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tutorial1solutions

# tutorial1solutions - Suggested Solutions to EC2102...

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Suggested Solutions to EC2102 Macroeconomic Analysis I Tutorial 1, Week 3 (January 24-28, 2011) Question 1 ( i ) Let us set up the maximization problem for Mr. j , dropping the superscript j for now. Mr. j wants to max c 1 ;c 2 u ( c 1 ) + °u ( c 2 ) s:t: c 1 + c 2 1 + r = y 1 + y 2 1 + r ° !: Rewriting the lifetime budget constraint, we have that c 2 ( c 1 ) = ( ! ± c 1 ) (1 + r ) : Using the above and the fact that u ( c t ) = p c t for t = 1 ; 2 , Mr j °s maximization problem is just max c 1 p c 1 + ° p ( ! ± c 1 ) (1 + r ) : ( ii ) The F.O.C. to Mr j °s maximization problem in ( i ) , dropping the superscript j , is 1 2 p c ° 1 + ± ° (1 + r ) 2 p ( ! ± c ° 1 ) (1 + r ) = 0 ; (1) which yields c ° 1 = ! ° 2 (1 + r ) + 1 = y 1 (1 + r ) + y 2 ° ° 2 (1 + r ) + 1 ± (1 + r ) : (2) From the ±rst period budget constraint, in equilibrium s ° 1 = y 1 ± c ° 1 = y 1 ± y 1 (1 + r ) + y 2 ° ° 2 (1 + r ) + 1 ± (1 + r ) : From the lifetime budget constraint, in equilibrium, c ° 2 = ( ! ± c ° 1 ) (1 + r ) = ² ° 2 (1 + r ) ° 2 (1 + r ) + 1 ³ [ y 1 (1 + r ) + y 2 ] : 1

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Putting the superscripts back and substituting y A 1 = 10 , y A 2 = 50 , and y B 1 = 50 and y B 2 = 10 ; we have that c A ° 1 = 10 (1 + r ) + 50 ° ° 2 (1 + r ) + 1
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tutorial1solutions - Suggested Solutions to EC2102...

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