handoutromersp06 - Romer's (1987) "Growth Based on...

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Increasing Returns Due to Specialization” 1 Environment Preferences: u ( C t ,L t )=ln C t where C t is the f nal good. Largenumberofintermediategoods X t ( i ) ,i { 1 , ..., A t } that are an input into the production of the f nal good. Final good production function (CRS in H t and X t ( i )): Y t = H 1 θ t A t X i =1 X t ( i ) θ . (1) Intermediate goods production technology: Fixed cost κ and one unit of X t +1 ( i ) can be produced from one unit of the f nal good Y t . Free entry into each industry. 2 Decentralized Equilibrium Final goods producer problem max { H d t ,X t ( i ) } X t =0 t Y j =0 R j 1 " A t X i =1 H 1 θ t X t ( i ) θ P t ( i ) X t ( i ) W t H t # where W t and P t ( i ) are the relative prices of labor and intermediate inputs (in terms of cons.) FOC wrt. H t : W t =(1 θ ) H θ t A t X i =1 X t ( i ) θ (2) FOC wrt. X t ( i ): P t ( i )= h H θ t P A t i =1 X t ( i ) θ i ∂X t ( i ) = θH 1 θ t X t ( i ) θ 1 p i ( X t ( i )) (3)
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This note was uploaded on 08/06/2008 for the course ECON 387 taught by Professor Corbae during the Spring '07 term at University of Texas at Austin.

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handoutromersp06 - Romer's (1987) "Growth Based on...

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