Comsumn
x
x
x
strictly
=>
to
a
weakly
peters
Cerve
depicts
Indiference
for
peter
y.
between
indifferent
=>
y
An
(a, y)
=>
wy
se
·
y
Behavior
which
you
to
y.
on
indifferent
y:either
all
the
alternative
strictly
pufe.
bundles
consumption
well-off.
equally
an
and
se
A
Nom-thick.
->
Comvex.
-
->
sloping.
Downward
-
ICz
↑
IC,
>
Proputies
of
Princes
Completness
ramk
always
any
·
x[y1y z
MRS:
the
↳
The
IC
slope
equally
·
good
(7
consumes
7
Convexity
->
you
intersect
the
Indiffuma
which
you
for
i
BudgetConstruint:I
The
x!
z
good
willing
are
y,
while
two
bundles
the
bundles.
MRS
ere.
when
better off
are
of
goods
combining
than
with
each
of
-
=
to
remaining
well-off.
=
·
of
at
nath
trade
cannot
Cowrex
=
Prmnus
less
=
↓
two
of goods
bundles
to
Comvex
prefund
is
↓
↓
can
More
Transitivity
y
Pyy
Prix
=
=
optimal
+
-Dia
bumble
Opportunity
consuming
of
good
Costof
good
imunee
a
y.
Budget
happens
when:
him
TANGENT
t
IC;
A
-Interior
Types
of
Solutions
8
-Conmu
U2
U1
n
PI
Maximisation
is
solved.
problem
Always
tre
when
&
is
xe, 4
an
so
interior
Solution.
·
Utility:Mostused utility
function
to
profences
convex
represent
is
the
lobb-Domglas.
U(x,y) xx.y
=
↳
MRS
based
Function:MRS=MUn
Utility
the
on
MUy
-
Magimal
·
Pefunus:when
Homothatic
two
only depends
MRS
the
Optimal
consumption
E
*.
Pr
=
a
A is
y*.Py
Positive
Momotomic
this
espect
Types
·
of
Cobb-Damyens
defined
be
two
by
Prufrmus
conditions:
Pu-x
=
Pyy
+
in
the
good
transformation
baskets
of
I
share
s
d
om good
thatstill
can
be
y.
respects
and
mate
the
is
a
of
all
numking
utility function.
Transformations
condition.
goods
PerfectSubstitutes:They
4
->
=
consumption
↳
the
I
Transformations:Amy
Momotomic
of
Combition:MRS=Price Ratio
spent
·
consumption
the
=
BudgetConstraint:1
S
( =)
will
buntle
Tangemcy
x
of
2,y
goods.
MRS
·
entir
the
on
utility of
are
still
convex
performas,
but
strictly.
not
a
MRS 1k1
=
-
-
se
·
PerfectComplements:Goods
thatyou
substitutability.
yM
·
MRS
00
=
-
&-
Nofin
MRS
0
=
3
always
Convex
want
combine
to
perfumes.
Ex:Gim
in
fixed
& Tomic.
proportions,
zo
·
Goods:Leaves
Neutral
indifferent.
you
Comvex
Violates
the
property
of
Can
be
"more
is
puffered
to
commx
on
less".
Preferences.
ya
MRS
=
00
->
->
x
·
Buts:Commodity
-
that
May
comvx.
pufer less
you
be
than
p. substitutes
yN
m o re .
yM
ya
↓
-
I
A
MRS
=
m
x
·
Perfect
S
Ex
>
Connu
mor-
complements.
p.
on
(strictly)
x
Solutions
substitute
↳.
The
tangemcy
optimizing
of
in
time
the
a
is
combitions
for
bundle
consumption
because
hold
not
may
the
consume
MRSF Pric
which
Ratio,
=*
(**)
Epy
(**)
most
(0,)
(0)
=
⑨
Tr
Pratio
Can
which
=
·
Tr
>
be
tru.
yN
MRS
may
-
MRS Pratir
we
have
perfectsubstitutes
Yes,
in
consumption
this
case,
bumble
is
the
Ratio?
MRS=
Price
and
optimal
completely
indiffrnt.
·
Perfect
yN
Complements:
-
optimal
consumption
minhas:y
*
.......
The
Es
bunth
is
dan-BY
always
=
on
the
Tangany
kink.
condition
defin
the
tres
mussete
not
optimum.
