## Homogeneity and Profits

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 pro fit function Pi(z). If F is homogeneous of degree k, show that the fi rm will make a pro fit 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