Course Related Pages

ECON 855/455

Instructor: Ruqu Wang, Dunning 304,

Teaching Assistant: Samuel Brien,


Link to ECON 855/455 Announcements (updated September 19, 2020)


Course Outline (Fall 2020-2021)

Economics 855/455   Introduction to Mathematical Economics  

  This course covers the techniques of dynamic optimization and their applications in economic analysis.  Topics include optimal control, and deterministic and stochastic dynamic programming.  Applications to economic optimization problems will also be discussed from time to time.

  This course is divided into two parts. The first part deals with continuous-time optimization techniques and follows mainly the analysis in Kamien and Schwartz's book Dynamic Optimization. Static optimization (constrained and unconstrained optimization) will be reviewed as an introduction. The second part deals with discrete-time optimization techniques. For this part, we follow some lecture notes, which be distributed in class. Whenever possible, recent papers utilizing the techniques we just learned will be discussed.

  The purpose of this course is to provide students with advanced optimization tools that are widely used in various fields of economics.  The course will be taught at a graduate level with some grading considerations given to undergraduate students.  Basic knowledge of and willingness to use calculus are required in this course.  Undergraduates with a solid mathematics background and graduates interested in economic theory are encouraged to take this course.


            Grading (tentative):

                                    class participation -- 20%

                                    homework -- 30%

                                    midterm exam -- 20%

                                    project -- 30%


Required textbook:

            Dynamic Optimization: The Calculus of Variations and Optimal Control in Economics and Management, (2nd ed.) by Morton I. Kamien and Nancy L. Schwartz, 1991, North Holland: New York.



            Optimal Control Theory and Static Optimization in Economics, by D. Leonard and N. Van Long, 1992, Cambridge University Press.

            Introduction to Stochastic Dynamic Programming, by Sheldon M. Ross, 1983, Academic Press, Inc.



The following is what we have covered in the past for the first part.   The outline for the second part of the course will be distributed at a later time. Please note that this plan will be adjusted because of remote teaching.

I.   Review

Appendix A.  Calculus and Nonlinear Programming, Sections 1 to 6


II.   Calculus of Variations

Sections 1, 3, 4 in Part I.: Calculus of Variations

Appendix B.  Differential Equations, Sections 1 to 5


III.   Optimal Control

Sections 1 to 9 in Part II.: Finite and Infinite Horizon Optimal Control


IV.  Dynamic Programming

Section 21 in Part II : Continuous-Time Dynamic Programming.


Please read the statement on Academic Integrity from Queen's University.


Please note: The material on this website is copyrighted and is for the sole use of students registered in this course. The material on this website may be downloaded for a registered student’s personal use, but shall not be distributed or disseminated to anyone other than students registered in this course. Failure to abide by these conditions is a breach of copyright, and may also constitute a breach of academic integrity under the University Senate’s Academic Integrity Policy Statement.


ECON 855/455 Announcements

1. This course will be delivered remotely. Assessment methods will be announced at a later time.

2. I have added everyone who has registered for this course or who has sent me an e-mail requesting access. Anyone whose name I have missed or added this course afterwards please inform me so that I can add your name to the group. This course will be delivered using MSTeams.

3. Grade composition has been updated given the number of students taking this course. Please note that this is tentative. It may be adjusted later on.

4. First lecture of this course is on Tuesday, September 8.

5. I will be running test meetings on Monday, September 7 to test my equipment around 11:00am. I will not teach anything, and participation is totally optional.  

6. For those who stay in different time zones, I can distribute your participation marks to the rest of assessments. You will need to send me an e-mail requesting this.

7. The worst assignment mark will be eliminated in your grade calculations, as suggested by some of you.

8. All past lectures are automatically posted on MS Teams. Lecture notes are posted there as well. In order for me to keep track of your class participation, please send me a message in the dialogue window, either right after you asked or answer a question, or before I end the lecture. 

9. For those who request no real-time participation due to time zone difference, the assessment composition is: 37.5% homework, 25% midterm, 37.5% project.

10. Assignment #1: p.28, #1 and #2; p.39, #2. Due Saturday, September 26, 2020. I plan to use OnQ for assignment submissions, but I haven't figured it out yet. Please check back for submission method. Thank you.

Note. I have now provided a link to the assignment above.

11. I have set up Assignment #1 on OnQ successfully. You should submit your assignment there. Many of the students are already in the class list. But I believe that the rest are not. Please check to see if you are enrolled in the course on OnQ. If not, send me an e-mail with subject title "Add (your name here) to ECON 855/455 on OnQ". Thank you.