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)