This preview shows pages 1–7. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Lecture 8 Recursive Competitive Equilibrium ECON 2130 VIII  2 Linear Regulator Problem Let the state space X = R n and suppose the choice space is U = R k . Given x , the problem is subject to x t +1 = Ax t + Bu t . R is n n and positive semidefinite. Q is k k and positive definite. A is n n and B is n k. Discount factor (0, 1). + = ] [ max t t T t t T t t Qu u Rx x ECON 2130 VIII  3 Linear Regulator Bellman Equation Let v : R n R denote the value function. For x R n , Suppose the value function has the form for some n n matrix P . { } ) ( max ) ( Bu Ax v Qu u Rx x x v T T u k + + = R Px x x v T = ) ( ECON 2130 VIII  4 Policy Function Given P , the policy rule is [ ] . 1 PAx B PB B Q u T T  + = ECON 2130 VIII  5 Linear Regulator Value Function Solving the Bellman equation, we find This is an example of a Riccati equation . It can typically be solved iteratively. Starting from a guess P , . ] [ 1 2 PA B PB B Q PB A PA A R P T T T T + + = A P B B P B Q B P A A P A R P t T t T t T t T t 1 2 1 ] [ + + + = ECON 2130 VIII  6 Production with Adjustment Costs Consider a market with n producers....
View
Full
Document
This note was uploaded on 01/09/2011 for the course ECON 7140 taught by Professor Kutler during the Spring '10 term at Utah Valley University.
 Spring '10
 Kutler
 Microeconomics

Click to edit the document details