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hw1 - Homework Assignment 1 Econ 121b Intermediate...

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Homework Assignment # 1 Econ 121b. Intermediate Microeconomics due January 19, 2011 (in class) 1. Blanche Carter devised a system for rating the boys in her economics class. She cares about their intelligence and their looks. She ranks each male on a scale of 1 to 5 for intelligence and 1 to 3 for looks (1 is the lowest). She defines a preference relation as follows: x y if boy x scores at least as high as boy y in either looks or in intelligence. Consider the following example of 3 boys x , y and z : x y z intelligence 1 2 2 looks 1 1 2 Are Blanche’s preferences transitive? Explain. 2. Leonard consumes positive amounts of goods 1 and 2. Leonard thinks that 2 units of good 1 is always a perfect substitute for 3 units of good 2. Which of the following utility functions is the only one that would NOT represent Leonard’s preferences? (a) U.x 1 ; x 2 / D 3x 1 C 2x 2 1000 (b) U.x 1 ; x 2 / D 9x 2 1 C 12x 1 x 2 C 4x 2 2 (c) U.x 1 ; x 2 / D min f 3x 1 ; 2x 2 g (d) U.x 1 ; x 2 / D p 30x 1 C 20x 2 C 10000 (e) More than one of the above does NOT represent Leonard’s preferences.
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