Qd = .aY - bP

Qs = e + fP

Qd = Qs when

P* = (aY-e)/(b+f)

muenster market

NB = b(Q) - c(Q)
maximized at b'(Q) = c'(Q)

Econ 421
An Introduction_to_Mathematical Economics
Fall 2022
Professor: Professor Roger D. Congleton .T/Th 4:00-5:15
Office: 411 Reynolds Hall
.Office Phone  

Office Hours: 2:30-3:30 Wednesday and Thursdays, and most other times by appointment
Required Text: (none, the class notes are sufficient)
Optional Texts:

: Course Description .
. Mathematical Economics is a lecture-based course that uses algebra and calculus to analyze economic decision making and market equilibria when consumers and firms are rational in the sense that they have clear consistent goals that can be represented as net benefits or utility levels. Although the main focus of the course is theory, applications to a wide range of choice and policy settings are used to illustrate the relevance of the tools developed in class.

There are some types of economic results that can be most easily derived and demonstrated using algebra and calculus; these are the main focus of the course. Part I uses calculus on exponential utility and production functions to characterize consumer and firm choices, and these are used to analyze competitive markets. Part II uses algebra and calculus to model choice under uncertainty  and inter-temporal choices (choices that affect the future).  Part III uses calculus and algebra to model settings where outcomes are jointly determined by the decisions of of small number of decision makers acting more or less independently of one another (game theory), again using concrete functional forms.  Part IV (if we have time) will show how abstract functional forms can be used to generalize the results from Parts I, II, and III. 

The goal of the course is to provide the student with an understanding of the mathematical models that ground contemporary micro-economics. It is a challenging course, and is most useful for students who are good at math and thinking about advanced degrees in economics or economic-related subjects.

. Tentative Course Outline and Links to Class Notes
Dates Topic
 Other Readings
18-Aug-22 1. Introduction to Mathematical Economics
Model building and methodological Individualism: Optimization as a modeling device for rational consumers and firms. Microeconomics as an implication of purposeful behavior. Models of rational choice using Geometry, Algebra, and Calculus as modelling tools (1 lecture)


I. Optimization and Competitive Markets
23-Aug-22 2. Optimization and the Shapes of Functions
The geometry of three types of concavity. Usefulness of assumption of strict concavity. The notation of derivatives. Derivatives as a method for determining concavity. Example: Consumer Choice using net benefit maximization with explicit functional forms.. (1 lecture)


3. Demand and Supply as Consequences of Net Benefit Maximization  Use of calculus to characterize marginal cost and marginal benefit curves for consumers and firms. Deriving consumer and firm level demand and supply curves. Equilibrium  (2 lectures)   E-Quiz-1

1-Sept-22 4. Demand and Supply as Consequences of Utility and Profit Maximization with Production Functions
Characterizing rationality with exponential utility functions. Advantages over the net benefit maximizing approach. Exponential utility functions and demand.  Exponential Production Functions and Supply. As an alternative grounding for competitive equilibrium and comparative Statics. (2 lectures)  E-QUIZ-2


5. Monopolistic Markets. Maximizing profits with a downward sloping demand curve. (1 lecture)
Review for First Exam
First Exam
Review of First Exam

II. Choice Under Uncertainty and Intertemporal Choice
22-Sept-22 5. Expected Utility Maximizing Choices
Expected values with discrete and continuous probability functions. Maximizing expected utility.  Individual demand curves when product quality is uncertain. Supply curves when market prices are uncertain. lottery games (2 lectures)  E-QUIZ-3

29-Sept-22 6. Intertemporal Choice
Present discounted values with finite and infinite time periods. Importance of time discount rates for intertemporal calculations.  Combining intertemporal choice and choice under uncertainty. (3 lectures)  E-QUIZ-4

III. An Introduction to Non-Cooperative Game Theory

5. Introduction to Non-Cooperative Game Theory: Game Matrices and the Concepts of a Nash Equilibrium and Best Reply Function (in games with 2 players with countable numbers of strategies).  (1 lecture) E-QUIZ-5
6. Games with Infinite (Continuous) Numbers of Strategies: Illustration: Lotteries with 2 and N players. Lotteries as contests, Dissipation Rates.  Application to politics: Rent Seeking. E-QUIZ-6
(2 lectures)


7. Imperfect Competition: Duopoly Models, etc, As Games
Cournot and Stackelberg Duopoly, the Effect of Entry in Cournot Markets (2 lectures) E-QUIZ-7

Review for Second Exam  STUDY GUIDE II.
Tentative Travel Day (PPE society) for Prof Congleton  / No Class

Second Exam
Review of Second Exam

14-18 Nov 22
Tentative Travel Week (Japanese Public Policy Association) for Prof Congleton / 8. Nash Equilibria to Finite Repeated Games (Prerecorded Lectures online unless Covid etc causes the conference in Japan to be on line via zoom or something similar)

19-27 Nov 22
Thanksgiving-Fall Recess / No Class

IV. Generalizing with Abstract Functional Forms

29-Nov-22 9. Demand and Supply with Abstract (but shaped) Functions

. Generalized Concave Utility Functions and Demand. Generalized Cost Functions and Supply. The Mathematics of downward sloping demand curves and upward sloping supply curves  Comparative Statics using the Implicit Function Differentiation Theorem (3 lectures). E-QUIZ-8
8-Dec-22 10. Overview of the course and Paper Workshop

Final Papers on an Economic or a Political Topic Using Mathetmatical Tools from this Course.
Due by Email at Midnight on the Scheduled Exam Day


Eight Quizzes
Class Participation
Two Exams
Final Paper
Marginal extra credit for extra-helpful class participation (up to 2-3% bonus)