D = a - bP + cY
S = d + eP

D=S requires:

P* =  (a+cY-d)/(e+b)

MA Math Econ (630)

George Mason University 

Fall 2010

Prof. Roger D. Congleton


U=u(X, Y, Z)
W = pxX +pyY+pzZ

Class Room:
  Arlington Campus, room 257
Day and Time:
  Thursday,  7:20 pm - 10:00 pm
Office Hours:
  Tuesday, 1:15-2:45, Thursday 1:15-2:45, 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)
CW: 1-3, 12.4
Scope of Course, Usefulness and limitations of deductive methodology
 Answers 1
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
CW: 6, 7.1-7.5,12.2-12.7
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
 Answers 2
Economic Applications: the profit maximizing firm, cost-benefit analysis
Problems: V3.1, 3.4, 3.5, 3.3, 4.1
CW: 9, 12, 13.4
Modeling constrained choices.  more applications of the substitution method, an overview of the Lagrangian method. Appendix: the Arrow-Enthoven 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
CW: 8.1-8.5 , 13.4-13.6
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.
 Answers 4
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
Help Session on Homework / no lecture / by TA

Choices in risky and/or intertemporal settings: Probability Functions, Expected Value, Present Discounted Value,  Infinite and Finite Planning Horizons, maximizing expected present values. 
 Answers 5
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 
 CW: 13.2-3,  14.1-14.5, 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 
 Answers 6
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)
CW: 16.4-16.5
To Crime: The Wealth Maximizing Criminal (Becker, JPE 1968: 169-217)
 Study Guide 1
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
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
 Paper Topic Ideas
Problems: V 17 1-6, 11,13, 
Representing interdependent choices with game matrices: strategy, payoff, non-cooperative 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  Non-Cooperative Game Theory 
M: 4-7 
. 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
Answers 9

. Problems M: 13B3, 13B4, 13B8, 14B1, 14B3, 14C4, 14C8 .
M: 3-7
More applications of game theory: signaling games, sorting games, etc. Appendix on matrix algebra, Cramer's rule, derivation of OLS estimator
 Study Guide 2
Applications developed in class, but also if time allows also 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

Problems V15.2, 15.7, M9:B5, B7, B11, B14
6-8 Page Papers Due
XIII. Review for Final
 Old PhD Final
Final Exam: 7:30-10:15 (necessarily comprehensive, but oriented toward material covered in second half of the course)