WELFARE ECONOMICS: Market failures
(externalities, commons, public goods, information
asymmetry and mechanisms)
Why we need helping hand?
What we do
• General idea about WELFARE ECONOMICS
– Externalities and commons
– PUBLIC GOODS
– Information asymmetries
– Mechanism design
– Discussion: Why we need a helping hand
(price of invisibility)
Kaire Põder (kaire.poder@ttu.ee)
2
Overview of welfare economics
• General equilibrium and distributional justice
– Pareto efficiency
– I and II welfare theorem
– Alternative principles in distributional justice
• Rawls, utilitarianism, Nozik, Dworkin
• Market failures
–
–
–
–
Externalities
Commons
Public goods
Asymmetric information
• Alternative to orthodox applications to look at SOCIAL
TRAPS
• NPM + mechanism design = new governance
Kaire Põder (kaire.poder@ttu.ee)
3
Market failures: Externalities 1
•
Definition of the externality:
– An externality is an effect of a purchase or use decision by one set of parties on others who did not
have a choice and whose interests were not taken into account.
– Production and consumption externality
– Positive and negative externality
•
Education and pollution
– Network externality:
•
•
the effect on a user of a product or service of others using the same or compatible products or services.
Positive network externalities exist if the benefits are an increasing function of the number of other users.
Negative network externalities exist if the benefits are a decreasing function of the number of other users.
The Problem:
– There is no market for externalities, thus we don’t know the prices of the externality and how to
internalise (is it possible to use Pigovian taxes and subsidies) externalities?
•
1. model ‘negative externality and Edgeworth box’
– Coase, Ronald H. (1960). "The Problem of Social Cost". Journal of Law and Economics 3
– Coase solution (Coase theorem: The size of the externality is not dependent on the distribution of
the property rights (in the absence of transaction costs)
•
if trade in an externality is possible and there are no transaction costs, bargaining will lead to an efficient
outcome regardless of the initial allocation of property rights
– Criticism: there are always transaction costs present + other obstacles to bargaining or poorly
defined property rights
– Implications of the Coase ‘social cost’ approach (political Coase theorem, efficient institutions and
laws)
•
Some have argued that the Coase Theorem applies to political markets as well. Acemoglu provides evidence
to the contrary, claiming that the Coase Theorem is only valid while there are "rules of the game" that are
being enforced by the government. But when there is nobody there to enforce the rules for the government
itself, there is no way to guarantee that low transaction costs will lead to an efficient outcome in democracies
Kaire Põder (kaire.poder@ttu.ee)
4
Market failures: Externalities 2
• Pigou’s solution to the social costs:
• Benevolent dictator or social planner:
– Arthur C. Pigou (1877-1959) The Economics of Welfare (1920)
http://www.econlib.org/library/NPDBooks/Pigou/pgEW.html
• Assume production externality (pollution) and two firms (e.g. Water polluting plant
and fishery)
• Mergery of two firms will make them produce less pollution (x*)
• Social cost of the pollution is MDx
• How to make polluting plant to produce x*
– Pigouvian taxes (MDx=t)
• Measurement problem (Baumol) – how to indicate the size of the tax (how to now the
size of the externality)?
• Overtaxation problem (Coase) -- the tax placed on an industry creating a negative
externality should not be changed after it is implemented.[Coase argues that a factory
emitting smoke is not entirely responsible for the social harm of smoky air. If the
factory were not there, no one would suffer from smoky air, and if the people were not
there, no one would suffer from smoky air. Because of this reciprocity of harm, neither
party should pay the full cost. The social harm gets worse by pigouvian taxes. If the
smoke-emitting factory must pay dearly for all its smoke, it will reduce its quantity of
production or buy the necessary technology to reduce its smoke rate. With the advent
of clean air, neighbors may move into the area. This immediately increases the marginal
social cost of smoke, which would require a tax increase on the factory. Essentially,
each time the tax increases, the population increases and the marginal cost of the
status quo increases again,
soPõder
the (kaire.poder@ttu.ee)
factory is punished for making conditions good 5
Kaire
enough that people want to move there. There is no optimal solution to the taxes.
