Another conventional (and trivial) assumption on technology cited by Debreu (1959, p. 41) is 0 Y,

Question:

Another conventional (and trivial) assumption on technology cited by Debreu (1959, p. 41) is 0 ∈ Y, which he calls the possibility of inaction. Show that the three assumptions
convexity Y is convex
additivity Y + Y ⊆ Y
possibility of inaction 0 ∈ Y
together imply that the technology exhibits constant returns to scale.