theorymidterm - Name Midterm Exam, Econ 210A, UCSB, Nov 5,...

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Unformatted text preview: Name Midterm Exam, Econ 210A, UCSB, Nov 5, 2007 Try to answer five of the six questions, including Question 6. 1) Suppose that the preference relation R is complete and transitive. We define the relation P such that xPy if and only if xRy and not yRx . a) Is P transitive? If so, prove it. If not give a counterexample by showing a transitive, complete R for which P is not transitive. b) Is P complete? If so, prove it. If not give a counterexample by showing a transitive, complete R for which P is not complete. 1 2) Define the relation P on the real line, so that for any two points x and y on the line, xPy if and only if x- y > 1. Is P transitive? Prove it if true. Show a counterexample if false. Suppose that we define the relation R on the real line so that xRy if and only if not xPy . Is R transitive? Prove it if true. Show a counterexample if false. 2 3) Define each of the following. Use a full grammatical sentence in your defini- tion....
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This note was uploaded on 02/01/2011 for the course ECONOMY 6 taught by Professor Fallahi during the Spring '10 term at Cambridge.

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theorymidterm - Name Midterm Exam, Econ 210A, UCSB, Nov 5,...

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