Cobbdouglasexample

# Cobbdouglasexample - (II Marginal Products MPL = M y M L =...

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Econ 464 Example of Cobb Douglas Production Function The Cobb Douglas production function : y = F(K, L) = K " L 1- " where 0< " <1 has all the properties we assumed in the H-O Model. We will let " = 1/3 in this example so: y = K 1/3 L 2/3 (I) Returns to scale: constant Proof: Let 8 be any positive number, then F( 8 K, 8 L) = ( 8 K) 1/3 ( 8 L) 2/3 = 8 1/3 K 1/3 8 2/3 L 2/3 = 8 1/3+2/3 K 1/3 L 2/3 = 8 K 1/3 L 2/3 = 8 F(K,L), We have shown that if % ) K= % ) L then % ) y=% ) K= % ) L Ex: Let 8 =1.10, in this case both L and K increase by 10 %. As a result y increases by 10%. Let 8 =0.50, in this case both L and K decrease by 50 %. As a result y decreases by 50%.
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Unformatted text preview: (II) Marginal Products MPL = M y/ M L = 2/3 L 2/3-1 K 1/3 = 2/3 (K/L) 1/3 MPK = M y/ M K = 1/3 K 1/3-1 L 2/3 = 1/3 (L/K) 2/3 Implications: If K constant, increases in L decrease MPL (standard negative sloped MPL curve). If L constant, increases in K decrease MPK (standard negative sloped MPK curve). If K/L increases, then MPL increases and MPK decreases. If MPL increases, then K/L has increased. If MPK increases, then K/L has decreased....
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## This note was uploaded on 08/08/2008 for the course ECON 464 taught by Professor Maria during the Spring '08 term at University of Wisconsin.

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