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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 Solow-Swan 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 long-run 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 Set-up Steady-state Comparative Statics Cobb-Douglas Golden-rule 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 labor-augmenting technological progress Also, F ( ) exhibits constant returns to scale (CRS), i.e., F ( qK , qAL ) = qF ( K , AL ) for all q > 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 Set-up Steady-state Comparative Statics Cobb-Douglas Golden-rule 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 ) > 0, f 00 ( k ) < 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 Set-up Steady-state Comparative Statics Cobb-Douglas Golden-rule 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 Set-up Steady-state Comparative Statics Cobb-Douglas Golden-rule 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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This note was uploaded on 03/08/2009 for the course ECON 407 taught by Professor Josétessada during the Spring '09 term at Maryland.

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slides2-handout - Econ407 J. Tessada Spring 2009 Intro...

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