D = a  bP + cY S = d + eP D=S requires: P* = (a+cYd)/(e+b) 
MA Math Econ
(630) George Mason University Fall 2010 Prof.
Roger D. Congleton 
Maximizing U=u(X, Y, Z) s.t. W = pxX +pyY+pzZ requirres ??? 



Class
Room:

Arlington Campus, room 257  
Day
and Time:

Thursday, 7:20 pm  10:00 pm  
Office
Hours:

Tuesday, 1:152:45, Thursday 1:152:45, and by appointment  
Required Texts:



Chaing, A. C. and K. Wainwright
(2005) Fundamental Methods of
Mathematical Economics [Paperback] McGraw Hill Higher Education;
4th edition (June 1, 2005)



Class Notes for Math Econ: AVAILABLE BELOW (via the web)


Supplemental Texts


McCain, R. A. (2009) Game Theory and Public Policy
(Edward Elgar  Dec 9, 2009)


TENTATIVE COURSE OUTLINE  
Date 


9/02



Scope of Course, Usefulness and limitations
of deductive
methodology



Models of Rational Choice:
net benefits, utility, weak ordering,
and transitivity Opportunity Sets and other Constraints. Mathematical
concepts:
convexity, closed and open sets, compact sets, continuity, functions


Economic Application: consumer theory, the
theory
of the firm



Problems V1.1, 1.6, 1.11


9/09



Modeling decisions to maximize an objective
function: partial derivatives,
the chain
rule, first and second order conditions, concavity,
quasiconcavity,
objective function, constraints, optimization using the substitution
method



Economic Applications: the profit maximizing
firm,
costbenefit analysis



Problems: V3.1, 3.4, 3.5, 3.3, 4.1


9/16



Modeling constrained choices.
more applications of the substitution method, an overview of the
Lagrangian
method. Appendix: the ArrowEnthoven
Sufficiency Theorem

Answers 3 

Economic Applications: Consumer Theory,
Social Welfare
Functions



Problems: C12.2 1,3,4; C12.5 1,2; V: 7.2, 7.5


9/23



How and why changes in
constraints affect choices. The Implicit Function Theorem and
differentiation rule, the envelop
theorem. Applications: how changing prices affect profit maximizing
firms and utility maximizing consumers.



Economic Applications: supply and demand,
Cournot
reaction functions, comparative statics



Problems: C8.5 1,2,3 C8.6 1,2,4 ; V 5.1,
5.2, 5.3,
5.4, 6.1,6.3


9/30 
Help Session on Homework / no lecture /
by TA 

10/7



Choices in risky and/or intertemporal
settings: Probability Functions,
Expected
Value, Present Discounted Value, Infinite and Finite Planning
Horizons, maximizing expected present values.



Economic Applications: Intertemporal Choice,
Decisionmaking
under Uncertainty, Household Finance



Problems: C6.6 1,2,3 C6.7 4 C13.5 4,5;
V11.5, 11.9,
11.11


10/14

CW:
13.23, 14.114.5, 20.4


Choices in risky and/or intertemporal
settings with continuous probabilities and/or time. The use of
integrals, integrands, definite
and indefinite
integrals, risk aversion, subjective rate of time discounting



Economic Applications: Intertemporal Choice,
Decisionmaking
under Uncertainty, Continuous Discounting, Calculating Totals from
Marginals,
Measures
of Risk Aversion



Problems: C13.2 1,2,4 C13.5 1,2 C13.6 2 ;
V11.7; K3:3,4,5,8


10/14 (supplemental)



. 
To Crime: The Wealth Maximizing Criminal
(Becker, JPE
1968: 169217)

Study Guide 1 
. 
To Politics: Tax Revenue Maximizing
Leviathan (Buchanan
and Brennan, JPubE, 1977: 25573)

. 
. 
To the Selection of a Conservative Central
Banker
(Waller, C. J., AER, 1992: 100612) 

.  To the assignment of liability to lenders: (Lewis and Sappington, AER, 2001:724730.)  . 


10/21



10/28

Midterm Exam


11/4

IX. General
Equilibrium, a Short Overview (Midterms
Returned)


Mathematical Concepts: weak preference
ordering, excess
demand correspondence, Walras' law. Appendix on sufficient assumptions
for the existance of a general equilibrium, Browers fixed
point theorem, Kakutani fixed point theorem


Economic Applications: Edgeworth Box and
Walrasian Equilibrium



Problems: V 17 16, 11,13,


11/11

X. Interdependent Decisions: (1)
An Introduction to Game Theory (2)
Essential
Concepts and Mathematics of Games


Representing interdependent choices with
game matrices: strategy, payoff,
noncooperative
games, best reply
functions. Named games: prisoner's dilemma game, zero sum games,
coordination games, etc.



Economic Applications: Duopoly, Competition,
Cartels,
Tragedy of the Commons


Problems V15.1, 15.3,16.10, V15.2, 15.7


11/18  XI.More on NonCooperative Game Theory 

.  Economic and Political games with strategy continua:
duopoly, monopolistic
competition, political competition, rent seeking. Technical ideas and
terms: Nash equilibrium, pure strategies, mixed strategies, subgame
perfect equilibria. Appendix material on the Existance of Nash
Equilibrium (Kakutani revisited) Applications from Economics and Politics, interest group politics, majoritarian competition, monopolistic competition 

.  Problems M: 13B3, 13B4, 13B8, 14B1, 14B3, 14C4, 14C8  . 
11/25  THANKSGIVING BREAK no class  
12/2



More applications of game theory: signaling
games,
sorting games, etc. Appendix on
matrix algebra, Cramer's rule, derivation of OLS estimator



Applications developed in class, but also if
time allows also
from:
R&D in Duopoly (D'Aspermont and Jacquemin, AER, 1988: 11331137.) Theory of Anarchy (Skaperdas, AER, 1992:720739.) Political Influence and Dynamic Consistancy (Garfinkel and Lee, AER, 2000: 649666) 
Answers 11


Problems V15.2, 15.7, M9:B5, B7, B11, B14


12/09

68 Page Papers
Due


12/09

XIII. Review for Final

Old PhD Final 
12/16

Final Exam:
7:3010:15 (necessarily
comprehensive, but oriented toward material covered in second half of
the
course)

