Varieties_SL

Varieties_SL - A Model of Growth and Innovation Prof. Lutz...

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A Model of Growth and Innovation Prof. Lutz Hendricks August 7, 2009 L. Hendricks () August 7, 2009 1 / 39
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Issues We study a GE model of growth driven by innovation. Innovation takes the form of inventing new goods. Alternative: Quality ladders. L. Hendricks () August 7, 2009 2 / 39
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A Model of Product Innovation Demographics: A representative household. Preferences: Z 0 e ρ t C 1 θ t 1 1 θ dt (1) L. Hendricks () August 7, 2009 3 / 39
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Technology Y t = ( 1 β ) 1 Z N t 0 x ( v , t ) 1 β dv ± L β (2) This is of the Dixit-Stiglitz form: write ²R x 1 β dv ³ 1 β 1 β to see that this is a CES aggregator of x . Production of intermediates from output: each unit of x requires ψ units of Y . L. Hendricks () R±D model August 7, 2009 4 / 39
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Technology Resource constraint: C t + X t + Z t = Y t Z X : Inputs into the production of x . L. Hendricks () August 7, 2009 5 / 39
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Innovation ˙ N = η Z t (3) Think of this as the aggregate (deterministic) outcome of the (stochastic) L. Hendricks () R±D model August 7, 2009 6 ² 39
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Market arrangements Final goods and labor markets are competitive. Innovators receive perpetual patents (monopolies) for their varieties. L. Hendricks () R±D model August 7, 2009 7 / 39
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Final goods producers Y t = ( 1 β ) 1 Z N t 0 x ( v , t ) 1 β dv ± L β (4) L and x ( v , t ) . Normalize the price Y to 1. Y t w t L t Z N t 0 p x ( v , t ) x ( v , t ) dv (5) L. Hendricks () R±D model August 7, 2009 8 / 39
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Final goods producers Demand function (cf. the Dixit Stiglitz discussion): x ( v , t ) = L p x ( v , t ) 1/ β (6) Labor demand is standard: w t = β Y t / L t (7) Solution L t , x ( v , t ) that satisfy the "2" L. Hendricks () R²D model August 7, 2009 9 / 39
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Intermediate input producers Problem after inventing a variety. x is produced at constant marginal cost ψ . V ( v , t ) = Z t e rs π ( v , s ) ds (8) π ( v , t ) = ( p x ( v , t ) ψ ) x ( v , t ) (9) L. Hendricks () R±D model August 7, 2009 10 / 39
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With constant demand elasticity: p x = ψ / ( 1 β
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This note was uploaded on 10/29/2009 for the course ECON 720 at UNC.

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Varieties_SL - A Model of Growth and Innovation Prof. Lutz...

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