Kaire Põder (kaire.poder@ttu.ee)
6
Market failures: The Tragedy of the commons 1
•
G. Hardin (1968) „The tragedy of commons“; Science: 1243-47
EXPECTED UTILITY MODEL OF POLLUTION
Let assume a „rational polluter” who clearly prefers a pure nature to polluted one. So our experienced consumer of natural beauty
faces the following costs and benefits. Benefits form beauty are B and cost of not polluting c. Also out consumer faces free possible
states of world: s1 , s2 or s3. s1 is the state where natural resources are public goods, so the pollution created by one individual will
be absorbed by nature itself. s2 is the state where our consumer “beaks the tie” causing the tragedy of commons; and the final state
(s3) is the “polluted world” where our consumers polluting or not has marginal effect. Our rational beauty consumer faces a following
choice alternatives: to pollute (D) or not to pollute (C). The situation can be summarised in table:
D
C
EU ( D)  p1 B
s1
B
B-c
p1
s2
0
B-c
p2
s3
0
-c
p3
EU (C )  p1 ( B  c)  p 2 ( B  c)  p3 c
Optimal strategy is to cooperate (weak domination) if:
p1 B  p1c  p2 B  p2 c  p3 c  p1 B
Leads to final condition
p2 B  c
What if include risks. Let assume that our individual is risk adverse
Kaire Põder (kaire.poder@ttu.ee)
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Market failures: The tragedy of commons 2
• Hardin original text:
http://dieoff.org/page95.htm
• Solutions (evolutionary view on institutions):
– Private property
– Social norms (evolutionary solutions to the social
traps)
• External enforcement (political power view on
institutions)
– laws, regulations, fines etc
Kaire Põder (kaire.poder@ttu.ee)
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Market failures: Public goods 1
• Definition:
– MC=0
– Cannot exclude
• Problem: free rider
• Public goods (Hardin, Russell. 1997. Economic Theories of the State. In
Perspectives in Public Choice. Ed. Muller, D. Cambridge: CUP.)
– Pure and ‘not-so-pure’ public goods
• Samuelson definition of public goods – two characteristics must be
satisfied: (1) nonrival supply; (2) nonexclusion. Latter depends a lot on
technology of exclusion.
• Extreme coordination theory – desirable state needs to provide few
public goods, it could merely enable individuals to provide such goods.
State provides just contract enforcement (regulatory framework) which
enables private actors to engage in profitable activities (profit in
competitive markets is a public
itself)
Kaire Põdergood
(kaire.poder@ttu.ee)
9
Problem of the free rider in ‘clean kitchen case’
Do you know what type of the game is this?
Examples:
Education. Education used to be a private good with positive externalities. Thanks to technology and
government largesse it is no longer the case. It is being transformed into a nonpure public good.
Technology-borne education is nonrivalrous and, like its traditional counterpart, has positive
externalities. It can be replicated and disseminated virtually cost-free to the next consumer through the
Internet, television, radio, and on magnetic media. MIT has recently placed 500 of its courses online and
made them freely accessible. Distance learning is spreading like wildfire. Webcasts can host - in principle
- unlimited amounts of students.
Defence. Small society cooperation can be achieved trough reciprocal interaction, large society legal
sanctions are needed for obtaining cooperation.
Important: the state itself is a public good – so the statement is strange – in frustration at failing to
provide ourselves with some public good, we merely provide ourselves another that then provides us
the one we failed to provide.
Kaire Põder (kaire.poder@ttu.ee)
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Market failures: Public goods 2
• General principles:
– How much to provide? What is the efficient amount?
– Samuelson condition:
• MRS1 +MRS2 = MRT
• Or differently: the efficient level of public goods production to be where the
ratio of the marginal social cost of public and private goods production equals
the ratio of the marginal social benefits of public and private goods
production.
• This condition is not the same as the efficiency conditions for an economy
with only private goods. With this new efficiency condition. It rahter means
adding demand curves vertically (For a public commodity, each consumer
consumes same amount of commodity but at a different price)
– Simple example: A community composed of just two consumers. The
government is considering whether or not to provide a park. Arthur is
prepared to pay up to $200 for use of the park, while Julia is willing to
pay up to $100. The total value to the two individuals of having the
park is $300. If it can be produced for $225, there is a $75 gain on its
production since it provides services that the community values at
$300 at a cost of only $225.
