# HW7 - Homework 7 Jonathan Heathcote due in class on Tuesday...

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Homework 7 Jonathan Heathcote due in class on Tuesday April 25th 1. Model Consider the simple RBC model that we discussed in class. A representative agent / social plannner solves the following problem: max { c t }{ k t +1 } E 0 X t =0 β t c t 1 γ 1 γ subject to c t + k t +1 = e z t k θ t +(1 δ ) k t z t +1 = ρz t + ε t +1 t +1 N (0 2 ε ) where { c t ,z t ,k t } are time t values of consumption, the technology shock and capital respectively. 2. Exercise 1. Write down the set of Euler equations and other equations that characterize equilibrium. 2. Compute the steady state of this economy and report it. Use the following parameter values: β =0 . 99 =0 . 02 =0 . 3 =2 =0 . 95 . 3. Linearize the system of equations by taking f rst order Taylor series approxima- tions to them around the steady state. 4. Solve the system of equations by following the steps outlined in class. Report: (i) Eigenvectors and eigenvalues for your linearized system (ii) A decision rule for the choice variable (

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HW7 - Homework 7 Jonathan Heathcote due in class on Tuesday...

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