Problem 3. Show that the Cobb-Douglas production function, F(K; L) = KaL¹-a (for K; L> 0 and

0 < a < 1) satisfies the following properties. Hint: The derivative of rª with respect to x is axª-¹.

a) is increasing in each input. [Hint: Show that the partial derivative regarding each input is positive];

b) has constant returns to scale; for every > 0.

c) Has diminishing returns to L holding K constant. [Hint: take the second partial derivative of F respect

to L and check that is negative.]