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slides5-handout - Econ407 J. Tessada Spring 2009 Intro...

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Unformatted text preview: Econ407 J. Tessada Spring 2009 Intro Model Equilibrium and Dynamics Comparative Statics The Effects of Government Purchases Econ407 Advanced Macroeconomics Lecture 5: Neoclassical Growth Model, Ramsey Model Jose Tessada University of Maryland - College Park March 3, 5 and 24, 2009 Econ407 J. Tessada Spring 2009 Intro Model Equilibrium and Dynamics Comparative Statics The Effects of Government Purchases Introduction In Solow we assume a fixed, exogenous savings rate However, we know that saving rates are not constant How important is the assumption of constant savings rate? It does affect the transition, but in the long-run the savings rate is indeed constant in equilibrium The model was originally developed by Ramsey (1928), Cass (1965) and Koopmans (1965) In this model we can explicitly derive the evolution of the economy from the interaction between households and firms Econ407 J. Tessada Spring 2009 Intro Model Equilibrium and Dynamics Comparative Statics The Effects of Government Purchases Introduction Households maximize utility and firms choose the combination of inputs given factor prices Prices are then determined in equilibrium in competitive markets We will see the Solow model is a particular case of the Ramsey model Explicit utility maximization = optimal consumption/savings = can study the effects of government policies and how they may affect the incentives to save and invest in physical capital can use the intuition behind the consumers problem to understand some of the results The model still incorporates several simplifying assumptions, but it is a good benchmark to study dynamic macroeconomic models Econ407 J. Tessada Spring 2009 Intro Model Households Firms Market Clearing Equilibrium and Dynamics Comparative Statics The Effects of Government Purchases Households Set-up There is a representative household of size L ( t ) = e nt , n > Population is also given by L ( t ) The household provides labor services (inelastically), earns interest on the assets it owns and decides how much to consume and save each period It maximizes utility subject to a dynamic budget constraint over an infinite horizon Think of household as a dynasty where the current generation cares about the future ones the same way they care about themselves This is called altruistic behavior Denote by C ( t ) total consumption at time t and by c ( t ) C ( t ) / L ( t ) total consumption per capita in a household Econ407 J. Tessada Spring 2009 Intro Model Households Firms Market Clearing Equilibrium and Dynamics Comparative Statics The Effects of Government Purchases Households Set-up Utility is given by U = Z u [ c ( t )] e nt |{z} L ( t ) e- t dt = Z u [ c ( t )] e- ( - n ) t dt (1) The function u ( ) sometimes called felicity function gives the value in utils of a flow of consumption We assume this function to be increasing and concave u ( c ) > 0 and u 00 ( c ) < Also assume it satisfies lim c u ( c )...
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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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slides5-handout - Econ407 J. Tessada Spring 2009 Intro...

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