Preferences, Binary Relations, and Utility Functions

  Nonlinear Programming and the Kuhn-Tucker Conditions

  Example: Linear Programming and the Kuhn-Tucker Conditions

  Pareto Efficiency

  Exercises on Pareto Aggregation

  Example: The Pareto Maximization Problem

  The Utility Frontier

  Using the MRS to Evaluate Trades

  Weak and Strong Pareto Efficiency

  Efficiency Prices: Decentralizing Pareto Allocations

  Disaggregated Definition of Walrasian Equilibrium

  The Welfare Theorems

  Summary of General Equilibrium Existence, Efficiency, and Welfare Theorems