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(K^0.75/L^0.75)/2 = (3L^0.25/K^0.25)/10

 

MPL/W = MPK/ R

 

What ratio of capital to labor minimizes jakes cost?

 Nov 16, 2014

Best Answer 

 #1
avatar+118723 
+5

$$\\(K^{0.75}/L^{0.75})/2 = (3L^{0.25}/K^{0.25})/10\\\\
5(K^{0.75}/L^{0.75}) = 3L^{0.25}/K^{0.25}\\\\
5(K/L)^{0.75} = 3(L/K)^{0.25}\\\\
5(K/L)^{0.75}= 3(K/L)^{-0.25}\\\\
$Let $ R=K/L\\\\
5(R^{0.75}) = 3(R)^{-0.25}\\\\
(R^{0.75})/(R)^{-0.25} = 3/5\\\\
R^1=3/5\\
r=3/5$$

 

I don't know about the minimize bit.

I just get the ratio of K to L  is  3:5

 Nov 17, 2014
 #1
avatar+118723 
+5
Best Answer

$$\\(K^{0.75}/L^{0.75})/2 = (3L^{0.25}/K^{0.25})/10\\\\
5(K^{0.75}/L^{0.75}) = 3L^{0.25}/K^{0.25}\\\\
5(K/L)^{0.75} = 3(L/K)^{0.25}\\\\
5(K/L)^{0.75}= 3(K/L)^{-0.25}\\\\
$Let $ R=K/L\\\\
5(R^{0.75}) = 3(R)^{-0.25}\\\\
(R^{0.75})/(R)^{-0.25} = 3/5\\\\
R^1=3/5\\
r=3/5$$

 

I don't know about the minimize bit.

I just get the ratio of K to L  is  3:5

Melody Nov 17, 2014

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