Consider a competitive firm with a constant returns to scale technology Y n (example 1.101). Let f (p, y) = I pi yi denote

Consider a competitive firm with a constant returns to scale technology Y ⊆ ℜn (example 1.101). Let f (p, y) = ∑I pi yi denote the net revenue (profit) of adopting production plan t with prices p.
1. If production is profitable at prices p, that is, there exists some y ∊ Y such that f(y, p) > 0, then Π(p) = + ∞.
2. Show that the profit function takes only three values, that is, for every p ∊ ℜ0+,
Π(p) = 0 or Π(p) = + ∞ or Π(p) = - ∞