exam2001 - Final Exam ARE 261 (2001) Answer all parts of...

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Final Exam ARE 261 (2001) Answer all parts of all three questions. The value of the question is given in parentheses next to the question number. Question 1) (45 points) S is an index of environmental quality and x is the f ow of pollution. The evolution of S is given by ˙ S = x g ( S ; α ) ,where gisincreasingandconcavein S ,and α is a parameter of the function g. The instantaneous ( f ow) payo f is x x 2 2 - S 2 2 and the instantaneous discount rate is r . You want to maximize the present discounted integral of the f ow of welfare from time 0 to in F nity. The initial condition S 0 is given. (i) Write the current value Hamiltonian and necessary conditions. (ii) Sketch the phase portrait in ( S, x ) , space. The portrait should include the0-isoclines,thedirectionalarrows,andthestablesaddlepath(theoptimal control rule). (iii) Write the equations that determine the optimal steady state. (iv) Explain how to
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This note was uploaded on 08/01/2008 for the course ARE 263 taught by Professor Karp during the Fall '06 term at University of California, Berkeley.

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exam2001 - Final Exam ARE 261 (2001) Answer all parts of...

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