; Students know different types of matrices; Students understand the concept of nonsingularity; Students can calculate determinants of different orders; Students can apply the Gaussian method to solve system of linear equations and to find an inverse matrix; Students can find the inverse matrix by expansion of s determinant by alien cofactors; Students can solve the system of linear equations by Cramer’s rule
  • Lessons learned by students: a. Students understand the concept of a derivative b. Students can identify continuity and differentiability of a function
  • Lessons learned by students: a. Students can find differentials and total derivatives b. Students can find derivatives of implicit functions c. Students can conduct a comparative statics analysis of general-function models
  • Lessons learned by students: a. Students can find relative maximum and minimum of a function b. Students know Maclaurin and Taylor series
  • Lessons learned by students: a. Students know logarithmic and exponential functions b. Students can find derivatives of logarithmic and exponential functions
  • Lessons learned by students: a. Students can find extreme values of a function of two variables b. Students can solve the problem of multiproduct firms
  • Lessons learned by students: a. Students can find stationary values b. Students understand quasiconcavity and quasiconvexity c. Students know homogeneous functions
  • Lessons learned by students: a. Students can apply Kuhn-Tucker conditions for Nonlinear programming b. Students know economic applications of nonlinear programming
  • Lessons learned by students: a. Students can apply the envelope theorem for unconstrained optimization b. Students know the Roy’s identity and Shephard’s lemma
Course Contents

Course Contents

  • Introduction
    Introduction of the course Ch1. The Nature of Mathematical Economics - Mathematical Versus Nonmathematical Economics - Advantages of the Mathematical Approaches Ch2. Economic Models - Types of Models (Visual Models, Mathematical Models, Empirical Models, and Simulation Models) - Static and Dynamic Models - Why Comparative Static Models are Usually Used?
  • Equilibrium Analysis
    Ch3. Equilibrium Analysis in Economics - The Meaning of Equilibrium - Partial Market Equilibrium-A Linear Model Versus A Nonlinear Model - General Market Equilibrium
  • Linear Models and Matrix Algebra
    • Ch4. Linear Models and Matrix Algebra  Matrix and Vectors  Matrix Operations  Linear Dependence of Vectors  Commutative, Associative, and Distributive Laws  Identity Matrices and Null Matrices  Transposes and Inverses • Ch5. Linear Models and Matrix Algebra (Continued)  Conditions for Nonsingularity of a Matrix  Test of Nonsingularity by Use of Determinant  Basic Properties of Determinants  Finding the Inverse Matrix  Cramer’s Rule • Ch6. Comparative Statics and the Concept of Derivative  The Nature of Comparative Statics  Rate of Change and the Derivative  The Derivative and the Slope of a Curve  The Concept of Limit  Inequalities and Absolute Values  Limit Theorems  Continuity and Differentiability of a Function
  • Differentiation and Comparative Statics
    • Ch7. Rules of Differentiation and Their Use in Comparative Statics  Rules of Differentiation for a Function of One Variable  Rules of Differentiation Involving Two or More Functions of the Same Variable  Rules of Differentiation Involving Functions of Different Variables  Partial Differentiation  Applications to Comparative Static Analysis  Note on Jacobian Determinants • Ch8. Comparative-Static Analysis of General-Function Models  Differentials  Total Differentials  Rules of Differentials  Total Derivatives  Derivatives of Implicit Functions  Comparative Statics of General Function Models
  • Comparative Statics of General Function Models
    • Ch9. Optimization: A Special Variety of Equilibrium Analysis  Optimal Values and Extreme Values  Relative Maximum and Minimum: First-Derivative Test  Second and Higher Derivatives  Second-Derivative Test  Taylor Series  Nth-Derivative Test
  • Optimization and Equilibrium
    • Ch9. Optimization: A Special Variety of Equilibrium Analysis (Continued)  Optimal Values and Extreme Values  Relative Maximum and Minimum: First-Derivative Test  Second and Higher Derivatives  Second-Derivative Test  Taylor Series  Nth-Derivative Test
  • Exponential and Logarithmic Functions
    • Ch10. Exponential and Logarithmic Functions  The Nature of Exponential Functions  Logarithmic Functions  Derivatives of Exponential and Logarithmic Functions
  • Multivariable optimization
    • Ch11. The Case of More Than One Choice Variable  The Differential Version of Optimization Condition  Extreme Values of a Function of Two Variables  Quadratic Forms  Objective Functions with More than Two Variables  Second-Order Conditions in Relation to Concavity and Convexity
  • Optimization with Equality Constraints
    • Ch12. Optimization with Equality Constraints  Effects of a Constraint  Finding the Stationary Values  Second-Order Condition  Quasiconcavity and Quasiconvexity  Utility Maximization and Consumer Demand • Ch13. Further Topics in Optimization  Nonlinear Programming and Kuhn-Tucker Condition  The Constraint Qualification  Maximum-value Functions and the Envelope Theorem  Duality and the Envelope Theorem
  • Non-Linear Programming and Kuhn-Tucker conditions
    • Ch14. Economic Dynamics and Integral Calculus  Dynamics and Integration  Indefinite Integrals  Definite Integrals
  • Duality and the Envelope Theorem
    • Ch14. Economic Dynamics and Integral Calculus (Continued)  Dynamics and Integration  Indefinite Integrals  Definite Integrals
Assessment Elements

Assessment Elements

  • non-blocking Assignments
  • non-blocking Attendance
  • non-blocking Midterm test
  • non-blocking Final Exam
    Platforms: Zoom, Socrative и Gradescope
Interim Assessment

Interim Assessment

  • Interim assessment (2 module)
    0.2 * Assignments + 0.1 * Attendance + 0.4 * Final Exam + 0.3 * Midterm test
Bibliography

Bibliography

Recommended Core Bibliography

  • Sydsæter, K., & Hammond, P. J. (2016). Essential Mathematics for Economic Analysis (Vol. Fifth edition). Harlow, United Kingdom: Pearson. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=nlebk&AN=1419812

Recommended Additional Bibliography

  • Jacques, I. (2015). Mathematics for Economics and Business (Vol. 8th ed). Harlow: Pearson. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1419610