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21 (a) The individual has utility function given by C1,t 1 C 2 ,t 11    1. (1) 1  1  The constraints expressed in units of money are (2) Pt C1,t  Pt A  M dt , and (3) Pt 1C 2 ,t 1  M dt . Combining equations (2) and (3) yields the lifetime budget constraint: (4) Pt C1,t  Pt 1C 2 ,t 1  Pt A . Note that  < 1 means that the elasticity of substitution, 1/, is greater than one. Thus when the rate of return on saving increases, the substitution effect dominates; the individual will consume less now and save more.

Dividing both sides of (26) by ALt+1 to convert this into units of effective labor, and using equation (25) yields © 2012 by McGraw-Hill Education. 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. 2-28 Solutions to Chapter 2  1   1  T  1  T  ,   (27) k t 1   w t      1  n   2    A  1  n  A which simplifies to (28) k t 1  1  1  n  1  2    w t .

C  0 [until t1] c  0 [after t1] B A The economy moves off to the northwest until at t1 , it is right at point B on the new saddle path. The tax is then put in place and the system is governed by the new c  0 locus. Thus c begins falling. The economy moves down the new saddle path, eventually reaching point ENEW . E k  0 ENEW k*NEW k* k (e) The story in part (d) implies the following time paths for consumption per unit of effective labor and capital per unit of effective labor. © 2012 by McGraw-Hill Education.

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Advanced Macroeconomics Solution Manual by David Romer

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