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Unformatted text preview: Lecture 5 The CassKoopmans Model ECON 7240 V  2 Reasons to Endogenize Saving • Positive – To see how policy variables affect saving and consequently growth • Normative – What is the optimal saving rule? – Can we do better than a constant saving rule? ECON 7240 V  3 Production Sector • We assume there are a large number of firms. • Each has a production function Y = F ( K , AL ). – We assume F has the same properties as in the Solow model. • A grows exogenously: g t A dt d = ) ( ln ECON 7240 V  4 Firm Behavior • Firms maximize profits, hiring labor and renting capital in competitive markets. – Let W ( t ) be the marketdetermined real wage at t . – The marketdetermined net rental rate of capital at t is r ( t ). – Capital depreciates at the rate δ , so the firm must pay the gross rate r ( t ) + δ to owners of capital. ECON 7240 V  5 Profit Maximization • The firm hires K and L to maximize • Firm will hire inputs to satisfy firstorder conditions • Realized profits are always zero. • This implies the incomeproduct identity : ). ( ) ) ( ( ) ( ) ( )) ( ) ( ), ( ( ) ( t K t r t L t W t L t A t K F t δ + = Π δ = )) ( ( ' ) ( t k f t r ))) ( ( ' ) ( )) ( ( )( ( ) ( t k f t k t k f t A t W = ) ( ) ) ( ( ) ( ) ( ) ( t K t r t L t W t Y δ + + = ECON 7240 V  6 Household Sector • We assume there is a large number H of households. • The total population L ( t ) grows exogenously: – Each household has L ( t )/ H individuals. • Every person supplies one unit of labor inelastically to the market. n t L dt d = ) ( ln ECON 7240 V  7 Rational Paradigm • We assume that households are rational. – They have preferences over all possible allocations of consumption. – Among those consumption bundles that are feasible, they choose the one they prefer the most. • We specify preferences by positing a utility function. – If the household prefers bundle A to bundle B , U ( A ) ≥ U ( B ). ECON 7240 V  8 Utility Function • The household lives forever and maximizes – C ( t ) is the flow of consumption to each member of the household at t ....
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This note was uploaded on 01/09/2011 for the course ECON 7230 taught by Professor Feigenbaum during the Spring '10 term at Utah Valley University.
 Spring '10
 Feigenbaum
 Macroeconomics

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