16.4 Competitive Market Efficiency Pareto Efficient
»No alternate allocation of inputs and goods makes one consumer better off without hurting another consumer
If another allocation improves AT LEAST ONE CONSUMER (without making
anyone else worse off), the first allocation
2
16.4 Competitive Market Efficiency Pareto Efficiency has three requirements:
1)Exchange Efficiency
Goods cannot be traded to make a consumer better off
2) Input Efficiency
Inputs cannot be rearranged to
produce more goods
16.4 Competitive Market Efficiency 3) Substitution Efficiency
Substituting one good for another
will not make one consumer better off
without harming another consumer
4
1) Exchange Efficiency Model Assumptions
• Assumptions:
–2 people
–2 goods, each of fixed quantity
This allows us to construct an
EDGEWORTH BOX – a graph showing all
the possible allocations of goods in a two-
good economy, given the total available
supply of each good
1) Edgeworth Box Example
• Two people: Maka and Susan
• Two goods: Food (f) & Video Games (V)
• We put Maka on the origin, with the y-axis
representing food and the x axis representing video games
• If we connect a “flipped” graph of Susan’s
goods, we get an EDGEWORTH BOX, where y is all the food available and x is all the video
games:
6
1) Maka’s Goods Graph
Video Games
Food
u
O x
Maka
Ou is Maka’s food, and Ox is Maka’s Video Games
1) Edgeworth Box
Video Games
Food
u
O x
O’w is Susan’s food, and O’y is Susan’s Video Games
w
r y O’
Susan
s
Total food in the market is Or(=O’s) and total Video
Games is Os (=O’r) Each point in the Edgeworth Box represents one possible good
8
1) Edgeworth and utility
• We can then add INDIFFERENCE curves to Maka’s graph (each curve indicating all
combinations of goods with the same utility)
– Curves farther from O have a greater utility
• We can then superimpose Susan’s utility curves
– Curves farther from O’ have a greater utility
Remember that: y
xy MUx MU
MRS
F
VF MUV MU
MRS
1) Maka’s Utility Curves
Video Games
Food
O
Maka’s utility is greatest at M3
M1 M2
M3
10
1) Edgeworth Box and Utility
Video Games
Food
O Maka
Susan has the
highest utility at S3
r O’
Susan
s
At point A, Maka has utility of M3 and Susan has Utility of S2
M1 M2
M3 S1
S2
S3
A
1) Edgeworth Box and Utility
Video Games
Food
O
If consumption is at A, Maka has utility M1 while Susan has utility S3
r O’
Susan
s
By moving to point B and then point C, Maka’s utility
increases while Susan’s remains constant
MM1 2M3 S3 A B
C
12
1) Exchange Efficiency
Video Games
Food
O Maka
Point C, where the indifference curves barely touch is
EXCHANGE
EFFICIENT, as one person can’t be
made better off
without harming the other.
r O’
Susan
s MM1 2M3 S3
C
1) Pareto Improvement
• When an allocation is NOT exchange efficient, it is wasteful (at least one person could be
made better off)…
• A PARETO IMPROVEMENT makes one person better off without making anyone else worth off (like the
move from A to C)…
• However, there may be more than one pareto improvement:
14
1) Pareto Improvements
Video Games
Food
O Maka
If we start at point A:
-C is a pareto
improvement that makes Maka better off
-D is a pareto
improvement that makes Susan better off
-E is a pareto
improvement that makes both better off
r O’
Susan
s MM1 2M3 S3
C S5
S4
A
D
E
1) The Contract Curve
• Assuming all possible starting points, we can find all possible exchange efficient points and join them to create a CONTRACT CURVE
• All along the contract curve, opposing
indifferent curves are TANGENT to each other
• Since each individual maximizes where his
indifference curve is tangent to his budget line:
F Susan V
Vf Maka
Vf
MRS P P
MRS
16
1) The Contract Curve
Video Games
Food
O Maka
r O’
Susan
s
1) Example: House and Chase
Assume that House and Chase have the following utilities for books and coffee:
C C
Chase H
H
House
B C U B C
U ,
The Exchange Efficiency Condition therefore becomes:
The Exchange Efficiency Condition therefore becomes:
C C
H H
Chase C
Chase House B
C House
B
Chase BC House
BC
B C
B C
MU MU
MU MU
MRS MRS
/
/
18
1) MATH – House and Chase
If there are 10 books, and 4 cups of coffee, then the contract curve is expressed as:
) 10
/(
) 4
( /
,
H H
H H
Chase BC House
BC
B C
B C
MRS MRS
If House has 6 books, an exchange efficient allocation If House has 6 books, an exchange efficient allocation
would be:
would be:
4 . 2
24 10
) 4
( 6 4
) 6 10
/(
) 4
( 6
/
H H
H H
H H
C C
C C
C
C
1) MATH – House and Chase
Therefore, House would have 6 books and 2.4 cups of coffee, and Chase would have 4 (10-6) books and 1.6 (4-2.4) cups of coffee, for utilities of:
52 .
