Principles of Microeconomics Notes

S G D P G Q
Opportunity Cost :
the value of Costs :
expenses a firm
Mct=s→
pt
Q in
the next best alternative incurs from engaging in its McT=s←
Pt QtAbsolute Advantage
:
fewer resources business activities D →
P T Q 4
D ←
P 1 Q 1
are used in production Profit :
total revenue ( TR ) minus
*
Comparative Advantage
:
lower opp .
total cost ( TC ) Determinants Of
cost of production Marginal Revenue :( MR ) addi -
Demand :
population ,
Terms of Trade : ratio of goods at tional revenue a firm receives income , prices of subs
Which countries agree to trade at from selling one more unit 4 complements ,
tastes 1
Production Possibilities Frontier :
Marginal Cost : ( MC ) the preferences , expectations
( PPF ) a
graphical representation of the additional Cost a firm incurs Determinants of Supply :
goods a
country can produce given When they sell I more Unit MC shifters , expect a -
their productivity E constraints Market Power :
the ability Of a tons ,
# of sellers
Consumption Possibilities Frontier : firm to set its own price p
( C PF ) :
graphical depiction of what Producer surplus : ( Ps ) differ .
'
E
price to Max
-
profit :
a
country can consume given its end between price received -
$66-
productivity ,
constraints ,
da trading da the cost of production
-
I
.
-
opportunities Law of Demand : The price
-
: Mc-
•Spontaneous (
emergent ) order :
of a
good or service is
-
,
iii.MR D
0 4 5 10
a phenomenon in Society that is inversely related to the •
individual Firm in
Perfect Competition
the result Of human action but quantity demanded ( PT Qtr ) c individual firm 's supply )
B = 5 p 1 1 1 1 1 1 1 H 1 1 1 1
not human design Law of Supply :
Prices Galan -
.
. =3
, ;;
.ly#..y.EIiYb?3IFr?
Demand : the relationship between titles supplied are directly QHOO " = '
a. ÷
.
a
EEM"
the price of a good or services related ( PTQT ) bk
(
Pqmerwagrgtoattsqwmweasitintion
the quantity demanded Perfectly Competitive Equili
-
100
•
S = MC
Inferior Goods : as income increases ,
brium :
occurs at a price where sellers .
demand decreases QD is equal to Qs
•
a
p
100 SOO 900
Normal Good : as income increases ,
Dead weight Loss : LDWL ) the 20
s=Mc
=
demand increases reduction in total surplus from I
= Ims
Substitute Goods :
an increase Market inefficiencies
12=11111
•%;y••
Iii ( ill
PE
-
-
nrr( decrease ) in the price Of One
8=1111
iii.111111
good causes an increase ( decrease ) Winners from Int
'
l Trade : =
shortage•
Consumers / producers from I I I D
In the price of the other good i i 1 i i 1 1 1 11 Q
increased variety
4001^600
Complimentary Goods : an increase QD=Qs
( decrease ) in the price of one
•
firms 1 Workers in export
p
mc=s
good causes a decrease ( increase )
intensive industries
in the demand for the other good
°
lower prices
Ts
§
"
SI" ' '
.
Consumer Surplus :
( CS ) differ .
Losers from Int
'
1
Trade :
a
end between consumers
'
•
firms 1 workers in import
willingness to
pay ( wtp ){ the
intensive industries s s→ s←
price ( p ) of the good or service
°
increased expenditures D P Q Pf QP PTQt
Revenue :
income a firm
On displaced Workers
D → pp QT p ? Qp Pga ?
receives for engaging in its
CPSGIPWIPMEP ts= ( s + Ps D ←
Pt
QtPTQ ? P ?Qt
business activities

Own price elasticity of demand :
If Demand increases . . .
S
a measure of the responsiveness
Income elasticity of demand :
Of consumers to a
change in a Measure Of Consumers
'
§
S p .
P ,
the price of a good or service responsiveness TO
Changes in Dz Dz
E D= !j?aQp
"
income . a
D '
a. a
.
D '
IE D= %4Q
's
t.IQ > tap tap ) t.IQ
E , ,
( Oas long as the law of
'
1. II when supply is more elastic When supply is more
inelastic
demand holds
IED ( 0 inferior good
If
Supply decreases . . .
IE , ,
71 elastic
E , ,
=1 unit elastic
IED=O no relationship
p
.
sz s
.
E
,
( I
inelastic
IED 7 0 normal good p ,
i
s
,
pp
s
,
Percent
change from x. toxz : Cross Price elasticity of Demand D D
×2
-
× '
•
100.1 .
( Good At Good B)
'
.
a measure Of QQ '
on a
X ,
t.AM/.LlQ t.IQ > tap
consumers
'
responsiveness for
when demand is more inelastic when demand is more elastic* The more horizontal a demand
Good A when the price of B
Curve is ,
themoreelasticitis
s s
p Changes
.
* Ifa profit
-
Maxim 't ,
IT
E¥"f
.EE#ggq2in9firmiscurrehHyxqD=yaQD(
Good A)
"
%¥¥t¥tEp±§ ( s
on
floor
=
1111 "
pricing in an inelastic
31111 11 11
Ceiling
=
=
.
'
1.41 >
( GOODB ) binding
ps shore
. = region of demand , ceiling 3000
p D
.
=
ii. iii. ii.
a
they should
KED )0 substitutes 489070¥ 38,0,§6%0
increase price
K If a profit -
maximizing firm is KE
D=0 Unrelated prefloor s
postfloors
currently pricing in an elastic
KEDCO
Complements
b¥o%Moo|cs
120451
, 11111 floor
region of demand ,
it is Unclear 1111 ,
new
'=
DWL
whether they should change
KASIKEDI increases ,
the - aa -
nonbinding Ps = Ps
-
price relationship blwthezgoods
floor
= is . is
* Revenue is maximized ata P soo 300
s ,
price where demand is
increases
unit elastic Price Floor :a government mandated a
sz
HIE ,>
1<1 EPT HIE ,,
I > I { PT minimum price g-
Cs
S B
§ D)
subsidy
Revenue Costs ( QH
RevenueCoststprice ceiling :a
government
Ernie DWL
,
F Wedge
Profitytproatpyofitt
Profitytprof.tl?Ygfittmandated maximum price
3-
¥
"
'
"
'
"
'
"
¥
"
I
B,PIsefTI×°Determinants of More Tax Burden : the amount by which stooyjo
Q D
Elasticity of Demand Elastic if ...
a tax causes prices to increase
•
need
•
less necessary ( decrease ) for consumers ( producers ) Presubsidy Post
Subsidy•
availability of •
more available * More inelastic side is more CS A + B A +
B+F+E
close substitutes substitutes affected by taxes subsidies
PS F +
G Ft G + Btc•
market definition •
more narrow
•
time horizon
•
longer Externalities :
an action
COST
-
( B+C+D+EtF )
•
percentage of
•
larger TS At B+F+G At B+F+G
-
D
consumer 's
budget percentage
Causesa positive Negative
* D= DWL
effect On a third party Negative Externality
Own Price Elasticity Of e§§giadhY+ social cost =
private # + external cost
supply :a measure of the Social Costs --
private
quantity
&Wm}efFfiFe
••
Sprivate cost
responsiveness Of producers outcome I
•••
competitive outcome
costs + external Costs
==TO Changes in prices = = D= private benefit - social benefit
Social Benefits -
private Asean
{ s=%}¥¥ benefits + external benefits
Positive
E×+emE¥.li?adYnys=priva+ecos+=sociaicos+
quantity
DWL from
Es ) Oiflawof supply holds
Cease Theorem : The
÷
women
've
{ s
) I
elastic competitive outcome ; =
social Benefit =
private benefit + external
Es =/ unit elastic Socially Efficient =
,
=
,
Dprivate benefit
benefit
Esc1
inelastic Outcome to an ex -
Qpcose
Determinants of More
Elasticity# supply Elastic if ...
lethality Will be teach -
K Transaction costs can be
•
time horizon
•
iongertimehori
.
Ed Privately if trans -
prohibitively high in some cases
zonslwlingoods ) action costs are low ,
so the initial assignment of property
•
production
•
shorter Production
regardless Of the rights is important for efficiencytime time ( across
goods ) .
•
perishability •
less perishable
Initial Property rights K The initial assignment of property
•
capital
•
lower capital Total Surplus :
Consumer surplus 't
rights affects payments blw parties
requirements requirements
Producer Surplus + 1-
externality

