SLIDE 4

# SLIDE 4 - CONSUMPTION-LEISURE FRAMEWORK (CONTINUED)...

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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 Consumption-Leisure Model ± Consumer’s decision problem: maximize utility subject to budget constraint – bring together both cost side and benefit side ± Choose ! and # subject to ± Plot budget line ± Superimpose indifference map ± At the optimal choice (1 ) 168(1 ) P ct W l t W ± ² ² leisure c slope = -(1- \$ ) % / & 168 optimal choice ( !'(#' ) (* ,* ) ) ) l c uc l tW ucl P ² CONSUMPTION-LEISURE OPTIMALITY CONDITION -key building block of modern macro models MRS (between consumption and leisure) After-tax real wage Derive consumption-leisure optimality condition using Lagrange analysis IMPORTANT: the larger is (1- \$ ) % / & , the steeper is the budget line

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2 February 2, 2011 3 L AGRANGE A NALYSIS The Mathematics of the Consumption-Leisure Model ± Apply Lagrange tools to consumption-leisure optimization ± Objective function: ! ( " , # ) ± Constraint: \$%"&# ) = 168(1- ' ) ( * +" * (1- ' ) (# , - ± Step 1: Construct Lagrange function ± Step 2: Compute first-order conditions with respect to " , # , Ǌ > @ (,, ) (,) 168 ( 1 ) ( Lcl ucl tW Pc tW l OO ± ² ² ² ² February 2, 2011 4 L AGRANGE A NALYSIS ± Apply Lagrange tools to consumption-leisure optimization ± Objective function: ! ( " , # ) ± Constraint: \$%"&#
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## This note was uploaded on 10/25/2011 for the course ECON 325 taught by Professor Chugh during the Spring '08 term at Maryland.

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SLIDE 4 - CONSUMPTION-LEISURE FRAMEWORK (CONTINUED)...

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