notes_macro_ch3 - MACROECONOMICS Georgios Karras University...

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Macro Notes © G.Karras 2010 MACROECONOMICS Georgios Karras* University of Illinois at Chicago * Professor of Economics; Mailing Address: Department of Economics, University of Illinois at Chicago, 601 S. Morgan St., Chicago, IL 60607-7121; e-mail: [email protected] . Lecture Draft Do not cite without permission
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Macro Notes © G.Karras 2010, p.2 ││ 3 ││ THE PRODUCTION FUNCTION & THE LABOR MARKET 3.1. The Production Function Algebraically, a production function is: { { { { ) , ( labor capital ty productivi r multifacto GDP real N K F A Y = Production Process GDP ( Y ) Output Labor ( N ) Capital ( K ) Other Inputs
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Macro Notes © G.Karras 2010, p.3 Example: A “Cobb-Douglas” Production Function = 7 . 0 3 . 0 N K A Y { ( ) ( ) 3 2 1 3 2 1 3 2 1 growth labor growth capital growth MFP growth real N K A Y Δ + Δ + Δ = Δ % 7 . 0 % 3 . 0 % % Interpretation: 0.3: labor elasticity; 0.7: capital elasticity % 10 % 10 by Y by A fixed N and K ⎯→ % 3 % 10 by Y by K fixed N and A % 7 % 10 by Y by N fixed K and A
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Macro Notes © G.Karras 2010, p.4 Implication: 7 . 0 income total income labor share labor = = = Y N w 3 . 0 income total income capital share capital = = = Y K r Î Labor and capital shares independent of K/Y ratio Evidence?
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Macro Notes © G.Karras 2010, p.5
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Macro Notes © G.Karras 2010, p.6 3.2. The Production Function with Respect to Labor Marginal Product of Labor ( MPN ): N Y MPN Δ Δ = MPN : how much Y goes up when N increases by one unit The Production Function with respect to labor: Assume A and K are held constant – only N is allowed to vary: ( ) 7 . 0 3 . 0 7 . 0 3 . 0 N AK Y N K A Y = = Two properties: (1) positive slope Î MPN > 0, and (2) curve flattens out Î MPN is diminishing
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Macro Notes © G.Karras 2010, p.7 0 Y = ( AK 0.3 ) N 0.7 N (number of workers) Y (real GDP) 50m 100m 150m $5tr $8tr $10tr A B C
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Macro Notes © G.Karras 2010, p.8 Property #1: N Y Î positive slope Î MPN > 0 Property #2: curve is concave Î diminishing MPN 0A range: ker 000 , 100 $ 0 50 0 $ 5 $ 0 wor per m tr N Y MPN A = = Δ Δ = AB range: ker 000 , 60 $ 50 100 5 $ 8 $ wor per m m tr tr N Y MPN AB = = Δ Δ = BC range: ker 000 , 40 $ 100 150 8 $ 10 $ wor per m m tr tr N
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notes_macro_ch3 - MACROECONOMICS Georgios Karras University...

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