Intro
Economics :
the study of how
goods Er services are
produced { allocated
Macroeconomics :
economy wide factors
-
Unemployment ,
interest rates ,
GPP ,
etc .
Microeconomics :
the study of how agents
make choices
↳ tradeoffs

Absolute G Comparative Advantage
Specialization
When can trade make people better off ?
Model of International Trade Elements
includes :
Could also include
-
Countries CZ )
transportation costs
-
goods (2) preferences
-
number of Workers cost of production
-
labor productivity
Model :
Average Worker Productivity
TVs T-shirts
Uxemburg 101 hour 501 hour
Burdini I 1 hour 401 hour
Luxemburg :
100 Worker hours
Burdini :
200 worker hours
Opportunity Cost :
the value of the next
best alternative
i. e. Opp .
cost of attending ND is the salary of
a full -
time job
Absolute Advantage L in producing a
good or
•
service ) :
fewer resources are Used in
production
→
comparative advantage
:
lower opportunity cost
of production
David Ricardo ( 1772 -
1823 )
Theory of Comparative Advantage
AH Countries Can benefit from trade by
specializing in their comparative advantages
regardless of absolute advantages

LUX has the absolute
advantage in
producing TVs E T-shirts
•
Opportunity Cost of 1 TV :
LUX -
10 TVs :
50 T-shirts ← Lux has
1 TV :
5 T -
shirts a
comparative
-
advantage in
opp .
cost of ITV
producing TVs
bk of lower
But -
Opp .
cost
1 TV :
Llotshirtsopp.
cost of 1 TV
•
Opportunity Cost of 1 T-Shirt
Lux -
50 T-shirts :
IOTVS Bur has a
1 T -
shirt :
'
15 TV -
comparative
But -
40 T-shirts :
| Tv
advantage in
1
T-shirt :
1,40 + v
/ Producing
T-Shirts
* In a 2 good ,
2
country economy ,
a
country
Can't have a comparative advantage in both
If split Labor Hours *
specialize 4
( wlih a country ) Don't Trade
TVs T-shirts TVs T-shirts
Lux :
50.10=500 50-50=2500 100.10=1000 0
Bur : 100
.
I =
100 100.40=4000 0 200.40=8000
600 tvs {
6,500t-shirts vs .
1000 tvs { 8000 shirts

.
Lux gives up
25¥ =
SOOTVS if they
T produce ZSOO
Stopp .
cost of producing 1 TV
+
-
Shirts
•
Most # of tvs LUX Would be Willing to give
up for 2. SOO +
-
shirts :
500
•
Min .
# of TVs that BUR needs to be
willing to
give up ZSOO t-shirts :
2500
-40
= 62 .
S
q
40 =
Opp . cost of
producing
1 TV
( Burundi gives up 2500/40=62 .
S tvs if
they produce 2500
t -
shirts )
Terms of Trade :
ratio of goods at which countries
agree to trade at
Suppose Luxembourg 4 Burundi trade 2. soot -
shirts
for 250 tvs
TVs T .
shirts
Luxembourg 1000 -
250=750 0+2500=2500
Burundi 0 + 250 =
ZSO 8000-2500=500
Production Possibilities Frontier LPPF ) :
A graphical
depiction of the goods a
country can produce given
their
productivity 4 constraints

PPFS and CPFS ; pros { Cons of Trade
Burundi 's PPF
Quantity *
straight
of Line because
TVs opportunity
slope : -
'
140 cost is
200 •
Constant
(1×200)
=
This Could
8000 Change L
guns
(40×200) G butter example
luantity of T-shirts
better resources
would be Used
first )
butter
↳
Consumption Possibilities Frontier LCPF ) :
graphical depiction of what a
country can
Consume given its
productivity ,
constraints {
trading opportunities
World Terms for Trade : 10 t-shirts for Itv
consumption with
specialization {
* held another country
trade all + -
shirts
to trade with blc
for TVs On Burundi can
only
g
s 1000 .
produce 8000 t-shirts
800.
3
g-
TVs
¢
slope
=
-
'
110 8
§
( PF
production §
s if complete X
S • specialization S
A
¢
J
200
¥800 50%0 10800
T-shirts

Winners da Losers from International Trade
Winners Losers
•
Consumers da producers
•
firms G workers in import
from an increased variety intensive industries
of
goods da services
.
reduced government revenue
•
firms G workers in export from tariffs ( taxes on imports )
intensive industries MAYBE
•
lower prices
•
increased expenditures on
displaced workers
Trade has
essentially the same impact ,
but
Viewed politically different
-
cheaper
-
displaced workers

