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TAsection05sol_extension

# TAsection05sol_extension - TA section 05 April 5 2009 The...

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Unformatted text preview: TA section 05 April 5, 2009 The representative household maximizes following lifetime utility 1 X t =0 & t [log c t + Â¡ log (1 & l t )] This household determines how much to consume, own capital and supply labor each period and source of income is the wage according to supply of labor, the rental rate from lending capital to &rms, and pro&ts earned from owning the share of the intermediate good producing &rm. There is no population growth in this economy. Labor supply is allocated to two sectors, intermediate good sector and research sector. However, household only determines the total level of labor supply since wages from two sectors are same and do not di/er in utility. Problem 1 Formulate the problem of the household. Solution 2 max c t ;k t +1 ;l t U = 1 X t =0 & t [log c t + Â¡ log (1 & l t )] s.t. c t + k t +1 = w t l t + (1 + r t ) k t + Z A t Â¢ t ( i ) di Problem 3 Derive FOCs of the household problem. Solution 4 The Lagrangian is: L = 1 X t =0 & t " log c t + Â¡ log (1 & l t ) + Â£ t w t l t + (1 + r t ) k t + Z A t Â¢ t ( i ) di & c t & k t +1 !# 1 with FOCs: 1 c t = & t Â¡ 1 & l t = & t w t & t = Â¢& t +1 (1 + r t +1 ) c t + k t +1 = w t l t + (1 + r t ) k t + Z A t Â£ t ( i ) di Final good producing &rm is competitive producer, i.e. takes all of prices as given and selectFinal good producing &rm is competitive producer, i....
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