ch4ans - Foundations of International Macroeconomics 1...

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Unformatted text preview: Foundations of International Macroeconomics 1 Workbook 2 Maurice Obstfeld, Kenneth Rogo f , and Gita Gopinath Chapter 4 Solutions 1. We follow closely the steps outlined in section 4.3.2. Equations (12) and (17) in the book remain unaltered. So does steady-state budget constraint (11), so that b Z = l & w, as before. In the traded goods sector the zero pro & t condition can be written as f k t E t ! F k t E t , 1 ! = r k t E t + w E t (1) where k K/L . Log-di f erentiation of eq. (1) yields, f k t E t ! k t E t & k t & E t = r k t E t & k t & E t + w E t & w & E t . (2) The & rst order condition for capital in the traded goods is f ( k t /E t ) = r. Substitution of this equality into eq. (2) above reduces it to & w = & E t . (3) Since b Z = l & w , the last equality implies b Z = l & E t . (4) Log di f erentiating the zero-pro & t condition for nontradables, pA n g ( k n ) = rk n + w , with A n and r constant, we obtain & p = & ln & w [recall the displayed 1 By Maurice Obstfeld (University of California, Berkeley) and Kenneth Rogo f (Prince- ton University). c & MIT Press, 1996. 2 c & MIT Press, 1998. Version 1.1, February 27, 1998. For online updates and correc- tions, see http://www.princeton.edu/ObstfeldRogo f Book.html 35 equation following eq. (8) in Chapter 4]. Since & ln = 1 in section 4.3.2, eq. (3) above implies & p = (1 ) & E t Substituting eqs. (4) and (5) above into equation (17) of Chapter 4, we express the change in steady state nontradables consumption as b F C n = { l (1 ) [ + (1 )] } & E t . Similarly we can solve for b L n as, b L n = { l (1 ) [ + (1 )] } & E t . (6) The sign of b L n is still ambiguous, as discussed on p. 224 in the book. Indeed, eq. (6) here looks precisely like eq. (18) of Chapter 4, with the only di f er- ence that & E t appears in place of & A t /& lt . Thus, the assumption of Harrod- neutral instead of Hicks-neutral technological change makes no di f erence for the likelihood that faster productivity growth causes a labor exodus from the tradables sector. 2. This is an intricate problem, so it is useful to start with an exceedingly simple case and gradually generalize it. irst, suppose that consumption preferences are of the Leontief type (with & xed consumption proportions of the two goods) and that technologies also are Leontief. Since nontradables are relatively labor intensive, a rise in r lowers their relative price in terms of tradables, p, and lowers the tradables wage, w . In the special case were now considering, the sole e f ect of that change is to atten the GNP line (by lowering p ) and to shift its vertical intercept: upward if w ( r ) L + F Q > 0, downward in the opposite case (the & rst case occurring, despite the inequality w ( r ) < 0, if & nancial wealth is su ciently high). The income expansion path stays put due to the assumed Leontief preferences. How can we be certainstays put due to the assumed Leontief preferences....
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ch4ans - Foundations of International Macroeconomics 1...

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