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econ122lec2slides (1) - Econ 122 Lecture 2: Current Account...

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Unformatted text preview: Econ 122 Lecture 2: Current Account Determination Joel M. David UCLA September 8, 2010 Joel M. David (UCLA) Econ 122 Lecture 2: Current Account Determination September 8, 2010 1 / 23 Current Account Determination We will now build a simple but formal model to examine the determinants of the trade balance and current acount. By analyzing the optimal behavior of economic agents, the model provides "microfoundations" for these aggregates. We can then study the response of these variables to various shocks to the economy, such as changes in income and the interest rate. Joel M. David (UCLA) Econ 122 Lecture 2: Current Account Determination September 8, 2010 2 / 23 A Two-Period Economy Consider a small open economy (de&ned below) that lasts for two periods, 1 and 2. Households (HHs) are endowed with Q 1 and Q 2 units of goods in periods 1 and 2, respectively. HHs are endowed with B & units of a bond. In period 1, these bonds generate income r B & , where r is the interest rate on bonds held between periods 0 and 1. HH income in period 1: r B & + Q 1 . In period 1, HH chooses its consumption C 1 and bond purchases B & 1 B & . Joel M. David (UCLA) Econ 122 Lecture 2: Current Account Determination September 8, 2010 3 / 23 Budget Constraint Consumption and bond purchases must equal income in each period: C 1 + B & 1 B & = r B & + Q 1 C 2 + B & 2 B & 1 = r 1 B & 1 + Q 2 No-ponzi-game condition: B & 2 0. HHs will not hold assets at end of period 2, since not around to spend income from those assets, i.e., B & 2 . Thus, B & 2 = Combine equations to get lifetime budget constraint: C 1 + C 2 1 + r 1 = ( 1 + r ) B & + Q 1 + Q 2 1 + r 1 (1) which says the PDV of consumption must equal initial wealth including net interest income plus the PDV of the endowment stream. Joel M. David (UCLA) Econ 122 Lecture 2: Current Account Determination September 8, 2010 4 / 23 Households Preferences are represented by a standard utility function U ( C 1 , C 2 ) . HHs choose consumption C 1 and C 2 to maximize U ( C 1 , C 2 ) subject to the lifetime budget constraint, i.e., to solve max C 1 , C 2 U ( C 1 , C 2 ) s . t . C 1 + C 2 1 + r 1 = ( 1 + r ) B & + Q 1 + Q 2 1 + r 1 Lagrangian L ( C 1 , C 2 , ) = U ( C 1 , C 2 ) + & ( 1 + r ) B & + Q 1 + Q 2 1 + r 1 C 1 C 2 1 + r 1 First-order conditions give U 1 ( C 1 , C 2 ) = ( 1 + r 1 ) U 2 ( C 1 , C 2 ) (2) Intuition: HH is indi/erent between consuming marginal unit in period 1 or purchasing a bond in period 1 and consuming in period 2....
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econ122lec2slides (1) - Econ 122 Lecture 2: Current Account...

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