lecture2

# Lecture2 - Lecture 2 Preferences and Utility Ranking bundles of goods If we have two real numbers its easy to say which is larger e.g 7 > 5 If you

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Lecture 2: Preferences and Utility

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Ranking bundles of goods • If we have two real numbers, it’s easy to say which is larger: e.g. 7 > 5 • If you have two products, it’s often easy to say which you like more—e.g. Coke > Pepsi or Pizza > Doritos—but not always… • What if you have two bundles of goods? Is {Coke, Doritos} > {Pepsi, Pizza}? This is getting tougher.
• In most (but not all) economics, we assume that people’s preferences are sufficiently “well behaved” that we can rank any two goods or any two bundles of goods • We place additional (realistic?) restrictions on preferences as well… Preferences and Utility

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Axioms of Rational Choice • Completeness – if A and B are any two situations, an individual can always specify exactly one of these possibilities: • A is preferred to B • B is preferred to A • A and B are equally attractive – Do these pref.’s satisfy completeness? •(x 1 ,x 2 ) > (y 1 ,y 2 ) if and only if x 1 > y 1 and x 2 > y 2 1 ,x 2 ) > (y 1 ,y 2 ) if and only if x 1 + x 2 > y 1 + y 2
Transitivity – if A is preferred to B, and B is preferred to C, then A is preferred to C assumes that the individual’s choices are internally consistent – Do these pref.’s satisfy transitivity? •( x 1 ,x 2 ) > (y 1 ,y 2 ) if and only if x 1 > y 1 and x 2 > y 2 x 1 ,x 2 ) > (y 1 ,y 2 ) if and only if x 1 + x 2 > y 1 + y 2 Axioms of Rational Choice

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• Continuity – if A is preferred to B, then situations suitably “close to” A must also be preferred to B • used to analyze individuals’ responses to relatively small changes in income and prices – Do these pref.’s satisfy continuity? •(x 1 ,x 2 ) > (y 1 ,y 2 ) if and only if x 1 > y 1 and x 2 > y 2 1 ,x 2 ) > (y 1 ,y 2 ) if and only if x 1 + x 2 > y 1 + y 2 Axioms of Rational Choice
Example of preferences • Consider Lexicographic preferences : • Bob strictly prefers (x, y) to (x’, y’) if and only if either (i) x > x’ or (ii) x = x’ and y > y’. Bob is indifferent btw the two if x = x’ and y = y’. • Do these preferences satisfy – completeness? – transitivity? – continuity? • Consider continuity: – Assume (x,y) > (x’,y’). We want to check if situations suitably “close to” (x,y) must also be preferred to (x’,y’). If so, these preferences are continuous. If not, they are not.

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## This note was uploaded on 12/21/2009 for the course ECON 1211 taught by Professor Govel during the Spring '08 term at Columbia.

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Lecture2 - Lecture 2 Preferences and Utility Ranking bundles of goods If we have two real numbers its easy to say which is larger e.g 7 > 5 If you

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