ECON 380
Math Economics
Summer Term 2025 |
Instructor: Staff |
Total sessions: 30 Sessions |
Office Hours: TBA |
Session Length: 145 Minutes |
Classroom: TBA |
Credits: 3 Units |
Class Length: 8 Weeks |
Language: English |
Course Overview:
This course introduces mathematical techniques used in economic analysis. The first part of the course focuses on optimization techniques, including both constrained and unconstrained optimization, with applications to consumer and firm behavior. The second part introduces
matrix algebra and its applications in economic models, particularly in analyzing production and allocation in interdependent economies. Students will develop quantitative skills essential for
modern economic analysis, including differentiation, optimization, Lagrange multipliers, and matrix operations. These mathematical tools will be applied to real-world economic problems, laying the foundation for more advanced economic modeling.
Required Material:
Chiang, A.C. & Wainwright, K., Fundamental Methods of Mathematical Economics, 4th Edition, McGraw-Hill, 2005.
Knut Sydsaeter, Peter Hammond and Arne Strom, Essential Mathematics for Economic Analysis, Pearson, 2022
Learning Objectives:
1. Apply differentiation and optimization techniques, including Lagrange multipliers, to economic models.
2. Interpret shadow prices and their role in constrained optimization problems.
3. Utilize matrix algebra to analyze interdependent economic systems and solve linear equations.
Course Outline: Week 1:
Lecture 1-4: Foundations of Mathematical Economics
Lecture 1: Introduction to Mathematical Economics
o The role of mathematics in economic modeling
o Key mathematical tools used in economics
Lecture 2: Basic Functions and Graphs
o Linear and nonlinear functions
o Economic interpretation of functions
Lecture 3: Limits and Continuity in Economic Models
o Limits and their application in economics
o The concept of continuity in economic functions
Lecture 4: Introduction to Differentiation
o Basic rules of differentiation
o Economic applications: marginal cost, marginal revenue
Assignment 1
More specific requirements (e.g., topic, formatting requirements, deadlines, etc.) will be provided in the course.
Week 2:
Lecture 5-8: Optimization in Economics
Lecture 5: Partial Differentiation and Economic Interpretation
o Partial derivatives and marginal analysis
o Cross-partial derivatives and their economic meaning
Lecture 6: Unconstrained Optimization
o First-order and second-order conditions
o Applications in firm and consumer behavior
Lecture 7: Constrained Optimization: The Lagrange Method
o Setting up and solving constrained optimization problems
o Interpretation of Lagrange multipliers
Lecture 8: Shadow Prices and Economic Interpretation
o Economic meaning of Lagrange multipliers
o Applications in labor-leisure and firm optimization
Week 3:
Lecture 9-12: Advanced Optimization Techniques
Lecture 9: Comparative Statics and Envelope Theorem
o Applications in consumer and producer theory
o Economic interpretation of total differentiation
Lecture 10: Applications of Lagrange Multipliers
o Utility maximization and expenditure minimization
o Cost minimization and profit maximization
Lecture 11: Kuhn-Tucker Conditions and Nonlinear Constraints
o Nonlinear programming in economic models
o Inequality constraints in optimization problems
Lecture 12: Introduction to Dynamic Optimization
o Concept of dynamic programming
o Applications in intertemporal consumption
Midterm Exam: multiple choice, short answer and Problem-solving questions (Contains topics in Lecture 1-12)
Week 4:
Lecture 13-16: Matrix Algebra in Economic Analysis
Lecture 13: Introduction to Matrices and Determinants
o Definition and basic operations
o Determinants and their economic applications
Lecture 14: Systems of Linear Equations and Economic Models
o Solving linear systems using matrices
o Applications in equilibrium analysis
Lecture 15: Inverse Matrices and Cramer’s Rule
o Computing inverse matrices
o Using Cramer’s rule in economic models
Assignment 2
More specific requirements (e.g., topic, formatting requirements, deadlines, etc.) will be provided in the course.
