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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 was Pareto Inefficient.
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
3
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 quantityThis 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
5
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
Foo
d
u
O xMaka
Ou is Maka’s food, and Ox is Maka’s Video Games
7
1) Edgeworth Box
Video Games
Foo
d
u
O xMaka
O’w is Susan’s food, and O’y is Susan’s Video Games
w
ry 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 allocation
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
xxy MU
MUMRS
F
VVF MU
MUMRS
9
1) Maka’s Utility Curves
Video Games
Foo
d
OMaka
Maka’s utility is greatest at M3
M1
M2
M3
10
1) Edgeworth Box and Utility
Video Games
Foo
d
OMaka
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
11
1) Edgeworth Box and Utility
Video Games
Foo
d
OMaka
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
M1M2
M3
S3A B
C
12
1) Exchange Efficiency
Video Games
Foo
d
OMaka
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
M1M2
M3
S3C
13
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
Foo
d
OMaka
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
M1M2
M3
S3C
S5
S4
A
D
E
15
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
VSusanVf
MakaVf P
PMRSMRS
16
1) The Contract Curve
Video Games
Foo
d
OMaka
r O’
Susan
s
17
1) Example: House and ChaseAssume that House and Chase have the following
utilities for books and coffee:
CCChaseHHHouse CBUCBU ,The Exchange Efficiency Condition therefore becomes:The Exchange Efficiency Condition therefore becomes:
CCHH
ChaseC
ChaseB
HouseC
HouseB
ChaseBC
HouseBC
BCBC
MUMU
MUMU
MRSMRS
//
18
1) MATH – House and ChaseIf there are 10 books, and 4 cups of coffee, then the
contract curve is expressed as:
)10/()4(/
,HHHH
ChaseBC
HouseBC
BCBC
MRSMRS
If House has 6 books, an exchange efficient allocation If House has 6 books, an exchange efficient allocation would be:would be:
4.2
2410
)4(64
)610/()4(6/
H
H
HH
HH
C
C
CC
CC
19
1) MATH – House and ChaseTherefore, 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
CCChase
HHHouse
CBU
CBU
20
2) Input EfficiencyModel 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
21
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
Cap
ital
u
O xApple
Ou is Apple’s capital, and Ox is Apple’s labor.
23
2) Edgeworth Box For Inputs
Labor
Cap
ital
u
O xApple
O’w is Google’s capital, and O’y is Google’s labor
w
ry 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 allocation
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
LLK MP
MPMRTS
25
2) Apple’s Isoquants
Labor
Cap
ital
OApple
Apple produces the mostat A3
A1
A2
A3
26
2) Edgeworth Box for Inputs
Labor
Cap
ital
OApple
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
27
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
A1A2
A3
G3A B
C
Labor
Cap
ital
Apple
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
A1A2
A3
G3C
Labor
Cap
ital
Apple
29
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
A1A2
A3
G3C
G5
G4
A
D
E
Labor
Cap
ital
Apple
31
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:
rwMRTSMRTS Google
klApplekl ,,
32
2) Input Contract Curve
O
r O’
sLabor
Cap
ital
Apple
33
2) Example: Apple and GoogleAssume that Apple and Google have the following
production functions:
3/23/13/13/2 4, klQklQ GoogleApple The Exchange Efficiency Condition therefore becomes:The Exchange Efficiency Condition therefore becomes:
Googlekl
Applekl MRTSMRTS ,,
34
The isoquant slope for Apple is:The isoquant slope for Apple is:
Apple
AppleApplekl
Applekl
Applek
ApplelApple
kl
l
kMRTS
kl
klMRTS
MPMPMRTS
231
32
,
3/23/2
3/13/1
,
,
35
The isoquant slope for Google is:The isoquant slope for Google is:
AppleTotal
AppleTotal
GoogleGooglekl
Googlekl
Googlek
GooglelGoogle
kl
ll
kk
l
kMRTS
kl
klMRTS
MPMPMRTS
)(2238
34
,
3/13/1
3/23/2
,
,
36
2) MATH – Apple and GoogleIf there are 1000 workers, and 125 capital in Silicon
valley, then the contract curve is expressed as:
Apple
Apple
Apple
Apple
Googlekl
Applekl
l
k
l
k
MRTSMRTS
1000
)125(22,,
37
2) MATH – Apple and GoogleIs the market input efficient if Apple has 200 workers and
50 capital?
