ps10macro2sp06

# ps10macro2sp06 - Econ 387L Macro II Spring 2006 University...

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Econ 387L: Macro II Spring 2006, University of Texas Instructor: Dean Corbae Problem Set #10 - Part I Due 4/11/06, Part II Due 4/14/06 I. A f rm has a production technology y t = F ( k t ,k t +1 ) where F : R + × R + R + . Assume that F is continuously differentiable, increasing in k t and decreasing in k t +1 (due to adjustment costs). Assume that: (i) F exhibits constant returns (i.e. F ( λk t ,λk t +1 )= λF ( k t ,k t +1 ) ,λ> 0 ); (ii) F is strictly quasi-concave (i.e. if ( k t ,k t +1 ) 6 =( b k t , b k t +1 ) ,F ( b k t , b k t +1 ) F ( k t ,k t +1 ) , and θ (0 , 1) , then F ( k θ t ,k θ t +1 ) >F ( k t ,k t +1 ) where ( k θ t ,k θ t +1 )= θ ( k t ,k t +1 )+(1 θ )( b k t , b k t +1 ); and (iii) F is such that the marginal adjustment cost becomes arbitrarily high as the reate of growth of capital approaches α> 0 (i.e. lim k t +1 (1+ α ) k t ∂F ( k t ,k t +1 ) ∂k t +1 →−∞ ). Let δ (0 , 1) be the depreciation rate and q

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ps10macro2sp06 - Econ 387L Macro II Spring 2006 University...

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