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homework2 2010

# homework2 2010 - P T of P is its inverse such that Λ = P T...

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ECN/APEC 7240 Spring 2010 Homework 2 Due 1/3/10 Let us now further generalize the CKR model with technology shocks. We introduce a government that purchases goods G t using a distortionary income tax on both capital and labor income with rate τ t . Thus we have G t = t ( W t + R t K t ). The tax rate t is exogenous but stochastic. We assume that t can take on one of two values 0 < l < h < 1. Given t , the probability that t changes to the other value is q [0, 1]. The probability that 0 = l = h is 1/2. a) Denote the transition matrix . 1 1 ] | Pr[ ] | Pr[ ] | Pr[ ] | Pr[ 1 1 1 1 - - = = = = = = = = = = Π + + + + q q q q h t h t h t l t l t h t l t l t What is Π n for n ≥ 1? (Hint: Find an orthogonal matrix P , meaning the transpose
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Unformatted text preview: P T of P is its inverse, such that Λ = P T Π P is a diagonal matrix of the eigenvalues of Π . Show that Π n = P Λ n P T .) b) Show that the unconditional probability that t = l = h = 1/2. c) What is the unconditional expectation of t ? The unconditional variance? The unconditional correlation of t and t +1 ? d) Suppose that u ( C ) = ln C , δ = 1, and F ( K , L ) = K α L 1-. What is the equilibrium consumption function C ( K , A , )?...
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