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TAsection04 - d t = l s t for t = 1 2 and k 2 = a 2 we...

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TA section 05 February 27, 2009 Imagine an economy where the representative agent preferences are log c 1 + ° log (1 ° l 1 ) + ± [log c 2 + ° log (1 ° l 2 )] and he or she chooses to decide how much to consume and work in period 1 and 2. The representative agent has a source of income by supplying labor with w 1 and w 2 for period 1 and 2 respectively. In addition, the representative agent chooses to save, a 2 , which has net return of r . Assume there is no initial asset, i.e. a 1 = 0 , and labor supply is normalized so that it cannot exceed 1 .The °rm produces a °nal good that uses labor and capital as input. Labor demand by the °rm is met by labor supply of representative agents and capital demand is also met by saving decision of representative agents, that is l d
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Unformatted text preview: d t = l s t for t = 1 ; 2 and k 2 = a 2 ( we assume k 1 = 0) . The &rm pays rental rate, r , for capital that is &nanced by representative saving asset in period 2 and also w 1 and w 2 for labor wage. The production function of the representative &rm is y = l 1 for period 1 and y 2 = k & 2 l 1 & & 2 with ² < 1 . Problem 1 Formulate the problem of the household. Problem 2 Solve the problem of the household. Problem 3 Formulate and solve the problem of the &rm. Problem 4 Does the &rm have pro&ts in both periods? Proof and explain. Problem 5 Find an equilibrium for this economy: Problem 6 Formulate the social planners problem: Problem 7 Solve the social planners problem: 1...
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