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Unformatted text preview: Foundations of International Macroeconomics 1 Workbook 2 Maurice Obstfeld, Kenneth Rogo f , 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 is given by k t +1 = (1 + r t ) k t + w t c t (where 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 = . 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 f ect eq. (33) in the text: c t +1 = [1 + f ( k t +1 )] [ c t n (1 ) k t +1 ] . (2) 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 75 (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 is reached at lower levels of c and k. The decline in k represents a &crowding out e f ect of balanced-budget government spending. (c) As can be seen in & gure 7.2, the impact e f ect of the announcement is an immediate decline in consumption from c 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...
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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.
- Winter '08