problem 3 show that the cobb douglas production function f k l kal a f
Question
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.]