Tutorial3solutions - Suggested Solutions to EC2102 Macroeconomic Analysis I Tutorial 3 Week 6(February 14-18 2011 Question 1(i First period budget

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Suggested Solutions to EC2102 Macroeconomic Analysis I Tutorial 3, Week 6 (February 14-18, 2011) Question 1 ( i ) First period budget constraint is: C 1 + S 1 = w 1 ( h l 1 ) : Second period budget constraint is: C 2 = w 2 ( h l 2 ) + (1 + r ) S 1 Combining the two period budget constraints, we get the lifetime budget constraint (LBC): C 1 + C 2 1 + r = w 1 ( h l 1 ) + w 2 ( h l 2 ) 1 + r : ( Note : This question is a partial equilibrium question, as it only says that the consumer takes w t and r t as given. If you were to think of this question as having a gets dividends, and if you wrote the above budget constraints with dividends, that is correct also.) ( ii ) Expressing C 1 as a function of C 2 ; l 1 ; l 2 from LBC: C 1 = w 1 ( h l 1 ) + w 2 ( h l 2 ) 1 + r C 2 1 + r ( 1 ) Hence, his utility maximization problem is: max C 2 ;l 1 ;l 2 u ( C 1 ( C 2 ; l 1 ; l 2 ) ; l 1 ) + ( C 2 ; l 2 ) where C 1 = w 1 ( h l 1 ) + w 2 ( h l 2 ) 1 + r C 2 1 + r 1
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( iii ) max l 1 ;l 2 ;C 2 u ( C 1 ( C 2 ; l 1 ; l 2 ) ; l 1 ) + ( C 2 ; l 2 ) C 1 = w 1 ( h l 1 ) + w 2 ( h l 2 ) 1 + r C 2 1 + r F:O:C: ( l 1 ) : u 1 ( C 1 ; l 1 ) @C 1 @l 1 + u 2 ( C 1 ; l 1 ) = 0 ( 2 ) , u 1 ( C 1 ; l
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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.

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Tutorial3solutions - Suggested Solutions to EC2102 Macroeconomic Analysis I Tutorial 3 Week 6(February 14-18 2011 Question 1(i First period budget

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