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. 
Supplemental Texts 
Mas-Colell, 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
LF: 1.1-4, 2.4-8, 7.1
H:Int-1, 14
Scope of Course, Usefulness and limitations of deductive methodology
 Answers 1
Mathematical Concepts: weak ordering, transitivity, convexity, closed and open sets, compact sets, continuity, functions
Economic Application: consumer theory, the theory of the firm
 see also 
C1,2; V7; M1
Problems V1.1, 1.6, 1.11
LF: 4, 6.2 -3
Mathematical Concepts: partial derivatives, the chain rule, first and second order conditions, concavity, quasiconcavity,  objective function, constraints, optimization using the substitution method
 Answers 2
Economic Applications: the profit maximizing firm, cost-benefit analysis
 see also: Ch 6,9  MC:Ap A,B
Problems: V3.1, 3.4, 3.5, 3.3, 4.1
LF: 7.1
Mathematical Concepts: Lagrangian multipliers, Lagrangian method, Kuhn -Tucker method, Kuhn Tucker Sufficiency Theorem, Arrow-Enthoven Sufficiency Theorem
Answers 3
Economic Applications: Consumer Theory, Social Welfare Functions
See also: C12,21; V9-10 
Problems: C12.2 1,3,4; C12.5 1,2; V: 7.2, 7.5
 LF: 5.2, 7.1 
Mathematical Concepts: implicit function theorem, derivatives of implicit functions, neighborhood, continuity, duality
 Answers 4
Economic Applications: supply and demand, Cournot reaction functions, comparative statics 
 see also: C8;V6, Mme
Problems: C8.5 1,2,3 C8.6 1,2,4 ; V 5.1, 5.2, 5.3, 5.4, 6.1,6.3
 LF: 4.4 
Mathematical Concepts: Probability Function, Expected Value, Present Discounted Value, Series, Infinite and Finite Planning Horizons, Convergence 
 Answers 5
Economic Applications: Intertemporal Choice, Decisionmaking under Uncertainty, Household Finance
See also: C6.6, 13.5; V11, Mmf 
Problems: C6.6 1,2,3 C6.7 4 C13.5 4,5; V11.5, 11.9, 11.11 
Mathematical Concepts: Integrand, definite and indefinite integrals, risk aversion, subjective rate of time discounting 
 Answers 6
Economic Applications: Intertemporal Choice, Decisionmaking under Uncertainty, Continuous Discounting, Totals from Marginals, Measures of Risk Aversion
See also: C13, V11, M6 
Problems: C13.2 1,2,4 C13.5 1,2 C13.6 2 ; V11.7; K3:3,4,5,8
 Study Guide 1
To Crime: The Wealth Maximizing Criminal (Becker, JPE 1968: 169-217)
To Politics: Tax Revenue Maximizing Leviathan (Buchanan and Brennan, JPubE, 1977: 255-73)
To the Selection of a Conservative Central Banker
(Waller, C. J., AER, 1992: 1006-12)
 Answers 7 +
. To the assignment of liability to lenders: (Lewis and Sappington, AER, 2001:724-730.) .
 2000 Midterm
Midterm Exam
IX. General Equilibrium (Midterms Returned)
 LF 6.3
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 15-17
Economic Application: Walrasian Equilibrium
 Paper Topic Ideas
Problems: V 17 1-6, 11,13, 
LF: 6.4-5, H:8
Mathematical Concepts: strategy, payoff, non-cooperative 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  Non-Cooperative Game Theory 
H: 5, 6, 7 
. Existance of Nash Equilibrium  (Kakutani revisited) Subgame Perfect Equilibrium
Contest Theory, Externalities, Elections, Rent-Seeking
Applications from H, but also, if time allows, to Externality Theory, Monopolistic Competition
Answers 9

See also: V15; K9, 13, 14; V25

. Problems M: 13B3, 13B4, 13B8, 14B1, 14B3, 14C4, 14C8 .
Mathematical Concepts: signaling games, sorting games, matrix algebra, Cramer's rule, derivation of OLS estimator
 Study Guide 2
Applications from H, but also if time allows from: 
       R&D in Duopoly (D'Aspermont and Jacquemin, AER,  1988: 1133-1137.)
      Theory of Anarchy (Skaperdas, AER, 1992:720-739.)
      Political Influence and Dynamic Consistancy (Garfinkel and Lee, AER, 2000: 649-666)
 Answers 10
Answers 11

See also V15; K8,9

Problems V15.2, 15.7, M9:B5, B7, B11, B14
Papers Due
XIII. Review for Final
 Study Guide for Final
Final Exam: 7:30-10:15 (necessarily comprehensive, but oriented toward material covered in second half of the course)