Microeconomic Theory ( 501 b ) Final Exam
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Final Exam Economics 501 b Microeconomic Theory
This is a closed-book exam. The exam lasts for 180 minutes. Please write clearly and legibly. Be especially careful in the definition of the game, the payoff function and the equilibrium notions. The allocated points are also a good indicator for your time budget. Please record the answer for each question in a separate bluebook.
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Answer: For the preferences to be the same, it must be that vi = aiui+bi for some ai and bi where ai is positive and ui and vi are the utility functions of i in the left and the right game, respectively. Since u1 (b,M) = 0 and v1 (b,M) = 3, we must have b1 = 3 (Row player is 1 and the column player is 2.) Since u1 (c,M) = 1 and v1 (c,M) = 5, we then have a1 = 2. But v1 (a, L) = 12 6 · 2+3 = 2 ....
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