Undergraduate Classes
Intermediate Micro with Game Theory
Here are my lecture notes (including exercises) of Intermediate Microeconomics with some game theory, taught at Carngie Mellon University during my visit there. The aim is again to provide a compact and self-contained set of materials that are accessible to students of diverse mathematical preparedness, and are rigorous enough to engage their mind. I select and sequence the game theory materials to convey a sense of continuance from the main component of this course, classic decision theory, to game theory. First come zero-sum games that can be solved as if a consumer's optimization, owing to the minimax theorem. Then are games with dominant strategies where a player can to some extent make decisions regardless of the actions of the opponents. Finally comes an introduction of Nash equilibrium, where decisions are truly interactive across players.
Chapter | Contents | |
1: Output Supply | first- & second-order conditions; cost curves; pure competition vs monopoly | |
2: Input Deployment | level surface; implicit function; supporting hyperplane; returns to scale | |
3: The Lagrange Method | mainly on equality constraints; gradients; some cases with inequality constraints | |
4: Preference and Utility | binary relation; preference relation; lexicographic ordering; expected utility | |
5: Consumer's Decision | quasilinear utility functions; corner vs interior solutions | |
6: Revealed Preference | substitution effect; interpersonal welfare comparison; axioms of revealed preference | |
7: Zero Sum Games | mixed strategy; convex hull; security strategy; security level; saddle point | |
8: Dominant Strategies | strict & weak dominance; backward induction; normal form & strategy; Stackelberg | |
9: Nash Equilibrium | pure & totally mixed strategy equilibrium; best response; fixed point; Cournot |
Intermediate Micro: Purely Decision Theory
Here are my lecture notes (including exercises) for the non-game-theoretic part of Intermediate Microeconomics. They are aimed at compactifying the various topics into just several chapters under a single theme of introducing the formal analysis of decision making in the pure competition context. I found such compactification conducive to striking a balance between the goal to engage the students in nontrivial economic reasoning---mathematics an integral part of the reasoning---and the constraints imposed by the large number of students and their vastly diverse levels of preparedness in critical reasoning. With only a few chapters to read, students would be less distracted by the burden of memorizing jargons in various topics but rather focus more on the recurring theme, which deepens along the sequence of the chapters and culminates in the epilogue that introduces the modern envelope theorem. The unconventional sequencing of the chapters, presenting first producer theory rather than consumer theory, is motivated by the fact that producer theory is simpler in substance, with explicit objective functions and without the income effect complication, and the concern that a consumer's decision tends to sound too close to students' daily experience for them to suspend the concrete for the abstract.
Chapter | Contents | |
1: Firm's Supply | derivative; first- and second-order conditions; L'Hôpital's rule; proof by contradiction | |
2: Input-Output Decision | concavity; supporting hyperplane; proof | |
3: Deployment of Inputs | partial derivative; implicit function; proof | |
4: The Lagrange Method | vector; gradient | |
5: Preference and Utility | binary relation; countability; continuity; gamble; expected utility | |
6: Consumer's Decision | corner solution | |
7: Demand Function | integration | |
8: Slutsky Equation | chain rule; partial derivative | |
9: Revealed Preference | logic; mathematical induction | |
10. The Envelope Theorem | partial derivative; measure zero |