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Unformatted text preview: Econ 310-2 Solutions to Problem Set TA: Robert Molony 1 Exercise 1 Remember that by assumption all social and individual preferences are tran- sitive. Further, note that all of the examples of social preferences are also complete (In order for completeness to be violated the social preference would have to not list one of the alternatives in its ordering). Therefore, UD is not violated FOR ANY of the examples here. (a) IIA is violated. Notice that from line 1 to 2 the ranking of B relative to A didn’t change for either consumer (Jesse prefers A to B in both cases and Erika prefers B to A in both cases). Yet, the social ranking did change (first A is preferred to B and then B is preferred to A). Hence, the IIA condition is violated (here, C is an irrelevant alternative for deciding between A and B that ends up changing the social ranking). (b) PC is violated. Both consumers agree A is better than B but the social preference ranks B * A . (c) Sarah is a dictator. The social ranking coincides with Sarah’s ranking for every preference profile. Note that a dictator always satisfies UD, PC, and IIA (as long as the individual’s preferences are complete and transitive). (d) IIA is violated. Notice that from line 1 to 2 both consumers maintain the same relative ranking between A and C (Howard thinks A is better than C and Michael thinks C is better than A). However, the social ranking between A and C changed (in line 1 A is better than C while the opposite is true in line 2). Thus, IIA is violated (here, B is the irrelevant alternative for deciding between A and C that ends up changing the social ranking). Notice that you can make the same argument with alternatives A and D. 2 Exercise 2 (a) UD could or could not be satisfied. If the constant social ranking is complete and transitive, then UD is satisfied. Otherwise UD will be violated....
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- Spring '08
- Microeconomics, Erika, Pairwise comparison, social ranking, preference proﬁle