Chapter8_NeoclassicalGrowth

Chapter8_NeoclassicalGrowth - Neoclassical Growth Model Juan

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Unformatted text preview: 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 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 . 3 Technology grows at a constant rate g . We have A t = ( 1 + g ) t A . Growth is exogenous. We can use the social planner&s problem to study the equilibrium path. Juan Rubio-Ramrez (DUKE) Neoclassical Growth Model February 10, 2009 2 / 24 Neoclassical Growth Model II Social Planner&s problem in per capita terms: max t = t log c t s.t. c t + ( 1 + n ) k t + 1 = k t & ( 1 + g ) t 1 & + ( 1 & ) k t where l = 1 and A = 1. Parameters: , n , g , , and . Juan Rubio-Ramrez (DUKE) Neoclassical Growth Model February 10, 2009 3 / 24 FOCs First order conditions: 1 c t = 1 + n c t + 1 & k & 1 t + 1 ( 1 + g ) t + 1 1 & + 1 & c t + ( 1 + n ) k t + 1 = k t ( 1 + g ) t 1 & + ( 1 & ) k t Juan Rubio-Ram&rez (DUKE) Neoclassical Growth Model February 10, 2009 4 / 24 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 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....
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Chapter8_NeoclassicalGrowth - Neoclassical Growth Model Juan

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