Qd = .aY  bP Qs = e + fP Qd = Qs when P* = (aYe)/(b+f) 
NB = b(Q)  c(Q) maximized at b'(Q) = c'(Q) 

Econ 421 

Fall 2022

WVU 
HODD336


Professor:  Professor Roger D. Congleton  .T/Th 4:005:15 
Office:  411 Reynolds Hall 
. 
.Office Phone  

.EMail 
roger.congleton@mail.wvu.edu 

Office Hours:  2:303:30 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
lecturebased 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
intertemporal 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 microeconomics. It is a challenging course, and is most useful for students who are good at math and thinking about advanced degrees in economics or economicrelated subjects. 

.  Tentative
Course Outline and Links to Class Notes 
. 
Dates  Topic 

18Aug22  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  
23Aug22  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) 

25Aug22 
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) EQuiz1 

1Sept22  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) EQUIZ2 

8Sept22 
5. Monopolistic Markets. Maximizing profits with a downward sloping demand curve. (1 lecture) 
STUDY GUIDE I

13Sept22 15Sept22 20Sept22 
Review for First Exam First Exam Review of First Exam 

II. Choice Under Uncertainty and Intertemporal Choice  
22Sept22  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) EQUIZ3 

29Sept22  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) EQUIZ4 

III. An Introduction to NonCooperative
Game Theory 

11Oct22 
5. Introduction to NonCooperative 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) EQUIZ5  
13Oct22 
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. EQUIZ6 (2 lectures) 

20Oct22 
7. Imperfect
Competition: Duopoly Models, etc, As Games Cournot and Stackelberg Duopoly, the Effect of Entry in Cournot Markets (2 lectures) EQUIZ7 

27Oct22 
Review for Second Exam  STUDY GUIDE II. 
3Nov2022 
Tentative Travel Day
(PPE society) for Prof Congleton / No Class 

8Nov22 10Nov22 
Second Exam Review of Second Exam 

1418 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) 

1927
Nov 22 
ThanksgivingFall Recess /
No Class 

IV. Generalizing with Abstract
Functional Forms 

29Nov22  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). EQUIZ8 

8Dec22  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 
.  
.  
Grades:  
Eight
Quizzes 
32.00%  
Class
Participation 
4.00%  
Two
Exams Final Paper 
44.00% 20.00% 

Marginal extra credit for extrahelpful class participation (up to 23% bonus) 