# lecture8 - Lecture 8 Recursive Competitive Equilibrium ECON...

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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....
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## 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.

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lecture8 - Lecture 8 Recursive Competitive Equilibrium ECON...

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