Kaire Põder (kaire.poder@ttu.ee)
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Kaire Põder (kaire.poder@ttu.ee)
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Market failures: Public goods 3
• How much to provide public goods
– To establish a market (a Lindahl market) for a pure public good
– Each consumer would have to voluntarily reveal and pay their
reservation price (their Lindahl price) per unit for a pure public good
• Summing reservation prices and equating sum to MRPT would determine
efficient allocation of pure public good
• Such markets generally are not feasible
– Mainly as a consequence of free-rider problem
– Consumers’ dominant strategy: Understate their preferences and rely on other
consumers to pay a larger share for pure public goods
– Nonexclusive characteristic of pure public goods fosters this free-rider strategy
– One solution to free-rider problem:
• For government to impose a per-unit tax on each consumer equivalent to their respective
Lindahl prices
• However, unlike reservation prices for private goods, Lindahl prices are not revealed in
market
• Consumers cannot adjust their level of consumption unilaterally
• To impose such a tax government agency must perfectly price discriminate among
consumers
– Such systems are difficult to achieve (but there is some hope, mechanism design)
Kaire Põder (kaire.poder@ttu.ee)
13
Market failures: Asymmetric information
• Problem: one agent has no incentives to reveal information (not that one has more
or different information than the other agent)
• Lemon market:
– G. Akerlof (1970)“The Market for Lemons: Quality Uncertainty and the Market
Mechanism“. The quarterly Journal of Economics, 87: 488-500.
– Conclusion –adverse selection
– Gresham’s Law (Bad (money) drives out good)
• Moral hazard
– Changes the incentives
– moral hazard is a situation where a party will have a tendency to take risks because the
costs that could incur will not be felt by the party taking the risk. A moral hazard may
occur where the actions of one party may change to the detriment of another after a
financial transaction has taken place.
• Solutions:
– Government (social planner)
– Market is able to find a solution:
• Signalling
• Screening (IQ test, interview, information search)
In political science and economics principal–agent problem or agency dilemma concerns
the difficulties in motivating one party (the „agent"), to act on behalf of another (the
„principal")
Kaire Põder (kaire.poder@ttu.ee)
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Example of the education market
(Spence 1973)
• Assumptions:
– Opportunity costs of education of more able student
(nature chooses the ability) is lower than the opportunity
costs of the less able
• Separating equilibrium (not pooling equilibrium): e* is
efficient only then opportunity cost of able students
are lower than opportunity costs for less able students
• Sheepskin effect
– If aforementioned is valid, then education certificate is a
separating signal in the labour market (indicating your
productivity)
End of the first lecture
Kaire Põder (kaire.poder@ttu.ee)
15
Alternative view to market failures: social
traps
• We are in social trap whenever individual
rationality will not lead to socially optimal
outcomes (Pareto efficiency)
– Thus markets (based on individual information
and incentives) fail
– Easy to model using game theory (next slide)
Kaire Põder (kaire.poder@ttu.ee)
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Normal form games
•
Assumptions about information:
– We know the number of players and their strategies (strategy or action profiles)
– Preferences (payoff profiles)
•
No inter-related utilities
– Simultaneous action (choice)
•
Normal form game (N, A, u)
– Players 𝑁 = 1, . . , 𝑛
– Action set 𝐴𝑖 𝑎 = 𝑎𝑖 , … , 𝑎𝑛 ∈ 𝐴 = 𝐴1 × ⋯ 𝐴𝑛 (a=action profile)
– Utility (payoff fn) 𝑢 = (𝑢1 , … 𝑢𝑛 ) (u= payoff profile)
•
Types:
– 0-sum games (matching pennies, heads and tales)
•
𝑎 ∈ 𝐴, 𝑢1 𝑎 + 𝑢2 𝑎 = 0
– Positive sum games (PD types or coordination games)
•
∈ 𝐴, 𝑢1 𝑎 + 𝑢2 𝑎 = c
In certain cases (e.g. Prisoners’ dilemma) the knowledge about preference order of the other
player is not important (or even about their strategies). We can still predict behaviour. Thus, we
need less information that usual critics of the games in social sciences assume.
Social traps: Catalogue of games
• prisoners’ dilemma (social trap)
– Public good provision
– Various competitive cases (think your own
example)
• Coordination games (coordination traps)
•
•
•
•
pure coordination
Battle of sexes
stag-hunt (assurance, trust dilemma)
Chicken (anti-coordination, hawk-dowe)
Kaire Põder (kaire.poder@ttu.ee)
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PD
II
C
C
I
D
b; b
a; d
D
d; a
c; c
Figure 1: Prisoners’ dilemma
In Figure 1, symmetric normal form games represent individual players’ choice
between hypothetical “cooperative” (C) and “defective” (D) actions. The
preference ordering of the payoffs is given in alphabetical order a b c d .
