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Rubinstein2005-page144

# Rubinstein2005-page144 - x t and y t 1 is independent of t...

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October 21, 2005 12:18 master Sheet number 142 Page number 126 126 Review Problems He is indifferent between a distribution that is fully concen- trated in location 1 and one which is fully concentrated in location 2. 1. Show that the only preference relation that is consistent with the two principles is the degenerate indifference relation ( x y for any x , y X ). 2. The decision maker claims that you are wrong as his preference relation is represented by a utility function | x 1 1 / 2 | . Why is he wrong? Problem 5 (Princeton 2000. Based on Fishburn and Rubinstein 1982.) Let X = + × { 0, 1, 2, . . . } , where ( x , t ) is interpreted as receiving \$ x at time t . A preference relation on X has the following properties: There is indifference between receiving \$0 at time 0 and re- ceiving \$0 at any other time. For any positive amount of money, it is better to receive it as soon as possible. Money is desirable. The preference between
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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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