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Unformatted text preview: 1 C ONSUMPTION L EISURE F RAMEWORK (C ONTINUED ) F EBRUARY 2, 2011 February 2, 2011 2 C ONSUMER O PTIMIZATION The Graphics of the ConsumptionLeisure Model Consumers decision problem: maximize utility subject to budget constraint bring together both cost side and benefit side Choose c and l subject to Plot budget line Superimpose indifference map At the optimal choice (1 ) 168(1 ) P c t W l t W leisure c slope = (1 t ) W / P 168 optimal choice ( c*,l* ) ( *, *) (1 ) ( *, *) l c u c l t W u c l P CONSUMPTIONLEISURE OPTIMALITY CONDITION key building block of modern macro models MRS (between consumption and leisure) Aftertax real wage Derive consumptionleisure optimality condition using Lagrange analysis IMPORTANT: the larger is (1 t ) W / P , the steeper is the budget line 2 February 2, 2011 3 L AGRANGE A NALYSIS The Mathematics of the ConsumptionLeisure Model Apply Lagrange tools to consumptionleisure optimization Objective function: u ( c , l ) Constraint: g(c,l ) = 168(1 t ) W Pc (1 t ) Wl = 0 Step 1: Construct Lagrange function Step 2: Compute firstorder conditions with respect to c , l , > @ ( , , ) ( , ) 168(1 ) (1 ) L c l u c l t W Pc t Wl O O February 2, 2011 4 L AGRANGE A NALYSIS The Mathematics of the ConsumptionLeisure Model...
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This document was uploaded on 11/01/2011 for the course ECON 325 at Maryland.
 Spring '08
 chugh
 Utility

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