technology Sets Flashcards
yl > 0
then the firm is planning to have a (positive) net output of good l
yl < 0
then the firm is planning to have a net input of good l. (using up more than it produces)
Y =
technology set
If play y in is in interior of Y then ?
If y on boundary then?
F(y) < 0
F(y) = 0
MRT ( ̄y ) =
the partial derivative of F( ̄y ) with respect to yl divided by the the partial derivative of F( ̄y ) with respect to yk
The marginal rate of transformation at ̄y tells us
how much the firm can increase the net amount of good k it produces if it decreases the net amount of good l it produces by one unit.
vice versa
Single Predefined output q what does z represent?
z = vector of input
Single Predefined output q what does q represent
q = net amount of good produced
Single Predefined output q
assumed output is good L
F(z) gives what that can be produced with what?
maximum output, inputs z
MRTSlk ( ̄z)
= ∂f ( ̄z) /∂zl divided by
∂f ( ̄z) /∂zk
Definition 1: The technology set Y is nonempty if there is at least one feasible
production plan y in Y
Definition 2
The technology set Y is closed if Y is
a closed subset of RL with the standard topology.
Definition 3
The technology set Y satisfies no free lunch if there
is no plan y in Y such that y ≥ 0 and yl > 0 for at least one good l
Definition 4
The technology set Y satisfies the possibility of inaction
if 0 is in Y .
