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 .
Definition 5
The technology set Y satisfies free disposability if Y is
comprehensive, that is, if whenever y is in Y and yl ≤ y then yl is in Y
Definition 6
The technology set Y satisfies irreversibility
if whenever y is in Y and y / 0 then y is not in Y .
“no free lunch”
suggests that things that appear to be free will always have some hidden or implicit cost to someone, even if it is not the individual receiving the benefit.
Inaction
Action is taken infrequently, and adjustments are large when they occur.
disposability
the inputs can be increased by the same factor which keeps their relative proportions unchanged.
