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Chapter8_NeoclassicalGrowth

Chapter8_NeoclassicalGrowth - Neoclassical Growth Model...

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Neoclassical Growth Model Juan Rubio-Ram°rez Duke University and Federal Reserve Bank of Atlanta February 10, 2009 Juan Rubio-Ram°rez (DUKE) Neoclassical Growth Model February 10, 2009 1 / 24
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Neoclassical Growth Model I We are going to use our basic model as a basic framework to think about growth and development. Assumptions: 1 We set T = . 2 Population grows at a constant rate n . We have l t = ( 1 + n ) t l 0 . 3 Technology grows at a constant rate g . We have A t = ( 1 + g ) t A 0 . Growth is exogenous. We can use the social planner±s problem to study the equilibrium path. Juan Rubio-Ram°rez (DUKE) Neoclassical Growth Model February 10, 2009 2 / 24
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Neoclassical Growth Model II Social Planner±s problem in per capita terms: max t = 0 β t log c t s.t. c t + ( 1 + n ) k t + 1 = k α t ° ( 1 + g ) t ± 1 ° α + ( 1 ° δ ) k t where l 0 = 1 and A 0 = 1. Parameters: β , n , g , α , and δ . Juan Rubio-Ram°rez (DUKE) Neoclassical Growth Model February 10, 2009 3 / 24
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FOCs First order conditions: 1 c t = β 1 + n c t + 1 ² α k α ° 1 t + 1 ° ( 1 + g ) t + 1 ± 1 ° α + 1 ° δ ³ c t + ( 1 + n ) k t + 1 = k α t ° ( 1 + g ) t ± 1 ° α + ( 1 ° δ ) k t Juan Rubio-Ram°rez (DUKE) Neoclassical Growth Model February 10, 2009 4 / 24
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Characterizing the Solution Previous FOCs are di¢ cult to characterize. We can do it, step by step: 1 Balanced growth path. 2 Transitional dynamics. Once we have characterization, we can go to the data. Juan Rubio-Ram°rez (DUKE) Neoclassical Growth Model February 10, 2009 5 / 24
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Balanced Growth Path I A balanced growth path (BGP) is the natural generalization of a steady state. All the variables in the model grow at constant (but potentially di/erent) rates. Do we have a BGP in the neoclassical growth model? We conjecture that consumption and capital grow at a constant rate g , i.e. c t = ( 1 + g ) t c and k t = ( 1 + g ) t k . We also conjecture that the economy will converge to the BGP. Later, we will show that both conjectures holds. Juan Rubio-Ram°rez (DUKE) Neoclassical Growth Model February 10, 2009 6 / 24
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Balanced Growth Path II We have: 1 ( 1 + g ) t c = β 1 + n ( 1 + g ) t + 1 c ° α k α ° 1 + 1 ° δ ± ( 1 + g ) t c + ( 1 + g ) t + 1 ( 1 + n ) k = ( 1 + g ) t k α + ( 1 ° δ ) ( 1 + g ) t k Simplifying: 1 + g 1 + n 1 β = ° α k α ° 1 + 1 ° δ ± c + ( 1 + g ) ( 1 + n ) k = k α + ( 1 ° δ ) k or: k =
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