ECON 702 Midterm: Micro I prelim August 2018 Steve Matthews
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This exam has four questions and is worth 100 points. Answer each question in a separate exam book. If you need to make additional assumptions, state them clearly. Good luck: (25 pts) consider a binary relation % on rl (a) (4 pts) de(cid:133)ne what it means for % to be representable by a function u : rl. R: (b) (4 pts) suppose % is representable. What are all the conditions % must therefore satisfy? (de(cid:133)ne these conditions, don(cid:146)t just name them. ) R that is c 2 and has a strictly positive gradient and a negative de(cid:133)nite hessian matrix at each z 2 rl(cid:0)1. + : assume that at a given initial price vector (p; w); the (cid:133)rm demands a positive amount of each input. Give an example of an economy for which the conclusion of the general equilibrium theorem in (b) holds, but for which the assumptions of the (cid:133)xed point theorem do not hold.