2 )
6 . 1 ( 4
79 .
3 )
4 . 2 ( 6
C C
Chase
H H
House
C B
U
C B
U
20
2) Input Efficiency Model Assumptions
• Assumptions:
–2 producers/firms
–2 inputs (Labor and Capital), each of fixed quantity
This lead to a EDGEWORTH BOX FOR
INPUTS– a graph showing all the possible
allocations of fixed quantities of labor and
capital between two producers
2) Edgeworth Box For Inputs Example
• Two firms: Apple and Google
• Two inputs: Labor (L) and capital (K)
• We put Apple the origin, with the y-axis
representing capital and the x axis representing labor
• If we connect a “flipped” graph of Google’s inputs, we get an EDGEWORTH BOX FOR
INPUTS, where y is all the capital available and x is all the labor:
22
2) Apple’s Input Graph
Labor
Capital
u
O x
Apple
Ou is Apple’s capital, and Ox is Apple’s
labor.
2) Edgeworth Box For Inputs
Labor
Capital
u
O x
O’w is Google’s capital, and O’y is Google’s labor
w
r y O’
s
Total capital in the market is Or(=O’s) and total labor is Os (=O’r)
Each point in the Edgeworth Box represents one possible input
24
2) Edgeworth and Production
• We can then add ISOQUANT curves to APPLE’s graph (each curve indicating all
combinations of inputs producing the same output) – Curves farther from O produce more
• We can then superimpose Google’s Isoquants
– Curves farther from O’ produce more
Remember that the slope of the Isoquant is MRTS and:
K LK
MP
LMP
MRTS
2) Apple’s Isoquants
Labor
Capital
O
Apple produces the most at A3
A1 A2
A3
26
2) Edgeworth Box for Inputs
Labor
Capital
O Apple
Google produces the most at G3
r O’
s
At point A, Apple makes A3 Google produces G2
A1 A2
A3 G1
G2
G3
A
2) Edgeworth Box and Utility
O
If production is at A, Apple produces A1 while Google produces G3
r O’
s
By moving to point B and then point C, Apple produces
more while
Google’s production remains constant
AA1 2 A3 G3 A B
C
Labor
Capital
28
2) Input Efficiency
O
Point C, where the isoquant curves barely touch is INPUT
EFFICIENT, as one firm can’t produce more without the
other firm producing less.
r O’
s AA1 2 A3 G3
C
Labor
Capital
Apple
2) Pareto Improvement
• When an input allocation is NOT input efficient, it is wasteful (at least one firm COULD produce more)…
• A PARETO IMPROVEMENT allows one firm to produce more without reducing the output of
the other firm(like the move from A to C)
• However, there may be more than one pareto improvement:
30
2) Pareto Improvements
O
If we start at point A:
-C is a pareto
improvement where Apple produces
more
-D is a pareto
improvement where Google produces more
-E is a pareto
improvement where both firms produce more
r O’
s AA1 2 A3 G3
C G5
G4 A
D
E
Labor
Capital
Apple
2) Input Contract Curve
• Similar to the goods market, a contract curve can be derived in the input market:
• All along the contract curve, opposing isoquant curves are TANGENT to each other
• Since each firm maximizes where their
isoquant curve is tangent to their isocost line:
w r MRTS
MRTS
lApple,k
lGoogle,k
32
2) Input Contract Curve
O
r O’
s
Labor
Capital
Apple
2) Example: Apple and Google
Assume that Apple and Google have the following production functions:
3 / 2 3
/ 1 3
/ 1 3 /
2
k , Q 4 l k
l
Q
Apple
Google
The Exchange Efficiency Condition therefore becomes:
The Exchange Efficiency Condition therefore becomes:
Google k
l Apple
k
l
MRTS
MRTS
,
,34
The isoquant slope for Apple is:
The isoquant slope for Apple is:
Apple Apple Apple
k l
Apple k
l
Apple k
Apple Apple l
k l
l MRTS k
k l
k MRTS l
MP MRTS MP
2
3 3 1
2
,
3 / 2 3
/ 2 3
/ 1 3
/ 1 ,
,
The isoquant slope for Google is:
The isoquant slope for Google is:
Apple Total
Apple Total
Google Google Google
k l
Google k
l
Google k
Google Google l
k l
l l
k k
l MRTS k
k l
k MRTS l
MP MRTS MP
) (
2 2
3 3 8
4
,
3 / 1 3
/ 1 3
/ 2 3
/ 2 ,
,
36
2) MATH – Apple and Google
If there are 1000 workers, and 125 capital in Silicon valley, then the contract curve is expressed as:
Apple Apple Apple
Apple
Google k
l Apple
k l
l k l
k
MRTS MRTS
1000
) 125
( 2 2
, ,
2) MATH – Apple and Google
Is the market input efficient if Apple has 200 workers and 50 capital?
