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# PS3 - Intermediate Microeconomics 2008 Problem Set No 3 due...

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Intermediate Microeconomics, 2008 Problem Set No 3 due: Jan, 16 / 17 Problems From Varian, p52: 1) Consider three people, A,B,C and the relation “at least as old as”. Is this relation transitive? Is it complete? 2) For the same group of three people, consider the relation “strictly older than”. Is this relation transitive? Is it complete? 3) Suppose a trainer wants to pick among a group of players and suppose he always weakly prefers someone who is bigger and faster. Is his preference relation complete? Is it transitive? 4) What is your marginal rate of substitution between \$10 Bills and \$1 Bills? 5) What is the marginal rate of transformation between a \$10 Bill and a 10Euro Bill? 6) What are some goods for which you might have concave (or at least not weakly convex) preferences? General Note: Unless otherwise stated, you can safely assume that all parameters and quan- tities are weakly positive ( 0). We will either clearly state if this is not the case or it will be clear from the content of the question. Note that parameters can still be zero! 7) We learned in class that utility is all about ordering. Suppose someone has preferences represented by the utility function U ( q 1 , q 2 ) = aq 1 + bq 2 . Suppose someone else has preferences given by the utility function U ( q 1 , q 2 ) = aq 1 + bq 2 + 5 . 1. Draw their indifference curves for fixed values of the parameters a and b . How would they rank the bundles A = (1 , 1) and B = ( 1 2 , 2 ) depending on a and b ? Do they rank A and B differently? 8) Suppose two individuals have utility functions U 1 ( q 1 , q 2 ) = q 1 q 2 and U 2 ( q 1 , q 2 ) = aq 1 q 2 . Do they have the same preferences? You might want to try the bundle from Problem 7. (Note well that a 0 includes a = 0.) 9) The book claims that the following two utility functions are the same: U 1 ( q 1 , q 2 ) = f ( q 1 , q 2 ) (where f ( q 1 , q

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