aps1x313_f05 - if the sign of the first derivative is yes....

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1) a) So, given the grading scheme in communications: u(x = 20 and y = 70) = 70 and u(x = 60 and y = 60) = 60, so she prefers (20, 70). b) c) Does Nancy have convex preferences over these combinations? ANS: NO! d) ANS: u(x = 20 and y = 70) = 20 and u(x = 60 and y = 50) = 60, so she prefers (60, 50). e) f) Does Nancy have convex preference over these combinations? ANS: YES! g) For Nancy’s communications class: u = max{x, y} or any monotonic transformation. For her economics class: u = min{x, y} or any monotonic transformation. 2) ANS: All you need to do is check for the sign of the first derivative and your answer us yes
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Unformatted text preview: if the sign of the first derivative is yes. a) f(u) = 3.141592 u YES since df/du = 3.14159 > 0 b) f(u) = 5,000 23 u NO since df/du = -23 < 0 c) f(u) = u 100,000 YES since df/du = 1 > 0 d) f(u) = log 10 u YES since df/du = (1/ln10)*(1/u) >0 e) f(u) = 1/ u NO since df/du = -1u-2 < 0 f) f(u) = -1/ u YES since df/du = 1u-2 > 0 Econ 313.1 - Wissink - Fall 2005 PS#1 XtraQ - ANSWERS 20, 70 60, 60 60 70 x y 70 60 communications scheme 60 50 20 20 50 70 (60, 50) 20, 70 x y economics scheme...
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