714s10_hw2_ans

714s10_hw2_ans - ECON 714: MACROECONOMIC THEORY II TA: TIM...

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Unformatted text preview: ECON 714: MACROECONOMIC THEORY II TA: TIM LEE MARCH 3, 2010 Outline to HW2 Solutions Mind you, I might be wrong...open to any disputes! 1. The state is c . If c 1/2, he will always choose q = 1/2. In that case, his continua- tion value is V u ( c ) = r r- 1 1 4 . Otherwise for c < 1/2, hell always choose q = c so V c ( c ) = max c c ( 1- c )- ( c- c ) 2 + 1 r V ( c ) . (a) Therefore V ( c ) = V u ( c ) if c 1/2 V c ( c ) if c > 1/2. (b),(c) Neither. If c 1/2, the value function is constant, so nothing is strict. (d) But it should still be differentiable. As long as c < 1/2, it satisfies all the assumptions. If c 1/2, its just constant, which is still differentiable. The only point where it may not be differentiable is at c = 1/2, but it still satisfies the assumptions here from the left, and we know its C 1 from the right - so it should be C 1 at c = 1/2 too. (e) This problem is actually easier than most weve seen up to now, because the return function is just a polynomial. Guess a polynomial and I get something like V c ( c ) =...
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714s10_hw2_ans - ECON 714: MACROECONOMIC THEORY II TA: TIM...

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