CONTRACTS – Exceptions To Coase’s Theorem – Empty Core October 31, 2006

CONTRACTS – Exceptions To Coase’s Theorem – Empty Core

October 31, 2006

Exceptions to the Theorem of Coase

• Coase Theorem• Exceptions To Coase Theorem

• Transaction Costs - October 17, 2006• Asymmetric Information - October 24, 2006• Empty Core - October 31, 2006


• COLOUR CODE FOR GRAPHS• Marginal Cost Curve for Agent (firm, individual)

under a strict liability rule• Marginal Cost Curve for Agent (firm, individual)

under a no liability rule• Marginal Cost Curve for Agent (firm, individual)

under a negotiated contract that follows the Theoem of Coase

• Demand Curve for the Agent’s output• Marginal Revenue Curve


• COLOUR CODE FOR GRAPHS• Expected Marginal Cost Curve for Agent (firm,

individual)


• COLOUR CODE FOR GRAPHS (con’t)• Average Cost Curve for Agent (firm, individual) with

no transaction costs• Average Cost Curve for Agent (firm, individual) with

transaction costs• Profit of Agent (firm, individual) • Portion of profit traded in exchange for property

rights • Portion of profit lost due to a trade in property rights• Portion of profit lost due to transaction costs


Theorem of Coase Review

Before Coase

The common law was believed to have had little practical deterrence against polluters.

Excise taxes or fines were proposed as the “efficient” way of internalizing the cost of harm against property owners

While not diminishing the precautions taken by victims of such harm.

Before Coase

The polluter pays the marginal cost of the harm it causes.

The victim must not receive a payment for the harm endured if that harm could have been avoided by the victim at lesser cost.

Theorem of Coase

The contract replaces the market as the Pareto improving mechanism

Social surplus increases and is Pareto optimal under the Coasean contract.

The least cost available Pareto improving technology is applied

No party can be worse off.

Pareto optimal social surplus means efficient use the property. Incompatible uses are converted to compatible uses.

Social surplus is improved by the same amount irregardless of which Agent has been granted property rights.

The distribution of the “equally improved” surplus can vary depending on which agent has the property rights.

Property rights are exchangeable or transferable. A “market” for such property rights is possible

Theorem of Coase

• In Sudbury, Ontario the government enacted “smoke easements” that were purchased by and transferable to the air polluters

Theorem of Coase

• Agent 2

S

DP

a2

PM

• Agent 1

S

a1

CMC

Maximum Joint Social Surplus




The Coase theorem collapses under high transaction costsmany partiesasymmetric informationcoalitional instability (empty core)


Exceptions to the Theorem of Coase Transaction Costs

Exceptions to the Theorem of CoaseTransaction Costs

• Perfectly Competitive-Agent 1 • Monopoly Market – Agent 1

SS = MC1

DP

a1

MC1 SATC SATC

PPC

PM

SATC + TC LATC

Transaction Costs


• High Transaction Low Transaction

Costs Costs

DAMAGESINJUNCTION


What is the most efficient or most socially optimal way of enforcing a strict liability rule:

(a) damages only(b) damages and injunction


Under a no liability rule, with:(a) one polluter(b) many property owners

harmedhigh transactions costs prevent a collective bribe without avoidance of free riding


Under a strict liability rule, with:(a) one polluter(b) many property owners

harmedOne owner could hold out for a bribe that would extract the entire surplus of the polluter.


Under the strict liability rule, with:

(a) one polluter

(b) many property owners harmed

The “damages only” approach has been applied in the United States by adoption of the “reasonable use” doctrine


• As McKie v. KVP showed, the common law applied by the courts in Canada did not adopt the “damages only” approach

• In both the Sudbury and KVP cases, the legislature applied a “damages only” rule in the interests of local economics


If two or more owners hold out, the polluter would have to shut down

This is what Justice Middleton believed to be the case with Sudbury farmers when he denied them injunctive relief but damages only against the air polluters


• It may be less costly for the polluters to internalize the pollution than to incur the transaction costs to ascertain the true level of harm in damages.

