1.1. Prove that the transitivity axiom (G2), which is defined in terms of the "weakly preferred" preference relation >, also implies that the indifference relation ~ (indifference) is transitive. [Hint: A - B is defined as "A > B and B > A". What you are looking for is a proof that "A - B and B - C" implies A - c.] 1.2. (Optional) Prove that axiom G2 also implies that the "strictly preferred" preference relation > is transitive. [Hint: A > B is defined as "not B > A" (i.e. when A > B then "B > A" is false and vice versa).]

1.1. Prove that the transitivity axiom (G2), which is defined in terms of the "weakly preferred" preference relation >, also implies that the indifference relation ~ (indifference) is transitive. [Hint: A - B is defined as "A > B and B > A". What you are looking for is a proof that "A - B and B - C" implies A - c.] 1.2. (Optional) Prove that axiom G2 also implies that the "strictly preferred" preference relation > is transitive. [Hint: A > B is defined as "not B > A" (i.e. when A > B then "B > A" is false and vice versa).]

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter15: Strategic Games

Section: Chapter Questions

Problem 15.2IP

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Suppose Katie buys the bundle (20,9) from the budget line 3x_1 + 5x_2 = 105. When the price of good 1 changes to p1 = 6 and the price of good 2 remains the same, she buys the bundle (5,15). On a later date when p1 = 5 and p2 = 4, by observing Katie’s choices we can say that the Weak Axiom of Revealed Preference (WARP) is violated if a) She buys the bundle (10,15). b) She buys the bundle (15,10) c) She buys the bundle (23,6) d) She buys the bundle (25,25). e) None of the above choices violates WARP.
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