# lecture5 - Lecture 5 Endogenizing Labor ECN/APEC 7240 V 2...

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Unformatted text preview: Lecture 5 Endogenizing Labor ECN/APEC 7240 V - 2 Endogenizing Labor • Thus far we have always assumed that households supply labor inelastically. – One unit of time corresponds to a forty-hour work week. • We endogenize the labor choice by assuming leisure is also a good that household’s value. • The household has one unit of time to allocate between labor and leisure. – One unit of time now corresponds to a 24-hour day. ECN/APEC 7240 V - 3 Household Problem • The household maximizes subject to - ∑ ∞ = ) 1 , ( t t t t N C u E β t t t t t t K R N W K C + = + + 1 t t t t K N A K F ) 1 ( ) , ( δ- + = t C ≤ 1 ≤ ≤ t N ECN/APEC 7240 V - 4 Leisure Bound • In general, the constraint that labor be nonnegative can be problematic. – There can be corner solutions. – In a lifecycle model, endogenous retirement is possible, as is delayed entry to the work force. • In this representative agent model, there is no output if N t = 0. – In equilibrium, we can ignore corner solutions. ECN/APEC 7240 V - 5 The Bellman Equation • We can formulate the household’s problem recursively. • The Bellman equation is subject to ] | ) ' ), , ( ' , ' ( [ ) 1 , ( max ) , , ( , ' , A A A K K K V E N C u A K K V a a N K C a β +- = K A K R N A K W K C a a ) , ( ) , ( ' + = + C ≤ 1 ≤ ≤ N ECN/APEC 7240 V - 6 First-Order Conditions • Euler equation: • Optimal labor-leisure tradeoff: ] | ) ' 1 , ' ( ) ' ), , ( ' ( [ ) 1 , ( A N C u A A K K R E N C u C a a C- =- β ) , ( ) 1 , ( ) 1 , ( A K W N C u N C u a C L =-- ECN/APEC 7240 V - 7 Balanced Growth Path • We need extrinsic variables to grow at the same rate g . • Intrinsic variables remain constant. – N is also intrinsic....
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lecture5 - Lecture 5 Endogenizing Labor ECN/APEC 7240 V 2...

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