Marginal products of labor and capital


Discuss the below:

Q: Let f(K,L) be a production function with constants returns to scale, where K denotes capital and L denotes labor.

(a) Show that if we scale both input factors up or down by t>0, the marginal products of labor and capital remain the same.

(b) Show that

f_(11)(K,L)K+f_(12) (K,L)L=0

for all K and L. Here f_(11)=d^2f/dK^2, the second order partial derivative of f with respect to K, and f_(12)=d^2f/dKdL, the second order mixed partial derivative of f with respect to K and L.

 

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Microeconomics: Marginal products of labor and capital
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