macro economics - Fishers Intertemporal Consumption Model...

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1 Fisher’s Intertemporal Consumption Model Formal Problem: 12 , 22 11 max ( , ) . . CC U C C CY s t C Y rr  This is a constrained maximisation problem. That is, we wish to maximise utility which depends on consumption in periods 1 and 2 respectively, but we are constrained by our intertemporal budget constraint (IBC). Example: Suppose a consumer has the following utility function: 1/2 1 2 1 2 ( , ) = U C C C C . Further suppose that his income is $120 in period 1 and $100 in period 2 and the real interest rate is 25%. Calculate the consumer’s optimal consumption in periods 1 and 2 and his saving in period 1. Using the method of Lagrangean Multipliers, we set up the Lagrangean as follows: 1 2 1 2 1 1 ( , , ) = YC L C C C C Y C     First Order Conditions (FOC) 1 1 0 2 L C (1) 2 1 0 21 L Cr  (2) 0 L (3)
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2 Equations 1, 2 and 3 can be rearranged to show:
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This note was uploaded on 11/12/2011 for the course ECON 2003 taught by Professor Macoeconomics2 during the Spring '10 term at University of the West Indies at Mona.

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macro economics - Fishers Intertemporal Consumption Model...

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