16
\ 3 16
/ 8
200 1000
) 50 125
( 2 )
200 (
) 50 (
2
1000
) 125
( 2 2
Apple Apple Apple
Apple
l k l
k
No – Apple needs fewer capital (Google needs more capital) AND/OR
Google needs fewer workers (Apple needs more
38
3) Substitution Efficiency
• Substitution Efficiency can be analyzed using the PRODUCTION POSSIBILITIES
CURVE/FRONTIER
– The PPC shows all combinations of 2 goods that can be produced using available inputs
– The slope of the PPC shows how much of one
good must be SUBSTITUTED to produce more of the other good, or MARGINAL RATE OF
TRANSFORMATION (x for y) (MRTxy)
Production Possibilities Curve
Robots
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
9 10
Here the MRTSpr is equal to (7-5)/
(2-1)=-2, or two robots must be given up for an extra pizza.
The marginal cost of the 3rd pizza, or MCp=2 robots
The marginal cost of the 6th and 7th robots, or MCr=1 pizza
Therefore, MRTxy=MCx/MCy Therefore, MRTpr=2/1=2
40
3) Substitution Efficiency and Production
• If production is possible in an economy, the Pareto efficiency condition becomes:
PersonB xy
PersonA xy
xy
MRS MRS
MRT
Assume MRTpr=3 and MRSpr=2.
-Therefore Maka could get 3 more robots by transforming 1 pizza
-BUT Maka would exchange 2 robots for 1 pizzas to maintain utility
-Therefore 1 pizza is sacrificed for 3 robots, increasing Maka’s utility through the 3rd robot -The Market isn’t Pareto Efficient
The First Fundamental Theorem Of Welfare Economics
IF
1) All consumers and producers act as perfect competitors (no one has market power)
and
2) A market exists for each and every commodity
Then
Resource allocation is Pareto Efficient
42
First Fundamental Theorem of Welfare Economics Proof:
• From microeconomic consumer theory, we know that:
y PersonA x
xy
P
MRS P
Since prices are the same for all people:Since prices are the same for all people:
PersonB xy
PersonA
xy
MRS
MRS
Therefore perfect competition leads to Therefore perfect competition leads to exchange efficiency
exchange efficiency
First Fundamental Theorem of Welfare Economics Proof:
• From microeconomic theory of the firm, we know that:
r MRTS
lFirmA,k w
Since each firm in an industry faces the same Since each firm in an industry faces the same wages and rents:
wages and rents:
FirmB k
l FirmA
k
l
MRTS
MRTS
,
, Perfect competition leads to input efficiencyPerfect competition leads to input efficiency
44
First Fundamental Theorem of Welfare Economics Origins
• From the PPF, we know that
xy
xy
MRS
MRT
Therefore a perfectly competitive market is Therefore a perfectly competitive market is Pareto Efficient:
Pareto Efficient:
y PersonB x
xy PersonA
xy y
x
xy
P
MRS P MC MRS
MRT MC
Efficiency≠Fairness
• If Pareto Efficiency was the only concern, competitive markets
automatically achieve it and there would be very little need for government:
–Government would exist to protect property rights
• Laws, Courts, and National Defense
• But Pareto Efficiency doesn’t consider distribution. One person could get all society’s resources while everyone else starves. This isn’t typically socially optimal.
