Consider the social planner formulation of the following stochastic growth model:

where c is consumption, h is leisure, i_s is investment in structures and i_e is investment in equipment. Here, the primes ^′ denote next-period value and the subscripts ₋₁ denote past
values. The non-negativity constraint on each type of investment means that machines cannot be removed once they are installed.

System (1) is a recursive formulation. One can also write the problem as an infinite horizon as follows:

 

Transcribed Image Text:

V (ks, ke, 9) = max 0 log c+ (1 – 0) log(1 – h) + BE,[V (k, k,, d)] s.t. c,h,is,ie c+is + ie = kas kdehl-as-ae k, = (1 – 8,)ks + is k = (1 – 8e)ke + qie c 2 0, i, > 0, ie 2 0 log q = Pq log q–1+E,€~ N(0, o) (1) V (ks, ke, 9) = max 0 log c+ (1 – 0) log(1 – h) + BE,[V (k, k,, d)] s.t. c,h,is,ie c+is + ie = kas kdehl-as-ae k, = (1 – 8,)ks + is k = (1 – 8e)ke + qie c 2 0, i, > 0, ie 2 0 log q = Pq log q–1+E,€~ N(0, o) (1)

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