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Unformatted text preview: Econ407 J. Tessada Spring 2009 Intro Basic Model Tech Progress Growth Rates and Transition Human Capital Conclusions Econ407 Advanced Macroeconomics Lecture 2: Neoclassical Growth Models  The Solow Model Jose Tessada University of Maryland  College Park February 5 and 10, 2009 Econ407 J. Tessada Spring 2009 Intro Motivation Basic Model Tech Progress Growth Rates and Transition Human Capital Conclusions Motivation I In the previous lecture we reviewed some basic facts about economic growth. We will now start studying a simple but yet useful and insightful growth model: the SolowSwan model We will see the role of capital accumulation and technological progress in the process of development The model will deliver important conclusions: Technological progress is the single variable explaining longrun growth It will also help us understand the variables behind differences in income levels Although we will learn a significant amount from this model, more will be needed for a deeper understanding of the process of economic growth Econ407 J. Tessada Spring 2009 Intro Basic Model Setup Steadystate Comparative Statics CobbDouglas Goldenrule Tech Progress Growth Rates and Transition Human Capital Conclusions Production Function I Production function: Y ( t ) = F ( K ( t ) , A ( t ) L ( t )) (1) where K ( t ) is the input of capital, L ( t ) is labor input and A ( t ) is laboraugmenting technological progress Also, F ( ) exhibits constant returns to scale (CRS), i.e., F ( qK , qAL ) = qF ( K , AL ) for all q &gt; 1 Let us assume for now that A ( t ) = 1 t . We will relax this assumption later on. Econ407 J. Tessada Spring 2009 Intro Basic Model Setup Steadystate Comparative Statics CobbDouglas Goldenrule Tech Progress Growth Rates and Transition Human Capital Conclusions Production Function II Define, k = K / L and y = Y / L as capital per worker and output per worker, respectively. (Note: we will maintain this notation throughout our study of economic growth) We can write: 1 L F ( K , L ) = F ( K / L , 1 ) y = f ( k ) . (2) We refer to eq. ( 2 ) as the intensive form of the production function. We assume that f ( ) = 0, f ( k ) &gt; 0, f 00 ( k ) &lt; lim k f ( k ) , lim k f ( k ) 0, where the last conditions are called Inada conditions Econ407 J. Tessada Spring 2009 Intro Basic Model Setup Steadystate Comparative Statics CobbDouglas Goldenrule Tech Progress Growth Rates and Transition Human Capital Conclusions Production Function III Notice that we can write: F ( K , L ) = Lf ( k ) Hence our assumptions imply positive but decreasing marginal product of K : F ( K , L ) / K = L f ( = k z}{ K / L ) K = f ( k ) Econ407 J. Tessada Spring 2009 Intro Basic Model Setup Steadystate Comparative Statics CobbDouglas Goldenrule Tech Progress Growth Rates and Transition Human Capital Conclusions Dynamics of K and L I Labor and total population are equal and grow at a constant rate n L ( t ) = L ( ) e nt...
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 Spring '09
 JOSéTESSADA
 Economics, Macroeconomics, per capita, Capital accumulation, J. Tessada Spring, J. Tessada

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