Markets da Demand
Unregulated markets can give the best outcome
Spontaneous ( or emergent order ) :
a phenomenon in
Society that is the result of human
action but not human
design-
prices companies must set prices in an attempt
to find the perfect price based on economic activity
-
ex :
language
How are prices determined ?
Why do they change ?
How do they affect market activity ?
* When the price of a
good goes up , people
want to
buy less of it
Law of Demand :
The price of a
good or service
is inversely related to the quantity demanded
Demand :
the relationship between the price
of a
good or service 4 the
quantity demanded
Quantity Demanded Price
price ( P )
200
- ••
Tickets
42 200 iso - •
42 150
52 100
ioo -
•
77 50 ← Dencaurnvde
86 0
so -
•
If a demand curve is
o
•, Quantity
downward sloping ,
it
412 154 717
86 ( Q )
satisfies the law of demand

* When the price of a
good increases ,
the demand for that
good stays the
same
If the price of a good increases ,
demand does
not
change ,
so instead the
quantity demanded
decreases ( movement along the curve )
p
Apples
A shift to the
right
in the demand
Curve is associated with an increase
→
in demand
D , Dz
p
Q
Bananas
As
population increases ,
demand increases
→
3-
-
- - -
,
- . .
,
pop 9
1 1
D →
! b ,
! Dz W
p
200 700
Q
demand increases
,
Overalls

If income
goes up ,
demand

decreases if inferior good
,

ex :
Would rather
buy nicer clothes

,

,
possible, Inferior Goods :
as income
Da D ,
i possible
a increases ,
demand decreases
Ormal Good : as income
increases ,
demand increases

P
Jelly p Peanut
Price of jelly 4
Butter
Quantity Demanded
of Peanut Butter ←
ii.=:: : !a
←
! !
Q
Dz D ,
Q
140 200
Increase in price of labor →
increase in demand
for physical capital
p
Physical
capital Price of labor T
Demand of Capital →
→
-
increasing
D , DZ
Q
* Determinants of Demand
-
population-
income
-
prices of substitutes E complements
-
expectations-
tastes 4 preferences
.
substitute Goods :
an increase ( decrease ) in
the price of one
good causes an increase ( decrease
in demand for the other good
.
Complimentary Goods :
an increase ( decrease ) in
the price of one
good causes a decrease
C increase ) in the demand for the other good

Demand ; Market Power
P
Doritos
If Cost of Production T
Then Demand stays the same
But price T
Q
P
TVs today )
If expectations 1
( expect price of TV to
decrease in future )
←
thlh 1)
today of tvs
←
Dz D '
Q
Consumer Surplus ( CS ) :
difference between
Consumers
'
willingness to
pay LWTP ) G the
Price CP ) of the
good or service
Cs =
WTP -
P
p P
Total CS= 125
10
-
10 -
WTP = 7 p =
5
P =
SO ( S =
I bh
WTP⇒
-
3O+h Unit =
'z( SO ) ( S )
p= s .
(S{ .
Pts
-
=
125
D D
310
Q
0
2's go Q

Supplier Behavior w/ Market
Theory of the Firm
Power
Revenue :
income a firm receives for
engaging in its business activities
Costs :
expenses a firm incurs from engaging
in its business activities
profit :
total revenue LTR ) minus total cost CTC )
TR -
TC
P
Coffee
io .
Total Revenue :
Price ×
Quantity
= TR when Q =3 is 7×3=5121
> -
a TR when Q=4 is 6×4 = $246
=
MR =TRy
-
TR 3=24-21 =
$3
= B c
4 T 4
=
D
Btc A + B C -
A
0
1 1
}4
1 1
11
i. to
Q
Marginal Revenue CMR ) :
additional revenue
a firm receives from selling 1 more Unit
i. e. derivative of total revenue function
P
p Q TR MR
i.
10 0 0
q
= •
9 1 9
7
i •
8 2 16
= •
7 3 21
5
i •
D
3
1 1 1 1 1 1 1 1 1 1
Q
6 4 24
,
5 5 25 -
i
* MR is twice as Steep as 4 6 24 -
3
demand { has same Vertical 3 7 21 -
s
intercept as demand
2 8 16
-
>
* is linear { firm can set
, q 9
prices
0 10 0
-
9

Marginal Cost ( MC ) :
the additional cost a firm
incurs when they sell 1 more unit of output
$ $ $ $
5
-
5 -
4
-
MC
MC
3-
3
-
a
capacity
↳ constraint
MC
| I Q
' -
1 1 Q Q Q
100 900 100 900
1100 £00
I no
capacity
constraint,
stable
cost structure

Market Outcomes
P
MAXTR :S
P .
For Q > 4
←
price tomax-
profit : MR< MC
I $6 produce less
-
= .
For Q< 4
.
-
o
GMRhp
Q
: F.mc MR > MC
- -
-
:
.mr D
produce more
TRTQT TRIVQT
0
' 1
its To
:
1. Find Q* where MR=MC
P*= 70 p . • a
,
MCsoi
:✓ 2. Trace
"
up
"
to the demand
s
*=
curve for P*
i.It's
!noB'' '
E Q
* =
best
.
Market Power :
the ability for a firm to set its Own
price
.
Cost :
whatafirmmustpayto produce something
.
Price :
what a firm
charges for what it produces
CS= WTP -
p
Producer Surplus ( PS ) =P -
MC
↳ Difference between price received 's the Cost
Of production

P
woo -
What is the CSG PS from
the transaction of the
wY*Eb88I
. ;:is , zothtv ?
=
÷I mc CS= 700-600=100
Ii MR D
Q
T
T
' '
zfto
' ' ' ' '
go WTP p*
PS = 600-200=400
T T
p* MC
P
Cs =
1 1 11
-
=
PS =
-
MC:MR D
Q
P
P,
Pz
•
mc
, MCT Pt QT
•
Mcz
MR D
Q
Q , Qz
P
D →
Pz
PT QT
P
, D ,
• •
MC
Dz
MR ,
MRZ
Q
Q ,
Qz

P
Income T
p ,
* Bananas are inferior good
D ←
Pz Pt Qtr
MC
• •
D
,MRZ Dz MR '
Q
Qz Qi
P
Us Autos
If Ds+ee|→
:'
•
Mcz
then Pstealn
•
MC ,
Mcauto T
MR
DQ
Panto T
Qz Qi
Qauto t
Types of Shifts
Changes in PEQ
D → pp QT
D ←
Pt Qt
MCT PT Qt
Mct Pt QT
) Pcorn T Mcchips T Pchipstn Qcnipst
2) Psalsat Dchips →
Pchipstn Qchipst
SO Pcnipstn Qcnips ?

