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 1Even 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 4.2beta = 0.5 | (PDF) |
Problem set 4 |
Persistence and inertia Invariant distributions and ergodic sets Optimal control | (PDF) |