A conventional assumption in production theory is free disposal, namely y Y y Y for every y y A technology is said to be monotonic if x V(y) x V(y) for every x x where x x means that xi xi for every i (see example 1 26) Show that free disposal implies that 1 The technology is monotonic and 2 The in...

1 2 Let x E V yThis implies that v x EYLet x x ...

A conventional assumption in production theory is free disposal, namely y Y y Y

Question:

A conventional assumption in production theory is free disposal, namely
y ∈ Y ⇒ yʹ ∈ Y for every yʹ < y
A technology is said to be monotonic if
x ∈ V(y) ⇒ xʹ ∈ V(y) for every xʹ > x
where xʹ > x means that xi > xʹi for every i (see example 1.26). Show that free disposal implies that
1. The technology is monotonic and
2. The input requirement sets are nested, that is, V(yʹ) ⊃ V(y) for every yʹ < y.