• studies• experts• hiring lawyers• going to court


• Professor Dewees concluded that injunctive relief, if this had been allowed by Justice Middleton, at Sudbury, might have succeeded in forcing the companies to internalize the costs and pursue optimal abatement


• T = 0 and Imperfect Information:• If a "polluter" cannot be persuaded to

settle for damages, because they suspect the “owner" is cheating, a tougher remedy is the injunction which can force a firm to shut down.

• So the polluter might be more inclined to "agree" to internalize the costs rather than risk being shutdown. (Note - on the evidence this approximates the K.V.P. case)


• In the wake of the Sudbury and KVP cases, the expansion of government invention in the market place came through various boards such as public health, regulation of professionals, slum housing, and local pollution.


Exceptions to the Theorem of Coase Asymmetric Information

Exceptions to the Theorem of CoaseAsymmetric Information

• Rules that compensate for market failures

• (a) moral hazard • (b) adverse selection


• High Transaction Low Transaction

Costs Costs

PERFECT INFORMATION

IMPERFECT INFORMATIONDAMAGES INJUNCTION

DAMAGESINJUNCTION


What is the most efficient or most socially optimal way of enforcing a strict liability rule:

(a) damages only(b) damages and injunction


• Protection of Possession• In trespass actions, where intent to

interfere with property rights is evident, the injunction against the trespasser is available.

• This is especially true when transaction costs are high.


Under the strict liability rule, the “damages only” approach becomes inefficient if the courts underestimate the damages – for example – the harm is ongoing


Asymmetric Information • In Sudbury, Ontario the government

measures underestimated the damages imposed on the farmers by the air polluters – for example – future damages when the harm is ongoing


Asymmetric Information • In Sudbury, Ontario why did INCO build

the world’s tallest smokestack?• Required by technology?• Render air pollution identification more difficult

so that private nuisance suits are more difficult to prove or

• Prosecution under the Ontario Environmental Pollution Act more likely to be unsuccessful


Exceptions to the Theorem of Coase Asymmetric Information – Breach Of Contract


• .CONTRACT

BREACH OF

CONTRACTPERFORMANCE

OF CONTRACT


• a1 = level of precaution invested by the agent-promisor (Agent 1) against breach of contract against (Agent 2)

• a2 = level of reliance invested by the agent-promisee (Agent 2) in Agent 1 (polluter)


• p(a1) = Probability of No Breach • Probability of Performance• A Completed Contract

• p’(a1) > 0• More effort results in more precaution against

breach

• p’’(a1) < 0• Diminishing “returns” to precaution as more

effort invested


• p(a1) = Probability of No Breach • Why would one expect a1 to be suboptimal

without a rule?• A2 cannot observe a1

• A1 knows that A2 cannot observe a1

• A1 will apply less that optimal a1 unless it can be assured that doing so will not minimize TOTAL expected damages


• “Liability rule” or “liability marginal cost curve” for Agent 1 is added in orange to the joint social surplus of the parties

• Max [p(a2)RP(a1) + [1 - p(a2)]RNP(a1)] - a1 - a2 - [1-p(e2)]De


• Imperfect Information•Decreasing Marginal Costs Due to Precaution

•Increasing Marginal Costs Due To Production

Strict Liabilty Rule –MC1

Contracted Liability Rule – MC1

Expected Liability – MC1

a1

$C1


• If the expectation damages rule is focused entirely on A1 this will create a second or “double” moral hazard

• What is it?• A1 cannot observe a2

• A2 knows that A1 cannot observe a2

• A2 will apply less that optimal a2 unless it can be assured that doing so will not maximize TOTAL expected damages it receives from A1

•


• p(a1U a2) = Probability of No Breach• p(a1U a2) = p(a1) + p(a2) - p(a1 ∩ a2)

• p(a1U a2) = p(a1) + p(a2) - p(a1 )p(a2)


• 1 - p(a1U a2) = Probability of Breach• p(a1U a2) = 1 - p(a1) - p(a2) + p(a1 )p(a2)

