Given a production function Q = f(K, L) = K0.5L0.5:
a. Derive the marginal product of capital and the marginal product of labor.
b. Derive the second order partial derivatives fKK, fLL, and use their signs to explain whether the Law of Diminishing Returns prevails in the use of capital and labor.
c. Derive the second order partial derivative fKL and use its sign to explain how capital and labor are related (substitutes or complementary to each other).
d. Derive fLK and then combine it with the above result to prove Young's Theorem.