Lecture 16: Input-Output Models in Economics
o Leontief input-output model
o Production and resource allocation analysis
Week 5:
Lecture 17-19: Applications of Linear Algebra in Economics
Lecture 17: Eigenvalues and Eigenvectors in Economic Models
o Stability analysis using eigenvalues
o Application in growth models
Lecture 18: Markov Chains and Economic Transition Models
o Stochastic processes in economics
o Application in labor market dynamics
Lecture 19: Quadratic Forms and Optimization
o Positive definite matrices in economic optimization
o Applications in portfolio theory
Week 6:
Lecture 20-23: Differential Equations and Economic Dynamics
Lecture 20: First-Order Differential Equations
o Solving first-order equations
o Applications in economic growth models
Lecture 21: Stability Analysis of Differential Equations
o Phase diagrams and stability conditions
o Applications in market equilibrium
Lecture 22: Optimal Control Theory in Economics
o Hamiltonian function and economic applications
o Optimal savings and capital accumulation
Lecture 23: Applications of Differential Equations in Macroeconomics
o Solow growth model
o Business cycle analysis
Week 7:
Lecture 24-26: Advanced Topics and Case Studies
Lecture 24: Game Theory and Strategic Behavior
o Nash equilibrium and strategic interaction
o Applications in oligopoly and auctions
Lecture 25: Dynamic Optimization and Ramsey Model
o Ramsey model of economic growth
o Intertemporal utility maximization
Lecture 26: Case Study – Economic Policy and Optimization
o Real-world applications of optimization techniques
o Policy evaluation using mathematical economics
Week 8:
Lecture 27-30: Course Review and Final Exam Preparation
Lecture 27: Review of Optimization and Matrix Algebra
o Key takeaways from constrained and unconstrained optimization
o Summary of matrix algebra techniques
Lecture 28: Review of Dynamic Models and Applications
o Stability analysis and optimal control applications
o Real-world examples
Lecture 29: Practice Problems and Final Exam Strategies
o Solving complex mathematical economics problems
o Exam preparation techniques
Lecture 30: Final Review Session
o Q&A and discussion of key topics
o Last-minute exam guidance
Final Exam: multiple choice, short answer and Problem-solving questions (Contains topics in All Lectures)
Grading Assessment:
Assignment 1 |
15% |
Assignment 2 |
15% |
Midterm |
30% |
Final exam |
30% |
Seminar Participation |
10% |
Total |
100% |
Assignments:
Students are required to complete one essay and one problem set during the semester. The essay should be 1500-2000 words and demonstrate analytical thinking, clear organization, and proper use of evidence to support arguments. The problem set will involve mathematical exercises related to course topics, requiring students to apply optimization techniques, matrix algebra, and economic modeling methods.
Grading will assess clarity of writing, logical coherence, mathematical accuracy, and depth of analysis, along with proper citation of references where applicable. Specific requirements regarding topics, datasets, and deadlines will be provided during the course. All submissions must be electronic, and students will receive detailed feedback on their essay to guide
improvement.
Attendance:
Students are required to attend a weekly seminar led by TA to focus on the week's topic and deepen understanding. Seminar time assigned by TA. Seminar attendance counts toward the final grade.
Exams:
The examinations in this course consist of multiple choice, short answer and Problem-Solving
questions. The final exam is cumulative.
Final Evaluation:
Letter Grade |
Percentage (%) |
Letter Grade |
Percentage |
A+ |
≥95 |
C+ |
64-67 |
A |
89-94 |
C |
60-64 |
A- |
84-88 |
C- |
56-59 |
B+ |
79-83 |
D+ |
54-56 |
B |
73-78 |
D |
50-53 |
B- |
68-72 |
F |
≤50 |
General Policies:
Academic integrity
Academic integrity is the cornerstone of academia and requires students and researchers to
maintain honesty, fairness, trust and responsibility in all academic activities. It includes not only avoiding dishonest behaviors such as plagiarism, cheating, and falsifying data, but also requires taking responsibility for one's own academic actions and ensuring that all work is done
independently and accurately cites the research of others. Violations of academic integrity can result in severe academic penalties, such as zero grades, suspension or even expulsion, and can cause serious damage to an individual's reputation and future career. Upholding academic
integrity is therefore essential to promoting a fair academic environment and facilitating the authentic dissemination of knowledge.
Accessible Resources Policy
The policy ensures that all students, especially those with disabilities, are able to participate equally in school learning and activities. The school provides a wide range of accessibility resources including, but not limited to, specialized classrooms, hearing aids, Braille textbooks, assistive technology, and flexible testing arrangements. Students are required to apply to the school in advance and provide appropriate medical or psychological evaluations so that an
individualized support plan can be developed for them. This policy is designed to remove barriers in the academic environment and to ensure that every student has access to equitable learning opportunities.
Withdrawal Policy
Students may choose to withdraw from a course within a specified period of time, and may not be able to do so after the expiration date. When withdrawing from a course, students are required to fill out a withdrawal form with a reason, which will be reviewed and processed on a case-by- case basis. Withdrawal from a course may not affect the student's academic performance. If a student withdraws from a course with incomplete requirements, a “W” may be assigned instead of a grade, depending on the course.