•


Exceptions to the Theorem of CoaseAsymmetric Information - Screening


• .CONTRACT

BREACH OF

CONTRACTPERFORMANCE

OF CONTRACT

LOW DISCLOSURE

PARTY

HIGH DISCLOSURE

PARTY

Exceptions to the Theorem of CoaseAsymmetric Information - Screening

• A principal in a private bilateral contract relationship writes a contract that may serve to “sort” or “separate” agents into more efficient contracts

• A court in a private bilateral agency relationship writes a rule that may serve to “sort” or “separate” contracts into more efficient outcomes

Expectation Damages Hadley v. Baxendale (1854), 9 Ex. 341, 156 E.R. 145

EH EL

A Court imposes a “complete” rule with the agents and principals

In this case two “different” agents – “two” different contracts“two” different rules

H – high disclosure principal and agentL- low disclosure principal and agent


The objective of the rule is that the two (2) types of principals reveal themselves through the choice of disclosure the principals reveal and the agents receive

This results in two distinct and separate damages measures for two distinct and separate principals (buyers, plaintiffs)


EH


The alternative, or “one size fits all” rule imposes a negative “non-disclosure” externality on low-disclosure agents (pooling)

Exceptions to the Theorem of Coase Asymmetric Information – Screening

• The court frequently “separates” the contracts that private parties negotiated as “pooling contracts” in order to increase “social surplus”

• How? By allowing:• Inequality of bargaining defences• Restraint of trade defences

• Note – in the market environment, such contracts would deter high quality types from entering the market – a form of adverse selection

Exceptions to the Theorem of Coase Asymmetric Information – Screening

• There are underlying questions that arise in assessing the way courts address contract types:

• What is the underlying probability distribution of contract types

» Is it uniform?» Is it normal (bell curve)?» Is it some other type of distribution?

• Probability distribution types can effect the type of rules a court might design. Court ordered auctions frequently reflect

» More than two types of buyers» More than one possible equilibrium price


• When issues and outcomes become too complicated, courts have developed “deference” to allow more “expert’ tribunals “sort out” the parties, subject to certain basic procedural guidelines

• In 1863, measures enacted for the demolition of "slum housing" were reviewed by the courts which concluded that, in the absence of express statutory language to the contrary, occupants must either receive notice of a decision pending or an opportunity to show cause why a decision taken should not be

acted upon. • Cooper v. Wandsworth Board Of Works (1863), 14 C.B.N.S. 180 at

194, 143 E.R. 414 at 420


Empty Core

Exceptions to the Theorem of Coase Core

.

Agent 2 has lost the exclusive use to its property rights to protect it against pollution

Agent 1 creates a harmful

nuisance that hurts

Agent 2 economically.


The legal problem of nuisance now becomes a contract problem:

Agent 2 wishes to make a payment to Agent 1 (a bribe) to induce Agent 1 to reduce its output from the market or private efficiency level of aP1 = 5/6. What bribe is Agent 2 willing to pay for a given level of output aC1 < aP1 = 5/6?


The “optimal” bribe or transfer payment lies within the interval:

25/48 < PAYMENT < 25/36

This interval is called the “core” of the contract, since any point in the interval would be a Nash equilibrium


• A coalition between three or more agents is unstable (no Nash equilibrium) if an allocation can be blocked by an alternative coalition, that is, there is a threatened breakaway or objection to the coalition by one or two of the agents.


• The core refers to allocations that are not dominated by what individual agents can achieve either independently or as part of any other potential coalition.

• So the core is a set of stable points at Nash equilibrium


• Example: What is the core in the standard prisoners dilemna game?

• It would be the point where the players’ strategies (reaction curves, incentive compatibility constraints) intersect

• So cores are not necessarily Pareto optimal


Axes

a2

a1

CORE = E[1/3(1-c), 1/3(1-c)]

Iso-Profit Curve For Agent 1

Iso-Profit Curve For Agent 2


Another example: What is the core in the bilateral agency game?

