Extended Outline

  1. Sets and Mappings

    1. Logic, Theorems and Proofs

      • necessary, sufficient, imply, contrapositive, theorem, equivalence, prove, contradiction.

    2. Sets

      • set, subset, equal set, empty, set difference, complement, union, intersection.

    3. Mappings

      • function, domain, range, one-to-one, onto.

  2. Preferences

    1. The Questionnaire Q

      • no order effect, transitivity.

    2. The Questionnaire R

      • completeness, transitivity.

    3. Equivalence of the Two Preferences

  1. Topology

    1. Metric Space

      • topology, metric, metric space, Euclidean metric, Euclidean space.

    2. Open and Closed Sets

      • open set, closed set, boundary point, interior point, bounded, compact.

    3. Continuity

      • continuous function, image, inverse image.

  1. Utility

    1. Utility Representation

      • represent, utility function, utility representation.

    2. Continuity

      • continuous preference, convex set.

    3. Monotonicity

      • bundle, monotonicity.

  1. Choice

    1. Choice Function

    2. Rational Choice

      • induced choice function, rationalize.

    3. Consumer Choice

      • budget set, consumer problem.

  1. Demand

    1. Convexity

      • convexity, strict convexity, quasi-convexity.

    2. Demand Function

      • Marshallian demand function, homogeneous of degree zero, Walras's law.

    3. Revealed Preferences I

      • fully rationalize, revealed, weak axiom of revealed preferences (WA).

  1. Optimization 1: Existence

    1. Revealed Preferences II

      • Hicksian (compensated) demand function, strong axiom of revealed preferences (SA).

    2. Extreme Value

    3. Sequence and Limit

      • converge, limit, differentiable, partial derivative, continuously differentiable, total differential.

  1. Optimization 2: Solving Method

    1. Unconstrained Optimization

      • critical point.

    2. Constrained Optimization 1: Equality Constraints

      • objective function, choice variable, constraint, feasible set, substitution, Lagrange's method.

  1. Optimization 3: Characterization

    1. Envelope Theorem

      • maximum-value function, theorem of the maximum, envelope theorem.

    2. Constrained Optimization 2: Inequality Constraints

      • Kuhn-Tucker condition.

  1. Consumer Problem

    1. Indirect Utility Function

      • indirect utility function, UMP, Marshallian demand function, Roy's identity.

    2. Expenditure Function

      • expenditure function, Hicksian (compensated) demand function, Shephard's lemma.

  1. Duality

    1. Dual Problem

    2. Slutsky Equation

      • substitution effect, income effect, Slutsky equation.

    3. Substitution Effects

      • normal good, inferior good, Giffen's paradox.

  1. Production and Cost Functions

    1. Technology

      • production, output, input, technology, production possibility set.

    2. Production Functions

      • production function, constant/increasing/decreasing returns to scale.

    3. Cost Functions

      • cost function, Shephard's lemma.

  1. Profit Maximization

    1. Firm's Objectives

    2. Cost Minimization

      • conditional (contingent) input demand.

    3. Profit Maximization

      • input demand function, output supply function, profit function, Hotelling's lemma.

  1. Expected Utility

    1. Uncertainty and Lotteries

      • prize, lottery, St Petersburg paradox.

    2. Expected Utility Theory

      • independence axiom, continuity axiom, vNM (Von Neumann-Morgenstern) utility function.

  1. Risk Aversion

    1. Some Issues on Expected Utility

      • Allais paradox.

    2. Lotteries with Monetary Prizes

      • monotonicity, first-order stochastically dominate (FOSD).

    3. Risk Aversion

      • risk averse, Jensen inequality, certainty equivalence, absolute risk aversion, invariance to wealth, relative risk aversion.

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