Coordination games
I
R
L
II
II
II
R
L
2; 2 0; 0
0;0 1; 1
A
B
2; 1 0; 0
0;0 1; 2
S
R
3; 3 0; 2
2; 0 1; 1
I
A
B
(a) pure coordination
Figure 2: Coordination games
(b) battle of sexes
I
S
R
(c) stag hunt
II
I
D
C
D
0; 0
1; 3
C
3; 1
2; 2
(d) chicken
Solution concepts
– Ideal cases unique equilibrium
•
•
•
Elimination of strictly/weakly dominated strategies (iterated elimination)
–
–
•
Only in the case of pure-coorindation or repetitive (iterated) games
Mixed equilibrium
–
–
•
involving two or more players, in which each player is assumed to know the equilibrium strategies of the other
players, and no player has anything to gain by changing only his own strategy unilaterally. If each player has
chosen a strategy and no player can benefit by changing his or her strategy while the other players keep theirs
unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium.
Tacit consent (or correlated equilibrium)
–
•
Strict domination. Strategy B is strictly dominant if strategy B strictly dominates every other possible strategy.
Strategy B is strictly dominated if some other strategy exists that strictly dominates B.
Weak domination. Strategy B is weakly dominant if strategy B dominates all other strategies, but some are only
weakly dominated. Strategy B is weakly dominated if some other strategy exists that weakly dominates B.
Nash equilibrium
–
•
There can be many equilibria (coordination games)
No equilibrium (kö-ollo-papir)
A pure strategy provides a complete definition of how a player will play a game. In particular, it determines the
move a player will make for any situation he or she could face. A player's strategy set is the set of pure strategies
available to that player.
A mixed strategy is an assignment of a probability to each pure strategy. This allows for a player to randomly
select a pure strategy. Since probabilities are continuous, there are infinitely many mixed strategies available to a
player, even if their strategy set is finite.
• Probabilities may indicate the share of players who choose certain pure strategies (in large n games)
• Probabilities just indicate is there ‘total randomisation’ or not
• Outcomes must be interpreted as prevailing norms, not as outcomes of free choice (Aumann)
Risk-dominance (Harsanyi, Selten) – we don’t do
–
–
Deviation loss
Probabilities included (what to use: a) averages, b) expected
Welfare optimisation ≠ equilibrium
• Welfare comparisons:
– The outcome 𝑎 Pareto dominates the outcome 𝑎 if
(a) For every player i, 𝜋(𝑎) ≥ 𝜋(𝑎)
(b) There exists at least one player j for whom 𝜋 𝑎 > 𝜋(𝑎)
– An outcome is called Pareto efficient (optimal) if there
does not exist any outcome which Pareto dominates
the outcome a*.
– Outcomes 𝑎 and 𝑎 are called Pareto non-comparable
if for some player i, 𝜋 𝑎 > 𝜋 𝑎 , but for some player
j, 𝜋 𝑎 < 𝜋(𝑎).
How optimistic can we be about
human cooperation?
• In PD type of games – not really
– Cooperation is just a cheap talk
• In coordination games –
– Some sort of social norms can emerge
• Can we help people to coordinate or to find
the way out of social trap without coercion?
– Alternative: mechanism design
Kaire Põder (kaire.poder@ttu.ee)
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Solution: Mechanism design
• Mechanism:
– Reverse game (designer is creating a game, that will lead to
the defined outcomes);
– I was taught in 2005 (Implementation theory)
Implementation problem is to devise a mechanism, or game form, g, which has the property that:
(a) when g is played a state  the unique equilibrium outcome is a; (b) when g is played in state 
the unique equilibrium outcome is b.
– Quasi-market (used in economics and pol.sci), allows to
mix equity and efficiency (or other political aims of the
distribution);
– Political science/public management applies NPM
• The provision of public goods should operate under the same
incentive structures as revealed by markets, thus market kind of
environment (choice) must be introduced in various phrase of the
human sphere: education (school and university choice), health
care (hospital choice, choice of GP general practitioner) etc.
Kaire Põder (kaire.poder@ttu.ee)
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Mechanisms: Theoretical background
• Implementation theory
– Hayek-Mises-Lange-Lerner. Hurwicz. Vickrey.
– Big questions: alternative mechanisms (to price mech.)
which will lead to efficient and equitable results?
– Additional questions: Cost of running mechanisms,
informational requirements, externalities.
– Theoretical core: How built them so that they are not open
to strategic manipulation?
– Today only ‘small questions’ have solutions: few agents,
monopolistic pricing, auction design, bargaining, theory of
organisations (Williamson).
