| Tentative
Course Outline and
Handouts for Math Econ (630) Fall 2004 Instructor, Roger D. Congleton |
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Required Texts:
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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).
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Class Notes, distributed weekly in class.
AND AVAILABLE BELOW (via the web) |
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Supplemental Texts
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Mas-Colell, A., Whinston, M. D., and Green, J. R.
(1995) MicroEconomic Theory. New York: Oxford University Press.
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Varian, Hal R. Microeconomic Analysis 3rd Ed.
New York: W. W. Norton and Co., 1992. ISBN 0 393 95735 7.
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Debreu, G. Theory of Value, Cowles Foundation
Monograph 17, New Haven: Yale University Press, 1959.
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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
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| COURSE OUTLINE | ||
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9/02
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H:Int-1, 14 |
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Scope of Course, Usefulness and limitations of deductive
methodology
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Mathematical Concepts: weak ordering, transitivity,
convexity, closed and open sets, compact sets, continuity, functions
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Economic Application: consumer theory, the theory
of the firm
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C1,2; V7; M1 |
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Problems V1.1, 1.6, 1.11
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9/09
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Mathematical Concepts: partial derivatives, the chain
rule, first and second order conditions, concavity, quasiconcavity,
objective function, constraints, optimization using the substitution method
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Economic Applications: the profit maximizing firm,
cost-benefit analysis
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see also: Ch 6,9 MC:Ap A,B | |
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Problems: V3.1, 3.4, 3.5, 3.3, 4.1
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9/16
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Mathematical Concepts: Lagrangian multipliers, Lagrangian
method, Kuhn -Tucker method, Kuhn Tucker Sufficiency Theorem, Arrow-Enthoven
Sufficiency Theorem
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Answers 3 |
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Economic Applications: Consumer Theory, Social Welfare
Functions
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Problems: C12.2 1,3,4; C12.5 1,2; V: 7.2, 7.5
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9/23
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Mathematical Concepts: implicit function theorem,
derivatives of implicit functions, neighborhood, continuity, duality
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Economic Applications: supply and demand, Cournot
reaction functions, comparative statics
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Problems: C8.5 1,2,3 C8.6 1,2,4 ; V 5.1, 5.2, 5.3,
5.4, 6.1,6.3
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9/30
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Mathematical Concepts: Probability Function, Expected
Value, Present Discounted Value, Series, Infinite and Finite Planning Horizons,
Convergence
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Economic Applications: Intertemporal Choice, Decisionmaking
under Uncertainty, Household Finance
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Problems: C6.6 1,2,3 C6.7 4 C13.5 4,5; V11.5, 11.9,
11.11
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10/7
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Mathematical Concepts: Integrand, definite and indefinite
integrals, risk aversion, subjective rate of time discounting
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Economic Applications: Intertemporal Choice, Decisionmaking
under Uncertainty, Continuous Discounting, Totals from Marginals, Measures
of Risk Aversion
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Problems: C13.2 1,2,4 C13.5 1,2 C13.6 2 ; V11.7; K3:3,4,5,8
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10/14
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| . |
To Crime: The Wealth Maximizing Criminal (Becker,
JPE
1968: 169-217)
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To Politics: Tax Revenue Maximizing Leviathan (Buchanan
and Brennan, JPubE, 1977: 255-73)
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To the Selection of a Conservative Central Banker
(Waller, C. J., AER, 1992: 1006-12) |
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| . | To the assignment of liability to lenders: (Lewis and Sappington, AER, 2001:724-730.) | . |
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10/21
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10/28
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Midterm Exam
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11/4
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IX. General Equilibrium (Midterms
Returned)
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Mathematical Concepts: weak preference ordering, excess
demand correspondence, Walras' law, upper semicontinuity, Browers fixed
point theorem, Kakutani fixed point theorem
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See also: Debreu 5,7 V17, 21; M 15-17 | |
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Economic Application: Walrasian Equilibrium
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Problems: V 17 1-6, 11,13,
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11/11
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X. Interdependent Decisions: (1)
An Introduction to Game Theory (2) Essential
Concepts and Mathematics of Games
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Mathematical Concepts: strategy, payoff, non-cooperative
games, prisoner's dilemma game, value, zero sum game, Best reply functions,
Mixed Strategies
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Economic Applications: Duopoly, Competition, Cartels,
Tragedy of the Commons
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See also: V15, M7 | |
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Problems V15.1, 15.3,16.10, V15.2, 15.7
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| 11/18 | XI. Applications of Non-Cooperative Game Theory |
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| . | 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 |
See also: V15; K9, 13, 14; V25 |
| . | Problems M: 13B3, 13B4, 13B8, 14B1, 14B3, 14C4, 14C8 | . |
| 11/25 | THANKSGIVING BREAK no class | |
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12/2
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Mathematical Concepts: signaling games, sorting games,
matrix algebra, Cramer's rule, derivation of OLS estimator
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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 11 See also V15; K8,9 |
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Problems V15.2, 15.7, M9:B5, B7, B11, B14
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12/09
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Papers Due
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12/09
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XIII. Review for Final
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Study Guide for Final |
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12/16
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Final Exam: 7:30-10:15
(necessarily
comprehensive, but oriented toward material covered in second half of the
course)
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