# ans1 - ECON 831 Solutions Homework #1 Exercise 1: i) The...

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Solutions Homework #1 Exercise 1: i) The present value of her lifetime earnings is: T X t =1 β t h t k t = T X t =1 β t φ ± k t +1 k t k t ii) - The state variable is: k t , the current human capital stock. - The control variable is: h t the number of hours worked. Alternatively, because we have a one-to-one relationship between h t and k t +1 when k t is known, it is equivalent to have the next period human capital stock as a control variable. We keep the second formulation which is slightly more convenient. iii) The equation of motion is: (1 - δ ) k t k t +1 (1 + λ ) k t iv) The dynamic optimization problem writes: max { k t +1 } T - 1 t =1 T X t =1 β t k t φ ± k t +1 k t s.t. (1 - δ ) k t k t +1 (1 + λ ) k t t and k 1 > 0 given Exercise 2: i) In stage 1, there are 2 options in stage 1 and 3 options in stages 2 and 3, resulting in a total of 18 possible routes. ii) Intuitive method: we start at the beginning point, A.

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## This note was uploaded on 02/19/2010 for the course ECON 831 taught by Professor Antoine during the Fall '09 term at Simon Fraser.

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ans1 - ECON 831 Solutions Homework #1 Exercise 1: i) The...

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