Market Outcomes
Between 2006 E 2008 ,
PinsuranceTQ=
Changes in Predictions supply
-
side problem
MC or D about PGQ
D→
Pt QT
ex
:
problems occurred when
D←
Pt Qt
insurance incorporated
MCT
PT Qt how health information
Mct
Pt QT
systems ( MCT )
Characteristics of Perfect Competition :
-
homogeneous goods
-
free entry E free exit ( no barriers to enter 1
exit market )
-
large number of firms
-
large number of customers
-
full information
*
In perfect competition ,
firms take market price as
given ( price takers )
P
Individual Firm
in perfect
.
At a price of $5 ,
firm can
competition
sell as many units as possible
market
•
firms have no incentive to
price
=
5 D= MR set lower price because they
can sell unlimited units at $5
Q
.
every firm is small ,
and there
p
vs .
are so many firms that if a
Firm w/ firm raised their price , no
Market Power
One would buy
MR D
Q

= y
individual firm 's supply curve
-
MC =s
If P =3 ,
Q =
60
-
If P= 6 ,
Q =
90
Pz = 6
;
••Dz =
MRZ
p ,
=3
't
.#D. = MR , * would not want to produce
=
l 1 i I l l 1 1 11 USS than 10 bk unprofitable
10 60 90
Q ,
Qz
.
MR ,
> MC ,
Law of
Supply
:
Prices E quantities supplied are
directly related
↳ As PTQT Or Pt Qtr
* s= Market supply
P
Individual Firm in
P
Perfect Competition
Market Level in
Perfect Competition
( individual firm 's supply )
( w/ 100 sellers )
MC = S s = MC
B = 5 1 1 1 1 1 1 1 1
1/1
11 D3= MR
}
•P
, =3 1 1 1 1
1
-
1 1
1=1
1 1 D ,
= MR , •
Pz = 1 1
-
i 1 1 1
1=1 1 1 1
[1 1 11 Dz =
MRZ
•
. 1 Q Q
tz § , 0,93
100 SOO 900
9
÷ 00
( because 100 sellers )
* When the price of a good goes up , supply
stays the same C i. e. an increase in the price of
a good does not
change supply but instead
Changes the quantity supplied )

P
*
s '
= Mc
'
shift to the right in
-
sz =
ME
Supply or demand is
4 t• ii iii. • i 1 1 1 1 i , 1
associated With increase in
Supply or demand
i
1 1 1
s
'
Q
Determinants of Supply :
-
marginal cost shifter
-
change in input prices
-
technological productivity change-
weather
-
expectations about future prices
-
number of sellers
P Individual Firm
p
in Perfect Competition Market Level
MC
S =
MC
myriad .
✓•=D= Mr
43 !"!."." ;. .
-
D
=
Q Q
Q*
¥

Perfect Competition E
supply
P
20 S =
MC
=
= •
At P= 12
-
surplus Qs =
600 Q D= 400
=
~
12=1
1 I 11
••
I 1
••
1 1 ( ( 11 QS ) Q
D
PE
" '
"
Surplus Of
600-400=8Ill11
itT.FI
1 1 11 (
200 units
-
.
At P= 8
=
shortage
Qs =
400 Q D= 600
= = =
D Qs < QD
= -
.
1 I I 1
I I I I 1 1
Q Shortage Of 600 -
400=400p 600 200 Units
QD =
QS
A perfectly competitive equilibrium occurs
at a price where the quantity demanded
is equal to the quantity supplied
P
MC=S
Cs PS =p -
MC
"
( '
b's" "
.io#surpfusEsYIEIps
D
Q

P p
S
S = MC
p=
7001-45
.
,
soap
# e-
DWL 500 -
pig-
DWL
P = 300
D
Ps
D
I 1
Q 1
Q
30 50 30 50
At P= 700 At P= 300
Q D= 30 Qs =
30
Dead Weight Loss ( DWL ) :
the reduction in total
surplus from market inefficiencies
p
S = MC
Mf negative surplus generated
D= WTP
Q
* total surplus tells
nothing about who benefits
A perfectly competitive equilibrium is both stable
4 efficient L i. e. maximizes total surplus )

Expectations C for seller ) T
s ← PT Qt
p p
S ,
52 S
,
B c-
A
→
52 S → Pz •
S ←
P ,
•
Pf Q T P
,
•
A PT Qf
pz
• B
.
Q Q
Q , Qz Qz Q ,
Shifts in S } D Changes in PdQ
Mct
=s→
Pt
QT
MCT
=S← PT Qt1) →
PT QT
D ←
Pt Qt

Elasticity
Own Price Elasticity of Demand :
a measure of the
responsiveness of consumers to a
change in the
price of a good or service
E. =
gallop
'
( percent change in
quantity demanded )
p
( percent change in price )
own price
elasticity
of demand
1 1
or
T 1
EDCO as long as the law of demand holds
If IE ,,
1
> 1
Demand is elastic it ¢Q'
' 1
> 1%4 PI
( big response )
If LED 1=1 Demand is Unit elastic 1%4 QDI =
ltllpl
If 19>1 ( 1 Demand is inelastic HIQDI ( It .
API
( little response )
If the absolute value of ED =
2 and P increases 10.1 .
the QP =
-
20%
a
,
/
10.1 .
|=2 Q D= -
2( 10%1=-201 .
If P increases from $2 to $34 QD decreases from
2000 to 1600 ,
is E ,>
elastic luhitelasticl inelastic ?
1600 -
2000 -
400
2000 2000
=
-20%3-
2
=
1
go ,
inelastic
2 2