46
Fairness
Video Games
Food
O Maka
r O’
Susan
s A
C
B Points A and B are Pareto efficient, but either Susan or Maka get almost all society’s resources
Many would argue C is better for society, even though it is not Pareto efficient
Fairness
• For each utility level of one person, there is a maximum utility of the other
• Graphing each utility against the other gives
us the UTILITY POSSIBILITIES CURVE:
48
Utility Possibilities Curve
Susan’s Utility
Maka’s Utility
O Maka
All points on the curve are Pareto efficient, while all points below the curve are not.
Any point above the curve is unobtainable
A C
B
Fairness
•Typical utility is a function of goods consumed:
U=f(x,y)
•Societal utility can be seen as a function of individual utilities:
W=f(U1,U2)
•This is the SOCIAL WELFARE FUNCTION, and can produce SOCIAL INDIFFERENCE CURVES:
50
Typical Social Indifference Curves
Susan’s Utility
Maka’s Utility
O Maka
An indifference curve farther from the origin
represents a higher level of social welfare.
Fairness
• If we superimpose social indifference curves on top of the utilities possibilities curve, we can find the Pareto efficient point that maximizes social welfare
• This leads us to the SECOND FUNDAMENTAL THEOREM OF WELFARE ECONOMICS
52
Maximizing Social Welfare
Susan’s Utility
Maka’s Utility
O Maka
ii is preferred to i, even though ii is not Pareto efficient
i
ii
iii
The highest possible social welfare, iii, is Pareto
efficient
Second Fundamental Theorem of Welfare Economics
The SECOND FUNDAMENTAL THEOREM OF WELFARE ECONOMICS states that:
Society can attain any Pareto efficient allocation of resources by:
1) making a suitable assignments of original endowments, and then 2) letting people trade
54
Video Games
Food
O Maka
r O’
Susan
s
Second Fundamental Theorem of Welfare Economics
Starting Point
Goal
By redistributing income, society can pick the
starting point in the Edgeworth box, therefore obtaining a
desired point on the Utility
Possibility Frontier:
Why Is Government so Big?
1) Government has to ensure property laws are protected. (1st Theorem)
2) Government has to redistribute income to achieve equity. (2nd Theorem)
3) Often the assumptions of the First Welfare Theorem do not hold (Econ 350)
56
Why Trade and Not Tax?
Taxes and penalties punish income-enhancing behavior, encouraging people to work less.
Subsidies and incentives give an incentive to stay in a negative state to keep receiving subsidies and incentives.
Lump sum transfers have the least distortion,
AND TRADE ALWAYS BENEFITS BOTH PARTIES…
16.5 Gains From Free Trade
• Trade ALWAYS makes society better off by increasing the productivity of scarce resources
• The basis for the gains from
specialization and trade is
Comparative Advantage
58
Theory of Comparative Advantage:
• Production Possibilities :
–Carl and Mike: retired neighbours:
hobbies are making wine and beer
Carl’s Production
Possibilities Mike’s Production Possibilities
A B C A B C
Wine (btls) 0 30 100 Beer (btls.) 1,000 700 0
0 40 80 80 40 0
PPF’s for 1 month’s production:
Carl’s Proposition
• “Lets each of us do what we do best and trade. This will give each of us
more than we now have without either of us working any harder.”
• Notice that voluntary trade does not
take place unless both parties benefit.
60
Mike’s Production Possibilities/ Opportunity Costs
Bottles of beer
•A
C
In a month Mike can produce either 80 bottles of wine or 80 bottles of beer
Opp cost of 80 wine is 80 beer
Opp cost of 1 wine is 1 beer
Opp cost of 80 beer is 80 wine
Opp cost of 1 beer is 1 wine
Bottles of
• wine
B Consumption choice before trade•
8040
40 80
Carl’s Production Possibilities/ Opportunity Costs
Bottles of beer
•A
C•
Opp cost 100 wine is 1000 beer Opp Cost 1 wine is 10 beer
Opp cost of 1000 beer is 100 wine Opp Cost 1 beer is 1/10 wine
•B Consumption choice before trade 700
100
62
Opportunity Cost Table
Opportunity
cost of 1 beer Opportunity cost of 1 wine
Carl 1/10 wine 10 beer
Mike 1 wine 1 beer
• When producer A has a lower opportunity cost of producing good A compared to
another producer, then producer A is said to have a comparative advantage in the
production of good A.
Theory of Comparative Advantage:
Comparative Advantage: Specialization
• Carl has a “comparative advantage” (lowest opportunity cost producer) in the production of beer and therefore specializes in beer
production.