·
Conclusions
optimality:
on
Assuming
Compute
i
budgetconstrainthas
the
inFind
all
possible
Points
a)
b)
Effects
·
Price
↳
of
price
to
optimal
·
-
the
the
results
well
not
is
find
to
fint.
p. complements:
best.
the
line
becomes
steper.
function?Itis
fumand
the
result
of
the
consumis
I
B
y*=
c
Pn4
p.
*
N
Budget
=
If
Py,
Demand
obtain
we
*
↳
compan
MRS
when
choice.
x
If
and
points
2nve
How
↳
for
changes
4=>
good
of
one
Demand
utility
solutions:
I,
tangency,
the
of
solutions:
interior
Kinks:look
out
types
a
are
solutions.
come
at
of
iiiCalculate
·
utility
the
then
kinks,
no
=>
movement
along
I
on
Commer
the
Preferences
couve,
change
Substitutes
Only good
Amy
bumble
*
Shift
in
·
se,
Only good
=>
se
y,
MRSC
MRS
of
BC,
P/Py
<
P/Py
MRS
PR/Py
=
E
demand
cure,
s*.
Demand
p. Complements
x*=
1.
I
B. Putx.Py
y*=
2. I
B. Px
x
+
Py
I
xx* By*
=
B. C.
·
Price
elasticity
Demant:
of
Prantchange
by
ofinQx
=
·
↳
Imlustic
quantity
demandat
when
the
price
immuses
1%.
En %
Ex
the
in
0
of
im
=
-
P
0x*.
Pr
Pro
Ro
Gere
=
-
Demand:
changes
Gb
in
than
smalle
Ex 1
are
im
change
price.
↳
Elastic
Demand:
changes
bigger
as
in
than
Ex
are
1
in
change
price.
↳
Unit
Elastic
PRY
Demand:2 1
=
*
O 1
·
Giffen
Goods:The
for
demand
good
a
immases
with
its
price,
i.e.
the
demand
is
upward
sloping,
Effects
·
Emyel
of
Income
Cerve:
·
the
gives
Px
Imcome
changes
ad
Elasticity:
optimal
change
in
↳
↳
Imfrion
% of
IP
goods:
↳
=>
of
when
imcom
imaD
im
24:* >
I
0
xt:a <0
goods:I4
Neussity goods:0
OD
=
·
Normal
for
m
each
Py.
Yx
↳
quantity
=
76
Luxury goods:2 >
1
*
<
1
changes.
G.
=
imcom
lival
I,
kuping
constant
·
Price
effectof
Decomposition
-
because
-
Substitution
income
Effect:If
We
should
total
consumen's
·
Giffen
own
Hicks
-
Demuse
stepe.
consumption
of
t he
good
same.
Consumption
the
when
&
of
set
makes
Substitute
y4.
from
one
up
for
lange
a
proportion
of
the
livel.
temams.
This
happens
thati t
the
whenever
the
outweighs
enough
income
effect
substitution
effect
of
the
(IEXSE).
immuse.
price
good
incore
or
sloping
strong
is
becomes
another.
expenditure
Behaviour:Upward
the
is
about
I .E.
came
B.C.
Pa4=>
the
to
good
↳
Pm4=>
the
Effect:If
Income
changes
Decomposition
Compensation
Px4
=>
allows
the
afford
consume
Consumer
Budget
to
SetShrinks
the
Becomes
=>
Likes
livel.
utility
initial
Elappiness,
porn (IE)
Px I
>Makes
the
ovnall
ambigmons.
d
->
Algebraical
Decomposition:
Zo:initial
i
ze:final
bundle
ImbirectUtility
Function,
Z:compensated
bunth
turmand
uplan
buble
se*
of
functions
and
y*in
the
function.
utility
~
(Pu, Py, I)
Solve:
is
I
T
-e
that
goes
Consuming
Z
through
Z
attains
is
the
tangent
same
to
a
budget
utility
line
livel
as
with
zo
slope
P
P
1- )
S
MRS(x',y')
B
=
r(x,y') u(x0,y0)
=
->
Substitution
Effect:the
of
consumption
good
P4
whose
down
yous
the
and
other
up,
Effect:the
Incor
->
-
the
gemeous
since
it
gives
New
I'=Ph.xo
Compute
x
->
afford
the
Loves
Hicks.
than
income
more
basket,
consumption
same
which
is
way
m o re
Morey.
