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.