The Nash equilibria that satisfy the sharing rule for two agents:

/(1- ) = (F22/F11)^1/4

Neary, Hugh and Winter, Ralph, “Output Shares in Bilateral Agency Contracts”,

(1995), 66 Journal of Economic Theory 609-614


• Problem: What happens if there are more than two agents in the bilateral agency?

• F(a1) = F(a2) = F(a3) = 0• F(a1,a2) = 12F• F(a1,a3) = 13F• F(a2,a3) = 23F• F(a1,a2,a3) = 123F


The existence of Nash equilibria that satisfy the sharing rules for three (3) or more agents is not always guaranteed.

In some cases, subgroups of agents (sub-agency) will find it more “profitable” to defect from coalitions of all the agents.


F(a1,a2,a3) < (1/2)[F(a1,a2) + F(a2,a3) + F(a1,a3)] or

123F < (1/2)[12F + 23F + 13F]

If this condition applies, the “core” is empty. This means 123F, though it may be Pareto optimal, is unstable


• Aivazian and Callen counterexample:

• Consider two factories 1F and 2F emitting smoke reducing the profits of a neighborhood laundry 3F.

• Suppose that the parties can negotiate costlessly.


• (1F) = $3,000 • (2F) = $8,000 • (3F) = $24,000• (12F) = $15,000 • (13F) = $31,000 • (23F) = $36,000• (123F) = $40,000


• The Coase theorem may break down when there are more than two participants

• For example, the core of the negotiations may be empty under the “no damages” property rule and not empty under the “common law nuisance” rule.

• This happens when the “third party” brings a second externality to the problem


• Note that the Pareto-optimal outcome corresponds to the grand coalition outcome (123F), where the externalities are fully internalized.


• Case 1 – Common Law Right of the Laundry C to Sue in Nuisance

• If 3F has the property rights to the air, then 1F and 2F have the incentive to offer side-payments to 3F.

• However, the maximum bribe 1F and 2F can jointly offer is only (12F) = $15,000



• The combined maximum liability of 1F and 2F is (123F) - (3F) = $40,000 - $24,000 = $16,000



• The “optimal joint surplus” is:Max [(123F) - (3F), (3F)] = Max [$16,000, $24,000] = $24,000

• So 1F and 2F close down and a Pareto-Optimal allocation of resources results.


• Case 2 – No Liability Rule • Suppose on the other hand, that 1F and

2F are not liable for the pollution damages to the laundry.

•3F now has the incentive to offer side-payments to 1F or 2F, and perhaps to both, to reduce their pollution activities.


• Case 2 – No Liability Rule • It is straightforward to show that all

potential coalitions, including the grand coalition, are unstable when 1F and 2F are not liable.

• Since all potential coalitions under the “no damages rule” are unstable, the core is empty.


• Case 2 – No Liability Rule • Suppose that the grand coalition were

to form. Consider the following distribution of profits to 1F, 2F, and 3F:

• (1F) = $4,750,

• (2F) = $9,750,

• (3F) = $25,500,

adding up to (123F) = $40,000


• Case 2 – No Liability Rule • The two-member coalition of 1F and 3F

with (13F) = (1F) + (3F) = $5,000 + $26,000 = $31,000

is preferred by 1F and 3F to the 123F allocation above.


• Case 2 – No Liability Rule • Although each firm earns more than it

would by acting independently, there are many two-member coalitions which could block this allocation.


• Case 2 – No Liability Rule • All potential coalitions in the example

are unstable.


• The Aivazian argument is that the principle of self-interest remains in the model

• This means individual rationality constraints apply

• Forming a separate coalition with another firm where both make more profits at the expense of a third party applies.

• Such behavior is competitive


Avoiding The Empty Core:Contractual Conditions


• Bernholz• Pareto Optimality can be achieved

when the core is empty by judicious use of penalty clauses and binding contracts.

• This is implicitly recognized in the Neary-Winter model where if there are three or more parties, the model does not permit sub-contracting.