Decomposition:
Calculate
is
to
consume
Algebenical
i
(when they
goods
both
of
Decomposition
Allows
->
less
consumes
and
poore
normal).
a
Statsky
gets
consumm
Level
Incom
PY
+
whatthe
yo
consum
would
x*(Ph,PY,I)
=
Substitution
y
Effect:the
livel.
incom
this
with
conserve
y* (P,PY,I')
=
consumption
of
good
P4
whose
down
yous
the
and
other
up,
->
Effect:the
Incor
Compensating
poore
less
consumes
and
Variation:tells
as
us
before
how
pain
change
the
much
the
thatreturns
price
the
has
the
thatis
change,
to
consume
to
ments
consumer
the
be
well-off
equally
adjustmentin
original
Hicks
Prices,
New
Original utility
>
A
La
Slutsky
Prices,
Original
-
Bumble
"I
E
-
·
z,
z
Zo
·
z,
Zo
·
Vo
Vo
Un
I
Pxx Pyy
=
I
+
Un
Pxx PyY
=
I
+
2
Pxx Pyy
=
I
+
Pxx PyY
=
+
2
x
How
Income
much
is
much
to
x
How
the
change
the
original utility?much
im
a
occurb.
=
New
income
after
utility
CV I
ÁLa
(when they
goods
both
of
normal).
a
·
gets
consumm
much
the
is
the
original
Incor
purchasing
change
power?
to
I
·
Equivalent
Variation:The
abjustmentin
utility
had
event
ALa
Hicks
Prices,
New
Old
7
to
equal
that
level
the
the
changes
income
thatwould
occen
ha
slutsky
A
Old
Utility
Prices,
New Bundle
ya
Zn
·
Zo
z,
·
Zo
Vo
⑤
I Pxx Pyy
u,
=
+
Vo
I
Pax Pyy
=
I =Pax
+
P,y
+
I
Pax
Pyy
+
Ex
>
x
How
would
much
benease
in
equivalent
loss
order
in
income
to
cause
utility
How
have
to
an
the
as
much
cause
power
would
the
power
decuase
to
equivalentloss
an
as
have
income
in
inmuse?
price immeuse?
r
(P, PY,
I) V (Pi,Py,I")
EV
·
the
if
happened.
A
to
consum's
Quasio linem
preferences:mon-line
U(x,y)
y
=
in
=
I
=
-
I
"
good,
one
f(x)
+
↳
strictly
&
concure
immasing
limem
in
the
other
goods.
im
onte
perchusing
Produce
Theory
i )
max
·
Production
(urenes
max
-
Costs]
F)
max
(p.a.Tecal)
function:0 f(k,2)
=
↓
2 Labor
↓
Capital
Quantity
Product
·
Short-rum:Fims
construind
are
in
some
their
of
choices,
production
cannot
i mmase
it
capacity.
·
Long-rum:Notconstruined
Production
Short
Rum
in
the
choice
all
of
imput
livels.
Function
MPL=
Ya
A.
b
20
f(k,L)
->
OL
.....
APL
O
=
a
->
L
slope
which
~
-
8
and
the
~
-
process
~
~
~
-
↳
L
N
APL
MPL
L
MPL APL=>
APL
MPLCAPL=>
APL
is
is
immusing.
demasing.
7
y
Costs
Te(a)
M2 2 Te(a)
x (a
=
F
+
=
20
moves
Variable
Costs
the
in
opposite
as
w.c =
=
direction
MPL.
Ac(a) TC(a)
=
O
Act
=>
MC
< Ac
AC =MC
>
Al
of
production
8.
-
Slope
cure.
the lim
of
comments
end
the
of
start
the
·
Economies
scale:
of
When
is
>
Ave Y.
AFC ↓
·
Diseconomics
of
LR,
the
SR,
the
Production
the
produce
Diminishing
can
optimizing
is
of
Consequence
immuses.
differentcombinations
decide
production
of
turs
in
not
Productivity:let's
8
=
the
of
consequence
ATCH (Ave 9.
of
imputs
which
in
Moving
costs.
it
can
to
the
be
also
Isoquants
livel
are
the
in
0
LR
the
in
assume
(MPLa
productivities
marginal
MPK)
non-negative.
O
222
2L
imports
a
AC
me
of
is
Function
produce
Marginal
O MPL
·
a
when
immusing
This
immenses.
efficient
economically
·
I
when
i
Lony-Rum
In
is
MC
A
·
Al
scale:When
demasing
Al
S2,K)
thatcan
Space
function.
production
t he
of
cenves
be
used
Depects
produce
to
given
a
all
the
possible
of
quantity
combinations
output.
A
Properties:
k prpriob
->
-Do
30
q=
from
Immuses
not
cannot
-
10
q=
origin
cross.
Dowmwant
-
20
q=
the
be
sloping.
thick.
