Teaching

EC 121 Intermediate Microeconomics

This course provides a rigorous treatment of microeconomic theory and serves as a bridge to graduate-level courses in general equilibrium theory. The course is organized into four parts.

(1) The first part develops consumer choice theory, examining how individuals make consumption decisions based on preferences, budget constraints, and utility maximization, and studies how changes

in market conditions affect consumer demand.

(2) The second part develops tools for welfare analysis, including compensating and equivalent variation, to evaluate the welfare impact of price changes.

(3) The third part covers the theory of the firm, analyzing production functions, cost minimization, and profit maximization.

(4) Building on these foundations, the final part covers partial equilibrium analysis, studying equilibrium conditions in individual markets and the effects of changes in supply and demand on prices and quantities. The course examines how government intervention, such as taxation, affects the welfare of consumers and firms, and introduces market failure due to monopoly. Through a combination of theoretical models and applications, the course develops the analytical skills needed for advanced work in economics.

Ec 150 (Mathematical Methods for Economics) is useful preparation but is not required.

EC 150 Mathematical Methods on Economics

This course equips students with the mathematical foundations required for graduate-level work in economics. The course is organized into four parts, and economic applications are discussed throughout to illustrate how each set of tools is used in practice.

(1) The course begins with a brief review of key concepts from real analysis and linear algebra---including sequences, open and closed sets, compactness, vector spaces, eigenvalues, quadratic forms, negative definite and semidefinite matrices, concave and quasiconcave functions, and convex sets---ensuring students have a common foundation before proceeding to more advanced material.

(2) Building on this foundation, the course develops constrained and unconstrained optimization---including Lagrange multipliers, Kuhn--Tucker conditions, and constraint qualification---the central framework through which economists model the behavior of consumers, firms, and planners. The implicit function theorem and the envelope theorem are developed alongside optimization as tools for comparative statics, enabling the study of how optimal decisions and equilibrium outcomes respond to changes in parameters.

(3) The course then takes a deeper look at the separating and supporting hyperplane theorems and the theorem of the alternative (Farkas' lemma), which appear frequently across various areas of economics, including welfare economics, decision theory, and mechanism design.

(4) The final part of the course covers correspondences, hemicontinuity, the theorem of the maximum, and fixed point theorems (Brouwer, Kakutani), which provide the mathematical machinery for proving the existence of Nash equilibria and competitive equilibria.

Throughout the course, students develop proof-writing skills and the rigorous mathematical reasoning required in graduate microeconomics, macroeconomics, and econometrics. The course is also suitable for graduate students seeking to reinforce material covered in math camp.