• The key assumption Bernholz makes is that once an agreement is signed it cannot be broken without the consent of all the parties.

• Once two parties enter into an agreement the only remaining question is whether they make a new agreement including all three parties.

• Since such a second agreement can make all three better off, the grand coalition forms and once formed it cannot come apart

• The Further Constraint: The Unanimity Rule


• What does Bernholz’s argument recall?• Contract Modification• Contracts Must Be Consensual• Opportunistic or Holdup Behaviour Not Allowed• Efficient Recontracting Is Not Necessarily Allowed in

Ontario


Avoiding The Empty Core:Additional Parties


• Mueller• The Coase theorem will not collapse

when the number of parties increases provided that the additional parties do not bring additional externalities with them.


• Mueller correctly attributes the emptiness of the core in the Aivazian example to the existence of two externalities rather than the existence of three agents

• So long as there is only one externality, the core will exist even as the number of polluters increases.


Avoiding The Empty Core:Matching Externalities


• Mueller’s “second” argument• Mueller argues that the empty-core

problem is due to the attempt to eliminate simultaneously multiple externalities with one liability rule.


• Mueller’s “third” argument• Mueller changes the structure of the

agency game from a horizontal (simultaneous) coalition game to a vertical (sequential) coalition game that contains a “Stackelberg” hierarchy


Avoiding The Empty Core:Vertical Agencies


• Case 2 – No Liability Rule • When 1F and 2F have the property

rights, if 3F’s negotiations of a bribe with 1F occurs independently of 3F’s negotiations with 2F then each externality problem becomes independently bilateral

• The core with respect to any given externality is never empty.


• Case 2 – No Liability Rule • The implication is that, with multiple

externalities, particular institutional arrangements or bargaining structures (restrictions on the sequence of negotiations) may be relevant for efficient resource allocation.


• (1F) = $3,000 → V(A) = 3• (2F) = $8,000 → V(B) = 8• (3F) = $24,000 → V(C) = 24• (12F) = $15,000 → V(AB) = 15• (13F) = $31,000 → V(AC) = 31• (23F) = $36,000 → V(BC) = 36• (123F) = $40,000 → V(ABC) = 40



• Case 2 – No Liability Rule • The remaining problem?

• Mueller’s arguments undermines the Coasean claim that specific institutional arrangements are irrelevant for Pareto efficiency when transactions costs are zero.



• Recalling the Aivazian example where the laundry firm 3F could sue in nuisance for damages, there were multiple externalities but the core existed



• The “optimal joint surplus” was:Max [(123F) - (3F), (3F)] = $24,000

• So 1F and 2F closed down but a Pareto-Optimal allocation of resources still resulted.


• Pareto efficiency is achieved regardless of whether negotiations are carried out sequentially or simultaneously

• Once a core allocation is reached, agents have no incentives to recontract


Avoiding The Empty Core:Independent Externalities


• De Bornier• De Bornier (1986) is also bothered by

the dual externality in the Aivazian example.

• De Bornier claims that the Aivazian counterexample is a general equilibrium problem

• Coase’s Theorem applies to a partial equilibrium framework.


• The problem for DeBornier stems from the fact that in the example, if 1F and 2F merge, the pollution effecting 3F is reduced, increasing 3F profits

• If 1F and 3F merge, the pollution effecting 2F is reduced, increasing 2F profits


• According to Aivazian and Callen, DeBornier assumes implicitly that there is only one pollution source in 1F’s factory that presumably affects both water and air simultaneously.

• This affects De Bornier’s conclusion that a mergers solve the legal problem in each case


• “Solutions” To The Empty Core• Pareto Optimality can be achieved when the

core is empty by judicious use of penalty clauses and binding contracts. (Bernholz)

• The common law imposes serious “coalition breaking” rules

• Match the externalities with the relevant agents (Mueller)

• Apply a property rule to each externality (Mueller)

• Create a hierarchy (Mueller and others)

Documents

CONTRACTS – Exceptions To Coase’s Theorem – Empty Core October 31, 2006