>
↳perprrt
·
Margimal
Rate
of
Technical
substitution
(MRTs):Absolute
slope.
MRTS MPL
MPK
Comvex
Production
Measures
between
=
if constant
function
=>
perfectsubstitutes
=
Comvex
Isoquent
Curve
value
the
two
of
how
MRTS
is
the
imputs
output.
=>
the
demasing.
Isoquant
firme
without
can
cure's
Switch
demasing
its
·
Production
functions
witely
(CD)
CobbDomgeas
R
↳
They
Recin
from
the
convenient
·Cost Minimization
·
Technological
the
Efficiency:relevant
in
Economic
only
·
All
the
=
·
We
could
and
first
nk
in
long
and
much
less
on
more
to
is
production
50
=
-
produce
the
of
imputs,
given
protum
the
using
problem
cost
mimimization
-
langemy
the
production
the
of
firm
such
costi s
to
you
produce
by
fixing
Condition:
MRTS=
Isoquant:0
↳
Proteen
3
will
)
(
q
=
f(k,1) E
=
-k(qf(x,)
use
4K
Mat.
and
1
rules
have
exception,
an
technology
a
(perfectcomplements).
proportions
CES Function
1
Solution
the
problem
I
k
q
=
~
-
e
e
L =E
P
w
+
E
~
+
w
-
With
more
by
=
MPL
cost
obtaining
fixed
to
extra
of
All
isoquant
an
thatquantity.
↓
=
cost
constant.
=
4/4
the
prices?
imput
xw
If
the
quantity?
given
the
using
2.
lowestisocostthatallows
S
·
product.
you
produce
the
runi
long-rum;is
the
factors
of
=)k
+
tepictthe
the
+
Isocost
combination
TC wL
short
combination
minimising
Lim
how
/
kP B.(P)
-
transformations.
of
imputs
amounts
Efficiency:relvant
Straight
about
more
momotomic
positive
=
(CEs)
Substitution
of
Problem
last
·
iti s
concepts,
Elasticity
(x
G
ondinal
not
are
Constant
L
x.
x
=
used:
one
of
unit
output
himing
Lor
K.
MPK
CD Function
S
(a.(=).()
((u,e,a)
=
(a.(v):()
k(w.e.a)
=
(a.(
reca)
Elasticity
of
substitution:measures
(k/2).
↳
High
Low
CES
I
Properties
Low
p 1
=
=
p
->-00
p
->
0
ofLR
=>
=>
Fixed
a
B
+
to
0
=
in
q
in
q
technology.
P
imports.
combination
of
(...).
00
=
0
=
Function
>
=
0
=
0
1
=
CostFunctions
both
imputprices
multiplied
are
by
4**
TC
the
is
multiplied
Non-Demeasing.
in
(Weakly)
iii
Concure
immuses,
imcenses
in
Scale
-
-
·
a
each
in
&
keeping
at
Imput
Individual
the
and
decensing
other
Price:When
import
Consequence
nute.
individual
imputprice
the
cost
constant,
price
of
one
total
imputsubstitution.
Economies:
No
in
Es
1
changing
immusing
production
-
demasing
is
constant
3
=
< 1
of
the
LRAC
=
Function
Pod.
1
1
by
=
=
I (MRTS)
prin changes
Function
1
<
I
changes
price
Prob.
CD
Homogemaity:when
i
Prob.
Limen
2
to
unction
o:
B
+
=
k/L
reaction
8:
+
x
flexibility
the
B
x
0 (((x)
MRTS
2 MRTS
High
I
(x +
=
o=G
↳
+
(@lat). ex
I
CRAC(C)
·
(x b)
x
=
Scale
(Dis)
Economies
Saul
Economies=)
Scale
Disecomomies=>
=)
LRAC
LRAC
LRAC
is
is
is
temeusing
limem;
im
immusing
TC
qiTe
in
is
is
lima;
comcare;
4;Te
is
convex;
K.
q
Returns
Scale
to
Scale
VS
Scale
Economis
Property
Related
of
·
·
the
SR
In
the
Since
k
The
optimal
SR,
is
to
Fixed!
LR
Rutmms
to
Property
Prof. Function
of
optimal
Apply
of
imputs
scale
t
any
combination
of
imputs.
LR
the
there
LRAC
the
to
combination
From
Economies
is
The
value
only
firm
of
one
is
K
is
way
not
the
to
produce
its
optimizing
or
more
(which
is
to
him
more
works
imputchorice.
that
minimizes
which
be
can
Jeriving
the
respectto
SRCF
SR
the
=
production
cost.
fome
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