By David Romer
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Extra resources for Advanced Macroeconomics Solution Manual
This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 2-24 (24) Solutions to Chapter 2 dk t 1 dk t k t k* (1 ) (1 n)(1 g) (1 ) (1 n)(1 g) . Simplifying further yields dk t 1 (1 )(1 ) (25) . (1 n)(1 g) dk t k t k* Replacing equation (17) by its first-order Taylor approximation around k = k* therefore gives us (26) k t 1 k * (1 )(1 ) (1 n)(1 g) k t k * . Since we can write this simply as (27) k t 1 k* (1 )(1 ) (1 n)(1 g) k t k * , equation (26) implies (28) k t k* (1 )(1 ) (1 n)(1 g) k 0 k * .
1 n)(1 g) (1 n)(1 g) Simplifying yields (1 n)(1 g) (1 ) s (19) k* k * , (1 n)(1 g) (1 n)(1 g) or (20) k*1- = s/(n + g + ng + ). Thus, finally we have (21) k* = [s/(n + g + ng + )]1/(1-). (d) (iii) Using equation (17): dk t 1 s 1 k *1. (22) dk t (1 n)(1 g) (1 n)(1 g) k t k* Substituting the balanced-growth-path value of k* – equation (21) – into equation (22) yields dk t 1 ( n g ng ) 1 s (23) .
This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. Solutions to Chapter 2 s 2-15 ( n g) k * 1 K ( k*) 0 . f ( k*) Thus the saving rate on the balanced growth path is decreasing in . (6) (d) (ii) Citizens in low-, high-k*, high-saving countries do not have the incentive to invest in lowsaving countries.