Unformatted text preview: ( x , t ) and ( y , t + 1 ) is independent of t . • Continuity. 1. De±ne formally the continuity assumption for this context. 2. Show that the preference relation has a utility representation. 3. Verify that the preference relation represented by the utility function u ( x )δ t (with δ < 1 and u continuous and increasing) satis±es the above properties. 4. Formulize a concept “one preference relation is more impatient than another.” 5. Discuss the claim that preferences represented by u 1 ( x )δ t 1 are more impatient than preferences represented by u 2 ( x )δ t 2 if and only if δ 1 < δ 2 . Problem 6 (Tel Aviv 2003) Consider the following consumer problem. There are two goods, 1 and 2. The consumer has a certain endowment. Before the con-sumer are two “exchange functions”: he can exchange x units of...
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- Fall '10
- Utility, princeton, preference relation, Fishburn