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detailed notes for two period economy

detailed notes for two period economy - International...

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International Macroeconomics 1 Stephanie Schmitt-Groh´ e 2 Mart´ ın Uribe 3 This draft: Spring 2009 1 The seeds for this manuscript were lecture notes taken by Alberto Ramos in a course on International Finance that Mike Woodford taught at the University of Chicago in the Winter of 1994. 2 Columbia University. E-mail: [email protected] 3 Columbia University. E-mail: [email protected]
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Chapter 2 A Theory of Current Account Determination In this chapter, we build a model of an open economy, that is, of an economy that trades in goods and financial assets with the rest of the world. We then use that model to study the determinants of the trade balance and the current account. In particular, we study the response of consumption, the trade balance, and the current account to a variety of economic shocks, such as changes in income and the world interest rate. We pay special attention to how those responses depend on whether the shocks are of a permanent or temporary nature. 2.1 A Two-Period Economy Consider an economy in which people live for two periods, 1 and 2, and are endowed with Q 1 units of goods in period 1 and Q 2 units in period 2. Goods are assumed to be perishable in the sense that they cannot be stored from one period to the next. In addition, households are assumed to be endowed with B * 0 units of a bond. In period 1, these bond holdings generate interest income in the amount of r 0 B * 0 , where r 0 denotes the interest rate on bonds held between periods 0 and 1. In period 1, the household’s income is given by the sum of interest on its bond holdings and its endowment of goods, r 0 B * 0 + Q 1 . The household can allocate its income to two alternative uses: purchases of consumption goods, which we denote by C 1 , and purchases of bonds, B * 1 - B * 0 , where B * 1 denotes bond holdings at the end of period 1. Thus, in period 1 the household faces the following budget constraint: C 1 + B * 1 - B * 0 = r 0 B * 0 + Q 1 . (2.1) 21
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22 S. Schmitt-Groh´ e and M. Uribe Similarly, in period 2 the representative household faces a constraint stating that consumption expenditure plus bond purchases must equal income: C 2 + B * 2 - B * 1 = r 1 B * 1 + Q 2 , (2.2) where C 2 denotes consumption in period 2, r 1 denotes the interest rate on assets held between periods 1 and 2, and B * 2 denotes bond holdings at the end of period 2. As explained in chapter 1, by the no-Ponzi-game constraint households are not allowed to leave any debt at the end of period 2, that is, B * 2 must be greater than or equal to zero. Also, because the world is assumed to last for only 2 periods, agents will choose not to hold any positive amount assets at the end of period 2, as they will not be around in period 3 to spend those savings in consumption. Thus, asset holdings at the end of period 2 must be exactly equal to 0: B * 2 = 0 . (2.3) Combining the budget constraints (2.1) and (2.2) and the terminal condition (2.3) to eliminate B * 1 and B * 2 , gives rise to the following lifetime budget constraint of the household: C 1 + C 2 1 + r 1 = (1 + r 0 ) B * 0 + Q 1 + Q 2 1 + r 1 . (2.4)
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