Cobbdouglasexample

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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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%.
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

Ask a homework question - tutors are online