229-08-L02a

# 229-08-L02a - Econ 229 Notes L/S Ch.10 P.1 Ljungvist/Sargent Ch.10 Setting N households infinitely-lived No uncertainty(Simplify N=1 all variables

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Econ 229 Notes L/S Ch.10 - P.1 Ljungvist/Sargent Ch.10 Setting: • N households, infinitely-lived. No uncertainty. (Simplify: N=1; all variables per-capita.) • Exogenous series of incomes y t ; exogenous series of tax payments τ t . Exogenous interest rate; R=1+interest rates; initial assets b 0 . Individual Problem • Maximize utility " t t = 0 # \$ u ( c t ) where "# (0,1) , u’>0, u”<0, lim c " 0 u '( c ) = # . Simplify: R = 1/ . • Budget equations (for all t) c t + 1 R b t + 1 " y t # \$ t + b t What constrains individual asset holdings? (1) No Ponzi condition lim T "# R \$ T b t + T = 0 . Assumed (Why?) (2) “Natural” debt limit b t " ˜ b t # \$ R \$ j j = 0 % ( y t + j \$’ t + j ) Follows from (1) & c t " 0 . (3) No debt b t " 0 . Stronger assumption! • Assume b = government bonds or international loans. (If b=capital, b " 0 would be “natural.”)

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Econ 229 Notes L/S Ch.10 - P.2 Optimal choices : • FOC (First order conditions): u '( c t ) = " R # u '( c t + 1 ) => c t = c t + 1
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## This note was uploaded on 12/26/2011 for the course ECON 229 taught by Professor Bohn during the Fall '09 term at UCSB.

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229-08-L02a - Econ 229 Notes L/S Ch.10 P.1 Ljungvist/Sargent Ch.10 Setting N households infinitely-lived No uncertainty(Simplify N=1 all variables

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