Percent Change from X.
→
Xz
:
Xz -
Xi
•
100%
X
,
Qz -
Qi
Qi
=
Qz -
Q ,
P
,
ED =
pz -
p , Q ,
•
Pz -
P ,
Pi
P
← a .
If P 8→9 ,
What is ED ?P
,=8=
I I -2
-
1
-
2 2
-
= =
-
4
= 9-8 1
-
8 8 elastic1 1
,
lz1 1 1 1 1 1 1
Q
QZQ ,
:
=
If P 2→1
,
what is Ep ?
= 9-8
1
=
8 8 1
.
-
-
1 -
2 -
1 4
FEE2 2
inelastic1 1 1 1 1 1 1 1
lqlqQ
Q , Qz
:
%6%
.
see
Feeney-
11 1 11 1
.
.
-
=
-
-
⇐1 1 1 1 1 1 1
Q

p
* The more horizontal a demand
P,
l '
' ' ' 1 ' 111
curve is ,
the more elastic it is
Pz 1 1 1 1 1 1 1 1 1
1
D ,
Dz
For D
, ,
there's a
large t.IQ
's
Q in comparison to % QP ,
so
D , is more elastic than Dz
P
Remember :
Mastic
If I EDI L I inelastic
yunit
elastic
IEDI = I Unit elastic
tgneiastic
IEDI > 1
elastic a
* If a profit maximizing firm is
currently pricing
in an inelastic region of demand , they should
increase price
* If a profit maximizing firm is currently pricing
in an elastic region of demand ,
it is unclear whether
they should change price
If IEDI ( I { PT If IEDI > I E. PT
Revenue T Costst ( Qd ) Revenue t Costst ( Qtr )
profit T Profitt Profitt Profitt
↳
profitTd ↳ profit ? 4
Revenue is maximized at a price where demand
is unit elastic
If demand is inelastic ,
an increase in price increases revenue
If demand is elastic ,
a decrease in price increases revenue

Determinants Of
Elasticity of Demand More Elastic If ...
•
need .
less necessary
.
availability of close substitutes .
more available substitutes
•
market definition .
more narrow definition
•
time horizon
.
longer time horizon
•
percentage
of consumer 's
budget
•
smaller
percentage
Own Price
Elasticity of Supply a measure of
the responsiveness of producers to changes in
prices
{
5
=
% QQ
s
% 4 P
If the law Of Supply holds ,
Es > 0
If Es > 1
supply is elastic
Es = 1
supply is Unit elastic
Es < 1
supply is inelastic
P
52
S ,
is more elastic than Sz
P, 11 11 11 1 ' ' '
5
'
The more horizontal a Supply
Be in i ,
curve is ,
the more elastic it is
Q
Jeterminants of
Elasticity of Supply More Elastic If ...
.
time horizon
.
longer time horizons L within goods )
•
production time •
shorter production time ( across goods )
.
perishability
.
less perishable
.
capital requirements
•
lower capital requirements

If Demand increases . . .
S
Be S Pz
P ,
P ,
Dz Dz
D ,
D ,
1 Qz Q I Qz
t.IQ > tap tap ) t.IQ
when supply is more elastic when supply is more inelastic
If
Supply decreases . . .
pz
52
Sz
.
S
,
PZ
S
,
P , P
,
D D
Qz Q ) QZ Qi
t.AM/.LlQ t.IQ >
'
tap
When demand is more inelastic when demand is more elastic

A B C
s s
inelastic
Pz 1 1
1 1 1 1 1
Pz 1 1 1 1 1 1
R S P, 1 11 1 1 11 = =
Dz
p ,
.
11 1
11 1 1 '
.
elastic
=
-
p
, 1 1 | , ,
-
-
-
-
Dz -
D Di
== = = 2
==
elastic
=
=D,
inelastic - =
D ,
- =
Q , Qz Q , Qz Qi QZ
* perfectly competitive market ,
firms don't have market power
A :
an academic hospital with excess capacity ( elastic supply )
treating high severity patients ( inelastic demand )
B :
a non -
academic hospital with moderate capacity
L relatively neutral supply ) with a
moderately severe
case load ( relatively neutral demand )
C :
A capacity constrained group of rural practitioners
C inelastic supply ) treating low severity patients
L elastic demand )
If there is an equivalent increase in demand ,
which
market would expect the largest increases in price ?
Market C

A B C
S ,
S
,
S ,
P,
I I I I I I 1 P, I I 1 1 11
I s
P
' l '
= s
€
s
Pz I I I 1 I i 1 1
- 2
% I I 1
-
I I I 1 1
-
DZ % I I I 1 I
[
1 1
-
2
I D inelastic = = elastic = = D
Qi Qz Q , Qz Q , Qz
A :
Gas stations close to car rental agencies at airports
L inelastic demand because of renters needing gas before
returning cars )
B :
Gas stations
operating in
large suburban shopping
areas ( elastic demand because large amount of
Competition )
C :
Gas stations clustered off of interstate exits ( relatively
neutral demand because
competing With other
gas stations
at exit { other surrounding exits )
Income Elasticity of Demand : A measure of Consumers
'
responsiveness to changes in income
I E D=
%aQ ' '
If IEDCO then inferior good
%dI IED =
0 tbheonaunsorghgtteogshib
between DEI
IE
's
> 0 then normal good
Cross price elasticity of Demand ( Good At Good B ) :
A measure of consumers
'
responsiveness for Good A
When the price of Good B changes
KEDAB =
%4QD( Good A) If KED > 0 substitutes
% Llp C Good B) KED =O Unrelated
KED ( 0 Complements
* As 1) ( EDI increases , the relationship blwthez goods increases

Government RegulationPrice Ceiling
:
A government mandated maximum
price
Examples :
interest usury laws ( maximum interest
rates ) ,
necessities ( utilities in US ) ,
rent control , price
gouging laws
often leads to
shortages because suppliers lose incentive
S
nnmgbkEEF.ly a
on
3 1 1 11
ItI 1
Ceilingbinding
ps shortage
Ceiling 3000
D
4000 7000
QS QD
Price Floor :
A government mandated minimum price
Examples : minimum
wage ,
agricultural support ,
alcohol }
tobacco
S
7
¥Y
floor
D
3000 6000
QD QS
prefloor postfloor
S S
CSbthodoirn
,9o§
.gs, , ,
120
twlpsl=L
1
bwld
floor
-
Old -
nonbinding Ps = Ps
-
floor
= D - D
500 300

wage wage
households
S
7
5
floor 7 floor
6 1 1 1 1
-
6 11
-
1 1 1
-
.
- -
- D
-
=
-
-
.
-
firms
-
D
a
= =
a
17500 200 500
490
10
people unemployed 300 people unemployed
The success of raising Minimum
wage depends on how elastic the
demand curve is .
P
Mcz
3-
in
$2 MC ,
$2 per Unit tax On producers
I -
Q
p D
Individual Market Level
-
Firm
-
MC post tax
7-
•
Sposttax-
( + $2 ) -
wpYff×=5 -
s -
• •
S pretax-
MC
pretax -
- 3 -
•
••
- -
-
1 - •
I I I I I I I 1 Q I I I I I I I I I Q
5 100 SOO 900
A
per unit tax on producers shifts the market
supply Curve
"
Up
"
by the amount of tax ( S← )
P
sposttax Consumers pay $5
consumers pay =
5.11iii.
s pretax After -
tax price for Sellers =
$3
sellers receive
=3i Iii -
-
D
=
Q

