For the Cobb-Douglas production function in Problem 6.7, it can be shown (using calculus) that MPK =

Question:

For the Cobb-Douglas production function in Problem 6.7, it can be shown (using calculus) that
MPK = aKa-1 Lb
MPL = bKa Lb-1
If the Cobb-Douglas exhibits constant returns to scale (a þ b ¼ 1), show that
a. Both marginal productivities are diminishing.
b. The RTS for this function is given by
RTS = bK/aL
c. The function exhibits a diminishing RTS.