• My source: Moore, J. 1992. Implementation, contracts, and
renegotiation in environments with complete information.
Chapter 5 in: Laffont, Jean-Jacque (ed.): Advances in economic
theory Sixth World Congress Vol. 1, Cambridge University Press,
182:282.
Kaire Põder (kaire.poder@ttu.ee)
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Mechanisms: An example
• Solomon’s decision (old testament)
– Anna and Bess – who is the mother
– Mechanism: if nobody is ready to disclaim that she is a mother then child should be cut
to half
– Is the mechanism efficient?
• Two possible states of nature:
– Anna is a mother or Bess is the mother
– 4 possible outcomes:
– Give a child to Anna; give a child to Bess; cut the child, kill all 
– ‘Good’ mechanism contains a: Revelation principle
TELLING THE TRUTH (SHOWING YOUR TRUE PREFERENCES) IS A WEAKLY DOMINANT
STRATEGY
Alternatives to Solomon’s mechanism:
Better mechanism for Solomon: Each woman has to announce: either “it is state ” of
“it is a state ” together with the integer form . If they disagree on their announced state
then outcome d is implemented. (Palfrey and Srivastava). Integer can be the loudness of
voice. Outcome: both will whisper the true state.
Economists design of mechanisms: introduce money and side payments as lubricants.
Free stage game with fines: (1 stage): Anna says “this is not my child” (child is given to
Bess) or “this is my child” (game continues); (2 stage) Bess agrees (child is given to Anna) or
“bids some amount” (game continues and Anna has to pay small fine); (stage 3) Anna
matches the bid (child is given to Anna who pays the bid and Bess pays the fine) or doesn’t
(child is given to Bess who pays the bid).
Põderstages
(kaire.poder@ttu.ee)
26fine
• Comments about mechanism:Kaire
(a) later
are not reached they are just suitable threats; (b)
can be small; (c) works even in the case where the woman don’t know each others valuations.
Mechanisms: revelation principle
• Mechanism should:
– Reveal the preferences
– Must be strategy-proof (not manipulating) – Meet incentive compatibility
constraint
– Efficient (usually this means maximisation of utility)
• In addition answer various questions:
– What kind of ‘equity’ or market failure we are correcting
– Who is the designer (legitimate)
– The cost of the mechanism
• In Economics there are mainly 3 types of mechanisms:
– Auctions
– Optimal provision of public goods (we only take a glimpse)
– Matching mechanisms
Kaire Põder (kaire.poder@ttu.ee)
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Matching mechanisms (example of school choice)
• There are three students (a, b, c) and three schools (s1, s2, s3), each with one
seat. Preferences are as follows:
– a: s2-s1-s3 s1: a-c-b
– b: s1-s2-s3 s2: b-a-c
– c: s1-s2-s3 s3: b-a-c
• Matching mechanisms:
– Student optimal stable mechanism (Gale-Shapley)
• Step1: Each student applies to her first choice. Each school tentatively assigns ist seats to its
applicants in their priority order, any remaining applicants are rejected
• In general, in step k. Each student who was rejected applies to her next best choice. Each
school considers the set consisting of the students it has been holding from previous steps and
new applicants, and tentatively assigns ist seats to these students one at time in priority order.
𝑎 𝑏 𝑐
• Result: 𝜇 =
𝑠1𝑠2𝑠3
– Boston mechanism
• Step 1: For each school consider the students who have listed it as their first choice. Assign
seats of the school of these studens in the order of priority
• In general, in step kth: consider kth choices of the students who are not assigned in an earlier
step. For each school with seats still available, assign in the order of priority
𝑎 𝑏 𝑐
• Result: 𝜇 =
𝑠2𝑠3𝑠1
What we did – SUMMARY
• WELFARE ECONOMICS – market failures
• What is public good?
– Definition and the problem of social traps
– Orthodox solutions to the public good problems
• Welfare economics and mechanisms
– how we situate within the wider context
– Mechanism design
• new public governance
• Case of school choice and matching
Kaire Põder (kaire.poder@ttu.ee)
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Suggested courses:
• The course ``Game Theory'' will run again
beginning on October 5, 2014.
– A description of the course and the sign up are
available at: https://class.coursera.org/gametheory004/class
• The course ``Game Theory II: Advanced
Applications'' beginning on January 11, 2015.
– The description of that course and sign up are
available at: https://class.coursera.org/gametheory2002/class
Kaire Põder (kaire.poder@ttu.ee)
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