P
s
post tax Consumers pay $5
5.tax wedge {
t
$2
s pretax After -
tax price for sellers =
$3
3-
is Total tax revenue :$ 2×500=511000
'
Q
500
Tax
Wedge:
The difference between the price
consumers pay G sellers receive due to tax
Tax Burden ( Or Tax Incidence ) :
The amount
by which a tax causes prices to increase
L decrease ) for Consumers ( producers )
Tax Burden
Consumers :
5 -
4 = $1 per unit
Producers :
4 -
3 =
$1 per unit
* The more inelastic side Will bear a
majority of
the tax burden
p Tax Revenue
# of units solid ×
per unit tax
S
post tax
500 ×
2
buyers pay =
5 i 1 l l I i
5 Pretax
$ 1000
severs receive
=3%sFn¥*Et
"
E. D
DWL= ÷ (2×200)=200
500 700
Q

Sposttax
-
S pretax
8- Original price =
$6
buyers pay > > -
±
•
'
=
$6 + $2 tax =
$8
6-
-
sellers receive > s -
-
=
If p= 8
÷ Qs= 40
-
= I D Q D=
20
2040
surplus
=
40-20=20 Units
↳
producers don't pass full Tax
onto consumers
P
A per unit tax on consumers
t .
$2
Shifts demand
"
down
"
by
D
pretax
the amount of tax
D
post tax
Q
p
Producersurplus
→
tax revenue
CS
s
-
tax -
S
$500
Revenue
DWL
,
3h's
"
'
"
'
"
'
'
E
'
I
ispjoesttatxax
consumer surplus →
tax revenue
5007100
Q
$500
In perfect competition ,
market outcomes ( P ,Q ,
surplus ) don't depend on which side of the
market
pays the tax
P
s
Tax Burden
buyers Consumers : 110 -
100=51101 unit
pay
= 110
4 Producers :
100-60=15401 unit
100 - •
srLIFE 60 -
•
D
pretax
40 so
QDPost tax

Subsidies
s ,
$2 subsidy to producers
- $2
52
t
s ,
$40 subsidy to producers
120
.
iii iii. Buyers pay $80
no
-
52
producers receive $120
80 1 1 1 1 1 1
it=
D Producer price =
Cost to consumers +
subsidy
, T 120 =
80 + 40
50 70
Total Cost of subsidy =
per unit subsidy × # of units sold
2800 =
40 ×
70
Pre -
subsidy Post -
Subsidy
CS 1250 2450
PS I 250 2450
Cost
-
2800
TS 2500 ) 2100
Total Surplus for 7Oth Unit :
CS 80-80 =
0
ps 120 -
120 = 0
Cost -
40
TS
-
40

5 ,
Presubsidy Post
Subsidy
CS A+B A +
B+F+E
A
52 ps F +
G F+G + B + C
B
§ D)
subsidy Cost
-
( B+C+D+EtF )
F Wedge TS A+B+F+G At B+F+G
-
D
G
* D= DWL
D
Total Surplus always decreases
*
$2 Subsidy to Consumers
$2
Dz
:$40 subsidy to Consumers
Dz After -
sub price for consumers :
D ,
$120 -
$40 =
$80
Producers receive : $120
$70 Subsidy to consumers
%
.
.
,
...,%
.
,
s NOSUB price for Consumers :$ 100
=
aftersubpricefor Consumers :
$40
==
Dz
Consumer benefit
'
.
$60
I I D ,
* More inelastic side gets more benefits

Externalities
Externalities :
an action causes a positive or
negative effect
on a third party ( a market inefficiency )
-
ex :
secondhand smoke
Social Efficiency :
the outcome maximizes total surplus
Private Costs :
the value of costs only incurred by the firm
External Costs :
the value of costs imposed by negative
externalities
Social Costs :
private costs + external costs
Ex : What is the socially efficient number of transactions if
there is a per unit external cost of $20 associated with the
production of the good ? 4,000 units
Sz =
S ,
+ social cost
70 -
I I I 1 S ,
so l ' '
÷
-
HOW many units Will be sold in
÷ a perfectly competitive market ?
=
=
D
1 1 5000 units
4000 5000
52
$20 per unit
externality
70 iii. '
.
s ,
Sale Of 4000
th
Unit :
so ill '
E
'
. ( S =
65 -
50 =
$15
÷ -
PS =
50 -
45 =
$5
÷)
External Cost =
$20
40005000
Total Surplus = 0

social Cost = after tax supply curve
private cost
45 -
zs -
What per unit tax should the
,
D
government impose ? $20
5000
Pigouvian Tax :
a tax designed to correct negative externalities
Absent government intervention ,
a competitive
market production level in the market for a
negative ( positive ) externality will result in more
( less ) units being produced
Private benefit :
value of benefit only to consumers
External Benefits :
Value of benefits imposed by positive
externalities
Social Benefit :
private benefit + social benefit
Pigouvian Subsidy :
a subsidy designed to account for
positive externalities

Negative Externality
socially
efficient
Social Cost =
private Cost + external cost
quantity
8Wm}efFfiFe
••
Sprivate cost
outcome
=
•••
competitive outcome-
.
÷-
D= private benefit = social benefit
QSELQPC
Positive Externality
socially
efficient S= Private cost social cost
quantity
DWL from
• Competitive
= outcome
competitive outcome •_ =
social Benefit =
private benefit + external
-
benefit
= = D
private benefitI 1
Qpc QSE

