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# tutorial1questions - ii Using i solve for Mr A and B&s...

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EC2102 Macroeconomic Analysis I Tutorial 1, Week 3 (January 24-28, 2011) Question 1 Consider an economy which consists of only two individuals, Mr A and Mr B . They each live for 2 periods only; they are both young in period 1 and old in period 2, and they die at the end of period 2. The lifetime utility function of Mr j , j 2 f A; B g , is U ( c j 1 ; c j 2 ) = u ( c j 1 ) + °u ( c j 2 ) ; where the subscript denotes period t; t = 1 ; 2 , and Mr j °s per period utility function is u ( c j 1 ) = q c j 1 and u ( c j 2 ) = q c j 2 . Mr A and B can borrow and lend freely at a real interest rate of r . Let us denote y j t as the endowment of Mr j at time t; j 2 f A; B g . These endowments are expressed in real terms as units of consumption goods. Let y A 1 = 10 , y A 2 = 50 , and y B 1 = 50 and y B 2 = 10 : ( i ) Write down Mr A and B °s maximization problems.
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Unformatted text preview: ( ii ) Using ( i ) solve for Mr A and B &s optimal consumption and savings choices ( c j & 1 ; c j & 2 ; s j & 1 ; s j & 2 ) , j 2 f A; B g : ( iii ) Using indi/erence curves and the Lifetime Budget Constraint, draw the en-dowment point, and illustrate your solution to Mr A &s maximization problem. Do the same for Mr B . Explain what a First Order Condition is and its role in an individual&s utility maximization problem. ( iv ) Show mathematically, for period 1, that Mr A and Mr B both have a marginal propensity of consuming out of current income that is strictly less than 1. 1...
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