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ch7ans - Foundations of International Macroeconomics1...

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Foundations of International Macroeconomics 1 Workbook 2 Maurice Obstfeld, Kenneth Rogo ff , and Gita Gopinath Chapter 7 Solutions 1. (The word °equiproportionate± in the third line of the statement of this exercise should be °lump-sum.±) (a) With the introduction of tax- ° nanced government spending in the Weil (1989a) model, the period budget constraint for a family of vintage υ is given by k υ t +1 = (1 + r t ) k υ t + w t τ c υ t (where τ is the lump-sum tax) instead of by eq. (30) in Chapter 7. We write the above expression in average per capita terms as k t +1 k t = f ( k t ) c t g 1 + n nk t 1 + n , (1) giving the analog of eq. (32) in the chapter. Here we have used the balanced- budget constraint g = τ . The introduction of government expenditure there- fore shifts the k = 0 locus down by g/ (1 + n ) in the phase diagram for per capita consumption and the capital-labor ratio ( ° gure 7.7 on p. 449). The presence of tax- ° nanced government spending does not a ff ect eq. (33) in the text: c t +1 = [1 + f 0 ( k t +1 )] [ β c t n (1 β ) k t +1 ] . (2) 1 By Maurice Obstfeld (University of California, Berkeley) and Kenneth Rogo ff (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 ff Book.html 75

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(b) Figure 7.1 shows the phase diagram. In that ° gure, an unanticipated permanent rise in g shifts the k = 0 schedule down. At the instant the shock occurs, consumption declines immediately from point A to point B . In subsequent periods, there is a gradual decumulation of capital, and con- sumption continues to decline until the new steady state A 0 is reached at lower levels of fl c and fl k. The decline in fl k represents a °crowding out± e ff ect of balanced-budget government spending. (c) As can be seen in ° gure 7.2, the impact e ff ect of the announcement is an immediate decline in consumption from c 0 to c 1 . The economy then moves along an °unstable± path relative to the initial steady state. Along that path, c gradually declines while k increases until the economy reaches point D on date T . Point D lies on the stable path corresponding to the new constant level of g . After date T , c and k
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ch7ans - Foundations of International Macroeconomics1...

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