Coase Theorem
Your roommate shores .
You value peace E quiet at $100
Roommate values not having to wear nasal strips at $50
socially Efficient Rules Protect Peace Rules Protect the
Outcome : E Quiet Right to Make Noise
Roommate wears Outcome :
Roommate Outcome : Roommate
nasal strips wears the nasal Wears nasal strips
strips ↳ You pay between
$50 G $100 to
roommate
Cease Theorem : The socially efficient Outcome
to an
externality program will be reached privately
if transaction costs are low , regardless of the
initial assignment of property rights
Transaction Costs :
the costs incurred in
making an
economic
exchange ( e.
g. time
,
contracting , litigation
Costs )
Property Rights :
Entitlements which holders Cannot
be forced to give up
Liable :
legally responsible to compensate another
party for
damages
Socially efficient outcome ( Coasian Framework ) :
Final assignment of property rights that maximizes
net benefits ( benefits -
costs )

Example :
Factory { Farmer # 1
-
cost of pollution reducing technology
=
$95,000
-
1,000 farmers
-
average Cost of pollution =
$1001 farmer
Socially efficient outcome :
factory adopts technology
95,000<100,000
1000 .
100
Property Rights Property Rights
Protect Farmers :
Protect Factory
:
Outcome :
adopt Outcome :
additional
the technology pollution if transaction
costs are
large
K Transaction costs can be prohibitively high in some
cases so the initial assignment of
property rights is
important for efficiency
Example :
Farmer { Railroad # 1
Cost of barrier =
$1,2001 year
Cost of Crop damage
=
$5001
year
Crops burn
ZERO TRANSACTION COSTS
Property rights protect railroad
Outcome :
Crops burn ,
no
payment between parties
Property rights protect farmer
Outcome :
payment between $500 E $1200 to farmer
* The initial assignment of property rights affects
potential payments /
agreements between parties
even when transaction costs are low

Example :
Farmer { Railroad # 2
Cost of barrier =
$10001
year
Cost of Crop damage
=
$20001
year
barrier is built
HIGH TRANSACTION COSTS
Property Rights Property Rights
Protect Farmers :
Protect Factory
:
Outcome :
barrier Outcome :
crops
burn if railroad Can
be held responsible
for
damages
The people who value the resource the most end up using
the resource
Efficiency is based on ability to
pay in addition to
fundamental evaluation

Tragedy of the Commons
A good is rival in Consumption if more than one person cannot
Use the same unit of the good at a time
A good is excludable if the supplier of that good Can
prevent people who do not pay for consuming it
Excludable Non -
excludable
Rival Private Goods Common Resource
-
car
-
fishing in the Ocean
-
groceries
-
swing at public Park
Non -
rival Quasi -
Public Goods Public Goods
( Or Club Goods ) -
national defense
-
toll road Luncoh -
-
public Park
gested
) ( Uncrowded )
-
cable 1 Netflix
Tragedy of the Commons :
the tendency for a non
-
excludable resource to be overused and lor under -
maintained

dad
If Farmer A keeps a small herd ,
Farmer B Will keep a
large
herd .
( 100 ,
000 > 70,000 )
large small
If Farmer A keeps a
large herd ,
Farmer B Will keep a
large
herd .
( 40,000 > 20,000 )
large small
Both farmers have a dominant strategy of always
Choosing a large herd
Solutions to
Tragedy of the Commons
-
private solution through negotiation
-
social norms
-
use restrictions
-
licenses
-
establish property rights
-
sanctions 1 punishments
-
littering fine
-
WTO
-
taxes
1.
generate revenue
2. Curb Use

Free Rider Problem :
individuals can benefit from
public goods without
paying a share of the cost
Spending on public goods can
generate a social
multiplier ( i. e. the total benefits exceed the benefit
received by the individual )
Solutions to DWL from
market power :
-
price ceiling at $5
•
↳ problem :
How does the
regulatorknow E Update this price ?
-
subsidy to consumers 1
producers
↳
problem :
rewarding the
firm for charging too high of
a price
S
post subsidy
price ceiling

Theory of the Firm
Industrial Organization ( 10 ) Building Blocks
Explicit Costs :
physical transfers of money for business
activities
Implicit Costs :
foregone profits from engaging in
business activities (
Opportunity costs )
( I . e. foregone interest )
Accounting profit =
Total Revenue
-
Explicit Costs
Economic Profit =
Total Revenue -
Explicit Costs -
Implicit Costs
If economic profit =
0
,
then the firm is
making exactly
as much
accounting profit as they would be in their
next best alternative
Note :
we will assume
"
costs
"
include explicit E
implicit costs
Sunk Costs :
a cost that has already been paid E cannot
be recovered
Sunk Cost Fallacy :
incorporating sunk costs into
decision making

Suppose a firm has made a $10,000 lease payment
at the
beginning of a month .
If it
pays $5000 in
labor
,
material ,
G implicit costs ,
it will generate $6000
in revenue .
Broad¥96000 -
sooo -
oooo =
-9000
}pwritdauceDon't Produce
profit = -
10000
Fixed Costs :
Costs that remain constant as output
Changes
Variable Costs :
Costs that change as output changes
Total Costs ( TC ) =
Total Fixed Costs CTFC ) +
Total Variable
Costs CTVC )
•
Short Run :
a period of time in which some costs are
fixed
•
Long Run :
a period of time in which all costs are Variable
Exit Rule :
exit the industry in the
long run if current
E future projected economic profit is negative
TC > TR
Total Cost ( TC )
= AFC + AVC.
Average Total Cost ( ATC ) =
Quantity of Output ( Q )
•
Average Fixed Cost ( Afc ) =
Total Fixed Cost CTFC )
Q
•
Average Variable Cost ( AVC ) =
Total Variable Cost ( TVC )
Q
•
Marginal cost =
TC
Q

;offing,
=PF.tatIFE.t8
70 ( 300 ) -
60 ( 300 ) =
3000
MR
DQ
3 Ways to Write Out Profit
1. Total Revenue
-
Total Cost
2 .
P .
Q -
ATC .
Q
3 .
Q (
P-A_TC)
profit per unit

Game Theory
Game Theory : the formal study of strategic decision
making pioneered by Jon von Neumann ( 1903 -
1957 )
Nash Equilibrium :
a set of strategies such that no player
has incentive to unilaterally deviate
i. e. Conditional on what everyone else does ,
no one
Wants to
change their decision
irm B
High Low
High 8 ,
8 0
,
IQ
Firm A
-
Nash Equilibrium
Low
1-0,0¥,
§payoff to pay off to
row
player column player
Dominant Strategy
:
a
strategy that leads to at least as
high of a payoff as any other strategy regardless of
other players
'
strategies
Prisoner 's Dilemma :
the Category of
games in which
players have a dominant strategy to
"
cheat
'
; preventing
beneficial cooperation from Occurring
Builders
Metric Us
Metric
5
,
LO
0,0
Toolmakers
us 0 , O,
2- ,
4-
2 Nash Eauilibria

