Here's the problem
(ii) A rm with production function F(z) buys goods at prices p and sells at price P,
operating at a critical point of its profit function Pi(z). If F is homogeneous of degree k, show that the firm will make a profit if k < 1.
I know that the profit funciton can be written as
Pi(z) = PF(z) - p'z (p' is the transpose of p)
I can also write Pi(tz) = (t^k)PF(z) -tp'z
But i'm not sure how to get that a profit must occur if k< 1....
Any ideas?
Thanks