Lecture_4_February_4

# Lecture_4_February_4 - LOGISTICS Read this week Chapter 2...

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February 4, 2010 1 L OGISTICS Read this week Chapter 2 (static consumption-leisure framework) Read for next week Chapter 3 and Chapter 4 (consumption-savings framework) The foundation for virtually all of the analytical frameworks the rest of the semester Recitations this week Review consumption-leisure framework Work through parts of Practice Problem Set 2 Numerical examples of the consumption-leisure theory

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C ONSUMPTION- L EISURE M ODEL (C ONTINUED ) F EBRUARY 4, 2010
February 4, 2010 3 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 c and l subject to Plot budget line Superimpose indifference map At the optimal choice (1 ) 168(1 ) Pc t Wl t W leisure c slope = -(1- t ) W / P 168 optimal choice ( c*,l* ) ( *, *) ) ( *, *) l c u c l tW u c l P CONSUMPTION-LEISURE OPTIMALITY CONDITION - key building block of modern macro models MRS (between consumption and leisure) After-tax real wage IMPORTANT: the larger is (1- t ) W / P , the steeper is the budget line

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February 4, 2010 4 R EAL W AGE Macro Fundamentals W / P a key variable for macroeconomic analysis Unit Analysis (i.e., analyze algebraic units of variables) Units( W ) = \$/hour of work Units( P ) = \$/unit of consumption Units( W / P ) = Economic decisions depend on real wages ( W / P ), not nominal wages ( W) Measures the purchasing power of (nominal) wage earnings… …which is presumably what people most care about \$ \$ unit of consumption hour of work \$ hour of work \$ unit of consumption unit of consumption hour of work Will sometimes denote using w (lower- case…)
February 4, 2010 5 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 c and l subject to Plot budget line Superimpose indifference map At the optimal choice (1 ) 168(1 ) Pc t Wl t W leisure c slope = -(1- t ) W / P 168 optimal choice ( c*,l* ) ( *, *) ) ( *, *) l c u c l tW u c l P 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- t ) W / P , the steeper is the budget line

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February 4, 2010 6 L AGRANGE A NALYSIS The Mathematics of the Consumption-Leisure Model Apply Lagrange tools to consumption-leisure 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 first-order conditions with respect to c , l , λ Step 3: Solve (with focus on eliminating multiplier) ( , , ) ( , ) 168(1 ) (1 ) L c l u c l t W Pc t Wl ** ( , ) ) ( , ) l l u c l tW u c l P CONSUMPTION-LEISURE OPTIMALITY CONDITION MRS (between consumption and leisure) After-tax real wage
February 4, 2010 7 M ICRO- L EVEL L ABOR S UPPLY Labor Supply in the Micro An experiment:

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## This note was uploaded on 03/08/2011 for the course ECON 602 taught by Professor Chugh during the Spring '11 term at Johns Hopkins.

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Lecture_4_February_4 - LOGISTICS Read this week Chapter 2...

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