Coordination Game :
the
category of
game in which
multiple Nash Equilibria exist ,
each
corresponding
to the players coordinating on their actions
Player B
ROCK Paper Scissors
ROCK 0,0
-
1,11
,
-1
Rafter paper
1
,
-
I 0,0
-
1
itScissors -
1,11 ,
-
I 0,0
Nash Equilibrium :
being as random as possible
Mixed Strategy Nash Equilibrium : a Nash Equilibrium
in which players randomize over a set of actions
[
enter I
fight C- S ,
s )
don't
fight ( 10 ,
10 )
don't
enter
( 0,20 )
payoff to first moveI tfay Off to second mover
( Eehters ,
I doesn't fight ) is a Nash Equilibrium E a
Subgame Perfect Nash Equilibrium
LE doesn't enter
,
I fights if entry ) is a Nash Equilibrium
Sequential Rationality :
players must behave optimally
at
every stage of the game

Sub game Perfect Nash Equilibrium : A Nash Equilibrium
that satifies sequential rationality Ci. e. it rules out non
-
credible strategies )
Backwards Induction : the process of working backwards
to ensure that sequential rationality is satisfied
product
L -
10 ,
-10 )
B
product don't
produce
( SO ,
l )
A
product
( I
,
50 )
don't
produce B
( 10 ,
10 )don't
produce
( A produces ; B doesn't produce if A produces ,
B produces
if A doesn
'
t ) is a Subgame Perfect Nash Equilibrium
doesn't satisfy sequential rationality
( A doesn't produce ; B produces if A produces
,d B
produces is A doesn
'
t ) is a Nash Equilibrium
product
( -10 ,
2)
B
$12 Subsidy product don't
produce
( SO ,
l )
to B if They A
product ( 1
, 62 )
choose to don't
produce B
produce don't
produce ( 10
,
10 )
SPNE : ( A doesn't produce ; B produces no matter What )

Industrial Organization
Industrial Organization ( 10 ) :
the study of the strategic
behavior of firms , regulatory and antitrust policy ,
and market Competition
Oligopoly : a market Structure dominated by a few
firms
Monopoly :
a
single entity producing a
good or service
with no close substitutes
Sources of Monopoly ( Market ) Power :
•
patents , copyrights ,
trademarks
•
access to rare resource ( e.
g .
DeBeers
'
diamonds )
•
production process
-
high fixed costs ( utilities )
•
innovation (
e.g. iPod )
•
tastes
•
government ownership ( e. g .
USPS )
Natural Monopoly
:
a
monopoly with decreasing average
total cost over the entire relevant range of output
:( AMTE
Q

How much profit does this natural monopolist make if
they are not regulated ?
:
.
Profit =
Total Revenue -
Total Costs
=
•
=
P .
Q
-
ATC •
Q
50
8000 = 60 ( 400 ) -
40 ( 400 )
I- ATC
-
MC
-
MR D
1 1 I I I I I I I
Q
500
What price ceiling would the government set to
ensure that the monopolist makes zero economic
profit ?
P profit =
P .
Q -
ATC .
Q =
Q ( P -
ATC )
: If P= ATC ,
profit = 0
: para
Price ceiling to ensure monopolist makes
so
:¥ zero economic profit =
$30
µ .
•
•
Mc
pricing
-
Atc If P= 30 ,
ATC =
30 → Profit =
0-
MC-
D
1 1 1 1 1 1 1 1 1
Q
soo

niwdpffiocinng
Average Cost Pricing :
Regulating a monopolist To price
at
average cost
In long run , monopolist probably Will not exit market
because still making accounting profit E making as
much as in 2nd best alternative
K Can't know accounting profit from graph
↳
accounting profit will always be greater than
economic profit ; so if economic profit =O ,
then
accounting profit is positive

:
Socially efficient quantity =
800
I socially efficient price =
$20
50
I- ATC
-
MC
-
MR D
I 1 I I I I I I I
Q
500
Marginal Cost ( Plus )
Pricing
:
regulating a monopolist
to price at
marginal cost ,
which requires a subsidy
to the firm in Order to Cover fixed costs
If P =
20 ,
ATC =
28
profit =
20 .
80 -
28 .
80 = -
$6400
If the monopolist is regulated to price at marginal
cost ( Without subsidy ) ,
the firm Will exit in The
long run because it is making negative economic
profit
Cons of ATC Pricing :
-
low quality products
-
firm doesn't have incentive to cut Costs
If entry occurs :
.
Competitive effect :
entry increases price competition
which leads to a
greater overall quantity C total
surplus increases )
•
cost effect :
firms individually Will produce less
which increases
average costs reduces surplus

Characteristics of Monopolistic Competition
-
large amount of buyers sellers
} same as perfect
-
low barriers to entry 's exit Competition
-
differentiated products
In the long run in monopolistic competition ,
•
If short run economic profits are positive
↳ increased entry
↳ reduced demand for individual firms
↳ reduced profits
•
If short run economic profits are negative
↳ increased exit
↳↳
increased demand for
remaining individual firms
increased profits
In
long run ,
in monopolistic competition E perfect
Competition ,
economic profits are zero

Health Economics
Health Economics :
a branch of economics that
analyzes both micro -
E macroeconomic health G
medical Care related issues in an environment with
scarce resources
Premium : the
payment made to an insurer solely to
Obtain
Coverage
Premiums T
P T
QT
Moral Hazard :
changes in behavior due to risk protection
Adverse Selection :
when an individual knows more
about their true risk level than an insurer and is thus
more likely to purchase ( select into ) insurance
-
i. e. history of breast cancer
Principal
-
Agent Problem :
occurs when an entity
L
"
the agent
"
) is able to make decisions on behalf
of another entity (
"
the principal
"
) ,
E their
incentives are not necessarily aligned
St. Joseph
Purchase Don't Purchase
Memorial
Purchase 30 ,
40 70 ,
30
Don't Purchase To,
8€50 ,
60

Principles of Microeconomics Notes

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Similar to Principles of Microeconomics Notes

Similar to Principles of Microeconomics Notes (20)

More from Laurel Ayuyao

More from Laurel Ayuyao (12)

Recently uploaded

Recently uploaded (20)

Principles of Microeconomics Notes