ch10ans - Foundations of International Macroeconomics1...

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Foundations of International Macroeconomics 1 Workbook 2 Maurice Obstfeld, Kenneth Rogo f , and Gita Gopinath Chapter 10 Solutions 1. (a) With a positive steady-state gross money supply growth rate of 1+ & , eq. (26) in Chapter 10 is replaced by m 0 = m 0 = χ 1 1 (1 + & )(1+ δ ) y 0 , (26 0 ) where (for this problem only) m M/P denotes the real money supply. The value for y 0 is the same as in the case with zero steady-state money growth. The log-linear version of the money demand equation becomes m real ,t = c t δ (1 + & δ ) 2 (1 + δ ) r t +1 1 (1 + & δ ) 1 p t +1 , (37 0 ) where m real ,t =d m t / m denotes the percentage deviation of real money bal- ances from their steady-state level, p t [( P t /P t 1 ) / (1+ & )] 1 denotes the percentage deviation of in & ation from its (gross) steady-state level of 1 + & , and the other variables are as de ± nedinthetext . Thefore igncoun terpart to (37 0 )is m real ,t = c t δ (1 + & δ ) 2 (1 + δ ) r t +1 1 (1 + & δ ) 1 p t +1 . (38 0 ) 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 109
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Denote by & t (a boldface & ) the percentage deviation of nominal money growth from its steady-state value . Note that & t = m real ,t + p t . Also, by consumption-based purchasing power parity, p t = p t + e t , where e t is the percentage deviation of the growth rate of the nominal exchange rate, E t / E t 1 , from its initial date-zero steady-state value of unity (recall that & = & ). It is then possible to derive & t & t e t = c t c t c t 1 c t 1 · 1 (1 + & )(1+ δ ) 1 ( e t +1 e t ) . (39 0 ) Solutions for steady-state equilibrium in & ation and nominal exchange rate growth follow immediately from eqs. (37 0 )-(39 0 ): & p =0 , (50 0 ) & p , (51 0 ) & & = e . (52 0 ) (b) Assume a permanent unanticipated rise in the home rate of money growth occurring on date 1, with prices preset a period in advance and adjusting to their & exible-price level after one period, absent new shocks. Given that in the initial steady state the exchange rate is expected to remain constant (because initially, & = & ), it follows that e = e , where e is the percentage deviation of the nominal exchange rate from its preshock steady state level&i.e., its level along the economy±s steady-state 110
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path. (As in the text, sans serif variables with overbars denote new post- shock steady-state values, for period 2 and beyond. Variables without bars denote postshock date 1 values; thus e e 1 e 0 .) Note that e can also be interpreted as the percentage by which the nominal exchange rate would change on impact if prices were fully & exible, so that e = e flex , (That is, e is the percentage deviation of E from its pre-shock steady state level, with E being the nominal exchange that would obtain on impact if output prices were fully & exible. ) It is then possible to rewrite eq.
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This note was uploaded on 10/21/2009 for the course ECON ECONOMICS taught by Professor Yu-chinche during the Winter '08 term at University of Washington.

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ch10ans - Foundations of International Macroeconomics1...

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