GrowthModel09 - One-Sector Growth Model Notes 1 The...

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One-Sector Growth Model Notes 1 The representative household's problem The representative household enjoys consumption and leisure time in all periods t = 0, 1,. .., f . The household has no exogenous income, but it has fixed time endowments in each period, h , and an initial capital endowment, 0 K . Assume that the household's utility function is time-separable, and takes the form 01 01 0 (,, . ,,, ) (, ) t tt t UC C L L uC h L E f ± ¦ where t C and t hL ± denote consumption leisure in period t , u(·,·) is a period utility function which is strictly increasing, strictly concave and satifies the Inada Conditions ( 0 lim ( , ) , lim ( , ) Ct t Lt t CL h uCh L oo ± f ± f ; these help ensure that the solutions are interior). (0,1) ² is the household 's discount factor . 1.1 The household's investment decision and its budget constraints The household makes investment decisions to increase its initial capital stock over time. The law of motion for capital is given by: 1 (1 ) , 0,1, ., t KK I t G ³ ±³ f where (0,1) ² depreciation rate , t I denotes investment in period t. In all periods, the household has capital t K rents it to the firm at a rental rate t r . After the firm uses the capital, it returns the remaining stock (1 ) t K ± to household. Once we include investment t I , the household gets the next period's capital stock 1 t K ³ .
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This note was uploaded on 09/21/2011 for the course ECON 3102 taught by Professor Econ during the Summer '10 term at University of Minnesota Crookston.

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GrowthModel09 - One-Sector Growth Model Notes 1 The...

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