Section notes for Econ 202
Choice Theory
A few choice theory problems solved.
Producer Theory I
Implicit function theorem, Differential envelope theorem, Lattice
theory, Topkis' Theorem
Producer Theory II
Kuhn-Tucker methodology, Integral envelope theorem
Consumer Theory I
Duality, homotheticity, and aggregation
Consumer Theory II
Welfare measures and path independence, nested optimization, the
LeChatelier Priciple
Choice under Uncertainty
Arrow-Pratt measures, proof methodology for insurance and portfolio
problems, precautionary savings and the third derivative
General Equilibrium I
Existence of Walrasian equilibrium, corner solutions, and zero
prices
General Equilibrium II
Continuous GE, market failure due to externality, market failure
due to increasing returns to scale
Final Exam Review
Exactly as advertised
An alternative to the Hicksian
demand
Hicksian demand compensates to keep utility constant.
An alternative is to compensate to keep purchasing power
constant.
Duality
Introduces the duality theorem and the idea of support
functions
LP Duality
Introduces linear programming duality
Euler's theorem and its
converse
Exactly as advertised
Assortion with continuous type
spaces
Discusses how to deal with assortion in continuous type spaces,
as used in continuous GE problems.
Hemicontinuity and fixed point
theorems
Hemicontinuity, Fixed Point Theorems, Theory of the Maximum,
and why you might care.
Expanding in a basis of mins
In the same way periodic functions can be expanded in Fourier
series, concave functions can be expanded in a series of min
functions.
Lagrange multipliers as shadow
prices
Two ways to justify the intuition of Lagrange multipliers as
prices.
All you wanted to know about Topkis' Theorem
(but were afraid to ask)
Start with univariate Topkis on the reals, move on to
multivariate Topkis on the reals, and then step up to Topkis on
a general lattice