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Lecture 5

# Lecture 5 - Economics 101A(Lecture 5 Stefano DellaVigna...

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Economics 101A (Lecture 5) Stefano DellaVigna September 10, 2009

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Outline 1. Properties of Preferences II 2. From Preferences to Utility (and viceversa) 3. Common Utility Functions 4. Utility maximization
1 Properties of Preferences Nicholson, Ch. 3, pp. 87-88 (69-70, 9th) Commodity set X (apples vs. strawberries, work vs. leisure, consume today vs. tomorrow) Preference relation º over X A preference relation º is rational if 1. It is complete : For all x and y in X, either x º y, or y º x or both 2. It is transitive : For all x, y, and z, x º y and y º z implies x º z Preference relation º is continuous if for all y in X, the sets { x : x º y } and { x : y º x } are closed sets.

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Example: X = R 2 with map of indi ff erence curves Counterexamples: 1. Incomplete preferences. Dominance rule. 2. Intransitive preferences. Quasi-discernible di ff er- ences. 3. Discontinuous preferences. Lexicographic order
Indi ff erence relation : x y if x º y and y º x Strict preference: x Â y if x º y and not y º x Exercise. If

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