14.451 | Fall 2009 | Graduate
Dynamic Optimization Methods with Applications

Assignments

ASSIGNMENTS TOPICS NOTES FILES
Problem set 1

Banach spaces

Contraction mapping

Theorem of maximum

Optimal saving in finite time

  (PDF)
Problem set 2

An adjustment cost model

Working and resting

Non-differentiabilities

  (PDF)
Problem set 3

Unique optimal plans and non-unique steady states

Optimal growth: a closed form example

Pricing iPhones

Cyclical paths

Problem 1

Even though the objective function is not strictly concave, you can still prove that there is a unique optimal policy using F being (weakly) concave in x and y and strictly concave in y. For an example of a strictly concave F that yields non-unique steady states try: F(x,y) = - (1/2)x2 + (18/19)xy - (9/20)y2 with beta = 9/10.

Problem 4.2

beta = 0.5

(PDF)
Problem set 4

Persistence and inertia

Invariant distributions and ergodic sets

Optimal control

  (PDF)
Course Info
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Fall 2009
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