ECON 702 Midterm: 702 PrelimAugust2018 Dirk Krueger
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1 the stochastic neoclassical growth model with preference shocks. The social planner in the stochastic neoclassical growth model chooses sto- chastic consumption, labor and capital allocations fct; lt; kt+1g to solve the following maximization problem max e0 s. t. t l1(cid:0)(cid:11) ct + kt+1 = k(cid:11) t. Xt=0 (cid:12)t exp(zt)u (ct; lt) with (cid:12) 2 (0; 1) and (cid:11) 2 (0; 1) being parameters. The initial endowment of capital k0 and the initial exogenous state z0 is given. The prefence shock zt follows a n -state markov chain. Let z = fz1; z2; : : : zn g be the state space of the markov chain, and let (cid:25)(zt+1jzt) denote the markov transition matrix of the chain. For questions that involve sequential notation, use zt to denote a complete history of preference shocks and (cid:25)t(zt) to denote its probability. For all (cid:23); (cid:24) 2 [0; 1] determine the set of stationary distributions: formulate the problem of the social planner recursively.