16\316/8
2001000
)50125(2
)200(
)50(2
1000
)125(22
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 workers)
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)
39
Production Possibilities CurveR
obot
s
Pizzas
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:
PersonBxy
PersonAxyxy MRSMRSMRT
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
41
The First Fundamental Theorem Of Welfare Economics
IF1) 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
xPersonAxy P
PMRS
Since prices are the same for all people:Since prices are the same for all people:
PersonBxy
PersonAxy MRSMRS
Therefore perfect competition leads to Therefore perfect competition leads to exchange efficiencyexchange efficiency
43
First Fundamental Theorem of Welfare Economics Proof:
• From microeconomic theory of the firm, we know that:
r
wMRTS FirmAkl ,
Since each firm in an industry faces the same Since each firm in an industry faces the same wages and rents:wages and rents:
FirmBkl
FirmAkl MRTSMRTS ,,
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
xyxy MRSMRT Therefore a perfectly competitive market is Therefore a perfectly competitive market is
Pareto Efficient:Pareto Efficient:
y
xPersonBxy
PersonAxy
y
xxy P
PMRSMRS
MC
MCMRT
45
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
Foo
d
OMaka
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
47
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
Mak
a’s
Util
ity
OMaka
All points on the curve arePareto efficient, while all points below the curve are not.Any point above the curve is unobtainable
A
C
B
49
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
Mak
a’s
Util
ity
OMaka
An indifference curve farther from the origin represents a higher level of social welfare.
51
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
Mak
a’s
Util
ity
OMaka
ii is preferred to i, even though ii is not Pareto efficienti
ii
iii
The highest possible social welfare, iii, is Pareto efficient
53
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
54Video Games
Foo
d
OMaka
r O’
Susan
s
Second Fundamental Theorem of Welfare Economics
StartingPoint
Goal
By redistributing income, society can pick the starting point in the Edgeworth box, therefore obtaining a desired point on the Utility Possibility Frontier:
55
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…
57
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 ProductionPossibilities
Mike’s ProductionPossibilitiesA 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:
59
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
••BConsumption choice before trade80
40
40 80
61
Carl’s Production Possibilities/ Opportunity Costs
0
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
Bottles of wine
•B Consumption choice before trade
700
100
30 100
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:
63
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: SpecializationComparative Advantage: Specialization
Theory of Comparative Theory of Comparative AdvantageAdvantage
• 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.
65
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 & Consumptio
n
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
67
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 gains for both parties participating in the trade
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 Beeror
1 Beer trades for 1/5 Wine
Mike (specializes in
wine)
Carl (specializes
in beer)
175 Bottles of Beer
To
Trades away
35 Bottles of Wine Trades a
wayTo
Before trade Mike gave up 1 wine to get 1 beer, after trade1/5 wineBefore trade Carl gave up 10 beer to get a wine, after trade 5 beer
69
Carl & Mike After Specialization & Trade
Carl
Mike
ProducesTradesFor (+)Away (-)
ConsumesAfterTrade
Produced & ConsumedBefore Trade
GainsfromTrade
Wine (btls.) Beer (btls.)
01,000
+35-175
35825
30700
+5+125
Produces
TradesFor (+)Away (-)
ConsumesAfterTrade
Produced & ConsumedBefore Trade
GainsfromTrade
Wine (btls.)Beer (btls.)
800
-35+175
45175
4040
+5+135
70
Mike’s Production Possibilities After TradeBottles 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
71
Carl’s Production Possibilities/ Opportunity Costs, After Trade
0
Bottles of beer
A•
C•
Bottles of wine
•B
D• Consumption after trade
Carl produces 1000 beer and trades 175 beerto Mike for 35 wine, leaving him with 825 beerand 35 beer, point D
700
100
30 100
825
35
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.
73
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
75
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 worse off.
76
Chapter 16 Conclusions
4) Pareto Efficiency requires exchange efficiency (goods can’t be traded), input efficiency (more can’t be produced) and substitution efficiency (substituting production won’t improve outcome)
5) The First Fundamental Theorem of Welfare Economics states that if all perfectly competitive markets exist, allocations are Pareto Efficient
77
Chapter 16 Conclusions
6) The Second Fundamental Theorem of Welfare Economics states that governments can redistribute wealth to reach any pareto efficient outcome
7) Free Trade is always beneficial to all parties
8) Economic truths, when properly applied and explained, can cut through ideologies and make people cry