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

Econ 421 

Fall 2022

Place and TIme 
HODD336 T/Th 4:005:15 

Professor:  Professor Roger D. Congleton  . 
Office:  4131 Reynolds Hall 
. 
Office Hours  Wednesday and Thursday 2:303:30 and most other times in the afternoon by appointment 

.EMail 
roger.congleton@mail.wvu.edu 

: 


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

.  PDF Syllabus 

:  Course Overview  . 
.  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 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 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 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  
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.
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 netbenefit maximizing model. Constrained and
unconstrainted optimization (2
lectures) Homework1
(Due Aug 31) 

1Sept22  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) 

13Sept22 
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) 

20Sept22 22Sept22 27Sept22 
Review for First Exam First Exam Review of First Exam 

II. Choice Under Uncertainty and Intertemporal Choice  
29Sept22  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) Homework3 (due Oct 5) 

6Oct22  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) Homework4 (Due Oct 12) 

III.
An Introduction to NonCooperative Game Theory 

13Oct22 
8. 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). (2 lectures) Homework5 (Due Oct 19)  
20Oct22 
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. Homework6 (Due Oct 26) (2
lectures) 

27Oct22 
10. Imperfect Competition as
Games Between Small Numbers of Firms Cournot and Stackelberg Duopoly, the Effect of Entry in Cournot Markets (1 lecture) Homework7 (Due Oct 30) 
Ideas for Paper Topics 
1Nov22 
Review for Second Exam  STUDY GUIDE II 
3Nov2022 
Second Exam Exam
to be proctored, Travel Day (PPE society) for Prof
Congleton 

8Nov22 
Election Day: No
Class 

10Nov22 
Review of Second Exam 

IV.
Optimization: Generalizing with Abstract Functional
Forms 

15Nov22  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 1419) / (2 Prerecorded Lectures online unless Covid etc causes the conference in Japan to be on line via zoom or something similar) 
Part 1: Comp Statics Part 2: Abstract Functions 
1927 Nov 22  ThanksgivingFall Recess / No Class  Ideas for Paper Topics 
11/29  121 
Chapter
11: Microeconomics with Abstract (but shaped)
Functions Continued. Homework8 (Due Dec 7) 

12/812/10  12.
A
Brief Overview of the Course and Intro to Model
Building / Paper Workshop Chapter 12 Appendices: Further Tools for Interested Students (entirely optional) 

14Dec22 
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 
. 
.  
Grades:  
Eight
Homeworks 
24.00%  
Bonus for
Class Participation 
4.00%  
Two
Exams Final Paper (add to your AOL file) 
54.00% 22.00% 

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