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Unformatted text preview: Suggested Solutions to EC2102 Macroeconomic Analysis I Tutorial 1, Week 3 (January 2428, 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...
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This note was uploaded on 01/18/2012 for the course ECONOMICS 2102 taught by Professor Tan during the Spring '11 term at National University of Singapore.
 Spring '11
 Tan

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