• Mike has a “comparative advantage” in the
production of wine and therefore specializes in wine production
• As long as opportunity costs differ, there is comparative advantage
64
Comparative Advantage: Specialization Comparative Advantage: Specialization
Theory of Comparative Advantage Theory of Comparative Advantage
•if specialization takes place according to comparative advantage (the lowest opportunity cost producer) and then trade takes place…. both parties can benefit: that is, move outside their
current PPF’s.
Carl & Mike Before Specialization & Trade
Carl Produces &
Consumes Mike Produces &
Consumes Total
Consumption
+ =
Wine (btls.) Beer (btls.)
30 700
40 40
70 740
Carl & Mike After Specialization, but Before Trade
Mike Produces &
Can Consume
+ =
Wine (btls.)
Beer (btls.) 0 1,000
80 0
80 1,000 Carl Produces &
Can Consume
Total Production &
Consumption
Total Gains +10 +260
66
• Carl proposes, after specialization, that he trade Mike 175 beer for 35 wine.
Carl gets wine for a reduced sacrifice
–35 wine for 175 beer instead of 350 beer, the opportunity cost before trade
Mike gets beer for a reduced sacrifice
–175 beer for 35 wine instead of 175 wine, the opportunity cost before trade
(terms of trade: 5 beer for 1 wine)
Trade: The Benefits of Specialization
Terms of Trade: 1 Wine for 5 Beer
• Since voluntary trade requires that both parties benefit from the trade.
• Before trade:
• Carl: 1 wine “trades” for 10 beer
• Mike: 1 wine trades for 1 beer After trade 1 wine “trades” for 5 beer
•The Terms of Trade are between the personal ones that exist before trade, thus producing
Carl is better off as he now only has to give up 5 beer for a wine
Mike is better off as he now only has to give up 1/5 wine for a beer
68
Trade Between Carl & Mike
1 Wine trades for 5 Beer 1 Beer trades for 1/5 Wineor
Mike
(specializes in wine)
Carl
(specializes in beer)
175 Bottles of
Beer To
Trades away
35 Bottles of Wine
Trades away To
Before trade Mike gave up 1 wine to get 1 beer, after trade1/5 wine Before trade Carl gave up 10 beer to get a wine, after trade 5 beer
Carl & Mike After Specialization & Trade Carl
Mike
Produces Trades For (+) Away (-)
Consumes After
Trade
Produced &
Consumed Before Trade
Gains fromTrade
Wine (btls.)
Beer (btls.) 0
1,000 +35
-175 35
825 30
700 +5
+125
Produces Trades For (+) Away (-)
Consumes After
Trade
Produced &
Consumed Before Trade
Gains fromTrade
Wine (btls.)
Beer (btls.) 80
0 -35
+175 45
175 40
40 +5
+135
70
Mike’s Production Possibilities After Trade
Bottles of beer
•A
C
Bottles of wine
• •
B •D Consumption after trade
Mike produces 80 wine and then trades 35 wine for 175 beer,
leaving him with 45 wine and 175 beer, point D
8040
40 80
175
45
Carl’s Production Possibilities/ Opportunity Costs, After Trade
Bottles of beer
•A
C•
•B
•D Consumption after trade
Carl produces 1000 beer and trades 175 beer to Mike for 35 wine, leaving him with 825 beer and 35 beer, point D
700 100
825
72
Absolute Advantage
• When a producer with of set of inputs can produce more output than another with the same inputs, the first producer has an
absolute advantage in production of the output.
• Carl has an absolute advantage in the
production of both wine and beer.
Gains from Specialization and Trade
• Specialization produces gains for both traders, even when one trader enjoys an absolute advantage in both endeavors.
• Unless two people/firms/countries have IDENTICAL opportunity costs, Trade is always beneficial
74
Why No Free Trade?
1) Misunderstanding: people misunderstand the
facts or hold to political or ideological dogma, or confuse voluntary jobs with enforced slavery
2) Short-run effects: in the SHORT-RUN, there may be some unpopular adjustments:
a) Richer, developed countries may lose jobs to developing countries with a comparative
advantage
b) Poorer, developing countries may have short- run environmental damage until the higher
incomes lead to environmental protection
Chapter 16 Conclusions
1) General equilibrium requires
simultaneous equilibrium in multiple markets
2) One change can cause a cascade of changes through markets until a new equilibrium is reached
3) An equilibrium is Pareto Efficient if no
other allocation of inputs can make one
person better off without making another
76
