Tentative
Course Outline and
Handouts for Math Econ (630) Fall 2004 Instructor, Roger D. Congleton 




Required Texts:



De La Fuente, A. (1999) Mathematical Methods and Models
for Economists. New York: Cambridge Univ Press (Paper Edition, Trd); ISBN:
0521585295
Hirschliefer, J. (2001) The Dark Side of the Force: Economic Foundations
of Conflict Theory Cambridge: Cambridge University Press, 2001, 366 pp
(paper).



Class Notes, distributed weekly in class.
AND AVAILABLE BELOW (via the web) 

Supplemental Texts


MasColell, A., Whinston, M. D., and Green, J. R.
(1995) MicroEconomic Theory. New York: Oxford University Press.


Varian, Hal R. Microeconomic Analysis 3rd Ed.
New York: W. W. Norton and Co., 1992. ISBN 0 393 95735 7.


Debreu, G. Theory of Value, Cowles Foundation
Monograph 17, New Haven: Yale University Press, 1959.


Dixit, A. K. and Nalebuff, B. J. (1993) Thinking
Strategically: The Competitive Edge in Business, Politics, and Everyday
Life. New York: W.W. Norton & Company; ISBN: 0393310353


COURSE OUTLINE  
Date 


9/02

H:Int1, 14 

Scope of Course, Usefulness and limitations of deductive
methodology



Mathematical Concepts: weak ordering, transitivity,
convexity, closed and open sets, compact sets, continuity, functions


Economic Application: consumer theory, the theory
of the firm

C1,2; V7; M1 

Problems V1.1, 1.6, 1.11


9/09



Mathematical Concepts: 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

see also: Ch 6,9 MC:Ap A,B  
Problems: V3.1, 3.4, 3.5, 3.3, 4.1


9/16



Mathematical Concepts: Lagrangian multipliers, Lagrangian
method, Kuhn Tucker method, Kuhn Tucker Sufficiency Theorem, 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



Mathematical Concepts: implicit function theorem,
derivatives of implicit functions, neighborhood, continuity, duality



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



Mathematical Concepts: Probability Function, Expected
Value, Present Discounted Value, Series, Infinite and Finite Planning Horizons,
Convergence



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


10/7



Mathematical Concepts: Integrand, definite and indefinite
integrals, risk aversion, subjective rate of time discounting



Economic Applications: Intertemporal Choice, Decisionmaking
under Uncertainty, Continuous Discounting, 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



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

. 
. 
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 (Midterms
Returned)


Mathematical Concepts: weak preference ordering, excess
demand correspondence, Walras' law, upper semicontinuity, Browers fixed
point theorem, Kakutani fixed point theorem

See also: Debreu 5,7 V17, 21; M 1517  
Economic Application: 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


Mathematical Concepts: strategy, payoff, noncooperative
games, prisoner's dilemma game, value, zero sum game, Best reply functions,
Mixed Strategies



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

See also: V15, M7  
Problems V15.1, 15.3,16.10, V15.2, 15.7


11/18  XI. Applications of NonCooperative Game Theory 

.  Existance of Nash Equilibrium (Kakutani revisited) Subgame Perfect
Equilibrium
Contest Theory, Externalities, Elections, RentSeeking Applications from H, but also, if time allows, to Externality Theory, Monopolistic Competition 
See also: V15; K9, 13, 14; V25 
.  Problems M: 13B3, 13B4, 13B8, 14B1, 14B3, 14C4, 14C8  . 
11/25  THANKSGIVING BREAK no class  
12/2



Mathematical Concepts: signaling games, sorting games,
matrix algebra, Cramer's rule, derivation of OLS estimator



Applications from H, but also if time allows 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 See also V15; K8,9 

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


12/09

Papers Due


12/09

XIII. Review for Final

Study Guide for Final 
12/16

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

