Intermediate Micro, Fall 2019

1. Production Fundamentals
'
Cost minimizing input blend :
f '
Az =
W'
lwz
'
Production Function :
y
= f CX . , Xz ,
. . .
,
Xn ) is the ( if using both goods )
amount of output , y ,
that can be
efficiently .tk/Wk=f4WL L
marginal productivity per
produced using X . . Xz ,
. . .
,
Xn dollar spent )
.
Efficient Production :
given inputs ,
firm produces Cost Minimization
largest amount of output possible
.
L =
W , X ,
t
Wz Xz t X ( q
-
f- LX , ,
Xz )
.
NO free lunch :
impossible to produce output
-
Factor Demand Function :
specifies
w/o using inputs relationship btw
prices of input goods ,
'
Possibility of inaction :
Xi 20 quantity of output produced . E amount
'
Free disposal :
inputs can be disposed of at no Of an input good a firm will select
cost ; dfldxi O for every input
.
Total Cost =
w , X , t Wzxz
.
Decreasing Returns to scale :
a production set
.
Cost Function :
Clq ,
w , , wz ) =
displays decreasing returns to scale if fctxlctfcx ) W , X ,
( q .
W , ,
Wz ) t Wz Xz ( q ,
w , ,
Wz )
for all t 71 Where Xn ( q . W .
,
Wz ) are the firm 'S
.
Increasing Returns to Scale :
f Ctx ) > tf Cx ) factor demand functions
.
Constant Returns to Scale : f Lt X ) =
tf Cx )
.
Market Demand Function :
sum of
'
Cobb -
Douglas Production Function : FCK ,
L ) = aka L
's
individual demand functions ( be
↳
If a t BC I →
decreasing careful of corner solutions ! )
↳ If a t B > I →
increasing Profit Maximization
-
Fixed Proportions Production Function :
.
IT L p ) =p Dcp ) -
C L Dcp ) )
f Lk ,
L ) =
min Lak ,
BL )
.
IT ( q )
=p L q ) q
-
C Cq )
.
Linear Production Function :
perfect subs ,
'
IT =p ( q )
q
-
C Cq ) Marginal
f- C K ,
L ) =
a K t
BL
=
Req ) -
C C q ) Revenue =
.
No monotonic transformations for production R
'
( q ) -
C
'
( 91=0 Marginal
functions ! R
'
( q ) =
C
'
(
q ) Cost
.
15090 ants :
graphical set of bundles that allow
.
DIT 1dg =p C q ) t
p
'
( q )
q
-
C
'
( q ) =
O
a firm to produce the same level of output
.
Marginal Rate of Technical substitution
'
lE÷pI=
-
¥
-
To =
=L
( MRTS × , , xz ) :
Max amount of input 2 firm .
p =
MC ( Markup
=
¥ )
would be willing to give up to get one more of
input I while
keeping total output the same ;
.
Profit w/ Fixed Prices :
(
negative of ) derivative of
isoquant Xz=fCx ,
) ; IT L q ) =
pq
-
C Cq )
MRTS a , B
=
fa
HB Lfa:
marginal productivity Wrt
Al p = MR = MC
.
ISO cost Line :
graphical set of input good
'
Market Supply Function Scp ) :
sum of
bundles that cost the same amount individual supply functions
.
Factor Price Ratio btw Input I da Input 2 :
.
Market Price in PC
amount of input 2 the firm must give up
1
.
Solve for each consumer 's demand
to
get one more of input I I maintain function for the specified good
the same cost level ; L
negative of ) the slope 2 .
Find market demand
of the boost line w/ input I on x
-
axis ;
if 3. Solve for q each firm will produce at
prices are fixed da
nothing is
being given a given price
away for free =
w '
lwz 4 . Find market supply
5 . Find p where Qs =
QD