a2Problem Set 2 Solutions - Econ 201A Fall 2010 Problem Set...

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Econ 201AFall 2010Problem Set 2 Suggested Solutions1. Prove that the lexicographic preference (defined in Example 3.10 in the course notes)is complete, transitive, and antisymmetric (ifx%yandy%x, thenx=y).
2. Prove Proposition 4.12 in the course notes: Ifurepresents%, then:(a)%is convex if and only ifuis quasiconcave.(b)%is strictly convex if and only ifuis strictly quasiconcave.Proof.Supposeurepresents%. Thenu(x)u(y)⇐⇒x%y(x, yX),(1)u(x)> u(y)⇐⇒xy(x, yX).(2)
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Econ 201AFall 2010Problem Set 2 Suggested Solutions3. Suppose the consumer’s utility function is Leontief:U(x1, x2) = min{x1, x2}Prove thatx*(p, w) is a singleton.

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