ECON 702 Midterm: PrelimJune2012-1_Krueger

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31 Jan 2019
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The stochastic aggregate en- dowment of the single consumption good is given by z 2 z; a (cid:133)nite set. z follows a markov process with transition matrix (cid:25) and associated stationary distribution (cid:5): There is a lucas tree that pays dividends d in every period equal to a fraction (cid:18) of the aggregate endowment, that is d(z) = (cid:18)z: The remaining part of the aggregate endowment (1 (cid:0) (cid:18))z is paid to households as labor income: suppose for this question that z = fzl; zhg with markov transition matrix is given by (cid:25) = (cid:18) 0:2. Determine the (set of) invariant distribution(s) associated with this markov transition matrix: suppose the economy is populated by an in(cid:133)nitely lived representative agent with lifetime utility function. Xt=0 (cid:12) tu (ct): with (cid:12) 2 (0; 1) and u satis(cid:133)es the usual properties. De(cid:133)ne a recursive competitive equilibrium for this economy.

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