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  1. Preferences

  2. Preference Relation • The consumer strictly prefers bundle X to bundle Y: • The consumer is indifferent between X and Y:

  3. Weak Preference • If or • Then:

  4. How are the relations related? Q: What do these two relations imply?

  5. How are the relations related? A: The consumer is indifferent between X and Y:

  6. Assumption I: Complete Preferences For any two bundles X and Y: • X preferred to Y: • Y preferred to X: • Indifference:

  7. Assumption II: Reflexive Any bundle X is at least as good as itself:

  8. Assumption III: Transitive • If: • And: • Then:

  9. Indifference curves Indifference curve Weakly preferred set

  10. Q: Can indifference curves cross?

  11. Perfect substitutes

  12. Perfect complements

  13. Satiation

  14. Well-behaved preferences • Let’s impose some extra assumptions to rule out less interesting situations • Well-behaved preferences satisfy two properties: • Monotonicity • Convexity

  15. Monotonicity • Consider two bundles: where Y has at least as much of both goods and more of one. • Then: • Monotonicity implies that indifference curves have negative slopes

  16. Indifference curves have negative slopes

  17. Convexity • Consider two bundles: • Convexity implies that, for

  18. Convex preferences

  19. Non-convex preferences

  20. The MRS is the slope of the indifference curve at a point MRS=derivative of indifference curve Marginal rate of substitution

  21. Interpretation of MRS • The MRS measures the rate at which the consumer is willing to substitute one good for the other. • If good 2 is measured in dollars, the MRS measures the consumer’s willingness to pay for an extra unit of good 1.