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

muenster market

Qd = .aY - bP

Qs = e + fP

Qd = Qs when

P* = (aY-e)/(b+f)
Econ 421
Fall 2022
Place and TIme
  HOD-D-336     T/Th 4:00-5:15

Professor: Professor Roger D. Congleton .
Office: 4131 Reynolds Hall
Office Hours   Wednesday and Thursday 2:30-3:30 and most other times in the afternoon by appointment

Required Text: (none, the web notes on this website and the lectures are sufficient)
. PDF Syllabus

: Course Overview .
. 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 several types of economic results that are 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 equilibria in competitive markets. Part II uses algebra and calculus to model choices 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
Notes and Misc
18-Aug-22 1. Introduction to Mathematical Economics
Model building and methodological Individualism: Optimization as a model of rational decision making by consumers and firms. Methodological Individualism. Microeconomics as an implication of purposeful behavior. Models of rational choice using Geometry, Algebra, and Calculus as modelling tools (1 lecture)


I. Optimization and Neoclassical Economics
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. Optimization and Some Core Insights from Neoclassical Economics   Use of calculus to characterize marginal cost and marginal benefit curves for consumers and firms. Deriving consumer and firm level demand and supply curves from the net-benefit maximizing model. Constrained and unconstrainted optimization  (2 lectures)   Homework-1 (Due Aug 31)

1-Sept-22 4. Constrained Optimization and Some Core Insights of Neoclassical Economics
Characterizing consumer demand using exponential utility functions and budget constraints. Advantages over the net benefit maximizing approach. Exponential Production functions and Market Supply. A more sophisticated grounding for competitive equilibrium and comparative statics. (3 lectures)  Homework 2 (due Sept 14)


5. Optimization by Firms Facing Downward Sloping Demand Curves .
Price taking and price making firms. Cost functions and market structure. Simultaneously determing output and prices. (1 lecture)
Review for First Exam
First Exam
Review of First Exam

II. Choice Under Uncertainty and Intertemporal Choice
29-Sept-22 6. Optimization and Uncertainty: 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)  Homework-3 (due Oct 5)

6-Oct-22 7. Optimization and Time: 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. (2 lectures)  Homework-4 (Due Oct 12)

III. An Introduction to Non-Cooperative Game Theory

8. 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).  (2 lectures) Homework-5 (Due Oct 19)
9. Games with Finite and Infinite (Continuous) Numbers of Strategies: More 3x3 games. Illustrations: Recipriocal Externalities and Lottery contests with 2 and N players. Dissipation Rates.  Application to law and politics, etc. Homework-6 (Due Oct 26) (2 lectures)


10. Imperfect Competition as Games Between Small Numbers of Firms
Cournot and Stackelberg Duopoly, the Effect of Entry in Cournot Markets (1 lecture) Homework-7 (Due Oct 30)
Ideas for Paper Topics
Review for Second Exam  STUDY GUIDE II
Second Exam  Exam to be proctored, Travel Day (PPE society) for Prof Congleton

Election Day: No Class

Review of Second Exam

IV. Optimization: Generalizing with Abstract Functional Forms

15-Nov-22 11. Chapter 11: Microeconomics with Abstract (but shaped) Functions

. Part I Comparative statics using general forms of concrete functions. Part 2 The Calculus of Abstract Functions, Implicit Function Theorem, Implicit Function Differentiation Rule, The Mathematics of downward sloping demand curves. Parts 3 and 4: Abstract Representations of Markets and Contests,  Comparative Statics using the Implicit Function Differentiation Theorem (4 lectures, the 3rd and 4th parts of the series continues after Thanksgiving break). 

(Travel Week for the Japanese
Public Policy Association, Nov 14-19) /
(2 Prerecorded Lectures online unless Covid etc causes the conference in Japan to be on line via zoom or something similar)
 Prerecorded Ch 11 Lectures
Part 1: Comp Statics
Part 2: Abstract Functions
19-27 Nov 22 Thanksgiving-Fall Recess / No Class Ideas for Paper Topics
11/29 - 12-1
Chapter 11: Microeconomics with Abstract (but shaped) Functions Continued.
Homework-8 (Due Dec 7)

12/8-12/10 12. A Brief Overview of the Course and Intro to Model Building / Paper Workshop

Chapter 12 Appendices: Further Tools for Interested Students (entirely optional)  


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


Eight Homeworks
Bonus for Class Participation
Two Exams
Final Paper  (add to your AOL file)
Marginal extra credit for extra-helpful class participation (up to 2-3% bonus)