Public Economics Externality &Property rights

Dr. Simona Montagnana

University of Bath

Fall 2017 Introduction Externality Tragedy of the commons Government Intervention Conclusion

Common pool/property resources

Definition are goods non-excludable but are rivalrous. For examples: fishery, clean water, grazing land, waste disposal, etc...

Problem The problem arises from the common right of access to a resource: tragedy of the commons. The inefficiency is the results from the divergence between the individual and the social incentives, that leads the competitive equilibrium to be inefficient. The problem depends due to the lack of property rights, that produce a negative externality.

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Externality

Definition An externality arises whenever the welfare (utility or profit) of an agent depends directly on the actions of another agent (consumer or producer) in the economy.

An externality is a link between economic agents that lies outside the price system Pollution from a factory. Nice garden of a neighbor. Externalities are not under the control of the affected agent Efficiency theorems do not apply. Competitive equilibrium unlikely to be efficient. Externalities are of practical importance for ”global warming” for instance

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Classification (1)

Externality can be: Consumption vs. production Positive vs. negative Pecuniary vs. non-pecuniary Examples: Consuming an apple vs. consuming loud music. Fisher’s production vs. Upstream oil refinery.

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Classification (2)

Any evaluation of how well markets work must include the costs or benefits to others affected by the consumption / production of the good: Consumption vs. production Consumption externality affects utility. Production externality affects profit.

Positive vs. negative an external benefit / social benefit (private treatment for contagious diseases) ⇒ positive externality: raises utility or profit. an external cost / social cost (pollution) ⇒ negative externality: reduces utility or profit. .

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Classification (3)

”Pecuniary” vs. ”non-pecuniary” Important distinction is between ”pecuniary” vs. ”non-pecuniary” externalities: The pecuniary externality: an external effect that works through prices. It is present in any competitive market but do not create inefficiency. The non-pecuniary externality creates inefficiency for this reason it justifies policy intervention.

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Example of Traffic Jams

Externality imposes by car drivers on each other. Model N commuters with a choice of train or car. Travel by train takes 40 minutes. The travel time by car increases as the number of car users increases. Commuters make the choice which minimizes their personal travel time.

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Choice of commuting mode

The car drivers take into account only their own travel time but not the fact that they will increase the travel time for all other drivers: congestion is a negative externality. 8/33 Introduction Externality Tragedy of the commons Government Intervention Conclusion

Solution

The travel time by car will equal the travel time by train. This has 40% of commuters choosing travel by car. The optimum choose minimizes total travel time, this occurs when 20% travel by car. The equilibrium has too many commuters choosing to use cars.

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Example of Job choice

Model A group of students must choose to be economists or lawyers. Income declines when more students make the same choice. An additional student choosing to be an economist lowers income for all economists: pecuniary externality. Each individual ignores this externality when choosing occupation.

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Job choice Graph

The income of each occupation is shown in figure. The proportion choosing each occupations adjusts until incomes are equal. This occurs when percentage E choose to be economists. A reduction in income is a cost for an employee but a benefit for an employer. This equilibrium is efficient. Pecuniary externalities do not cause inefficiency of the market equilibrium.

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Example: Rat Race Problem

The rat race is a contest for relative position. Assume performance is judged in relative terms and not absolute terms. An advantage is gained over rivals only by competing harder than they do. If all competitors compete hard the extra efforts cancels out. All competitors could gain by making an agreement to reduce effort.

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Rat Race Matrix

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Solution

Making high effort has a cost of c. High effort is a dominant strategy so the Nash equilibrium is (high, high). The Pareto-efficient outcome is (low, low). Committing to low effort is a Pareto-improvement.

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Main questions

1 Theoretical: what is the best way to correct externalities and move closer to the social optimum? 2 Empirical: how to measure the size of externalities?

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Tragedy of the commons

The central question about commons dilemma, is to explain the inefficient management of natural resources (lakes, oceans, lands, etc...). It is important to made a distinction between resources held as common property and those subject to open access: Common property involves a well-defined community of users who are able in practice, if not under the law, to prevent outsiders from exploiting the resource: inshore fisheries, grazing lands, or forest areas are examples. Open access resources can be exploited without restrictions, other than those imposed by states: ocean fisheries,forests ,or the atmosphere as a carbon sink, for instance.

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Common pool resources Model

Assumptions Perfect competition: free entry for fishermen. Perfect information.

Model Consider that in the village there is lake with a stock of fishes, as common resource, where anyone is free to catch and sell. B is the total number of boats that can be hired on a given day. Average return per boat F (B) Returns per boat is decreasing F 0(B) < 0. Paid employment per day if they chose not to fish w For each fisherman the equilibrium number of boat B∗, must satisfy: π = F (B∗) − c = w (1)

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Decision: number of boat

From the perspective of society as a whole, what is the optimal number of boats? Optimisation problem (1) The social planner should therefore choose the number of boats, B, that maximises Total number of boat that maximises the total profit for the village:

MaxB [F (B) − c − w] The socially optimal number of boats, it is find with FOC: F (B0) − c − w + BF (B0) = 0 (2) | {z } F 0(B0) < 0 since an increase in number of boats reduces the quantity of fishes caught by each fisherman, and the equation (1) and (2) are contrasting → B0 < B∗, we can conclude that the efficient number of boats is less than the number in a competitive equilibrium. 18/33 Introduction Externality Tragedy of the commons Government Intervention Conclusion

Graphically

Revenue per boat

w + c Total cost per boat

F(B)+BF'(B) F(B)

BO B* Number of boat

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Reasons of Inefficiency and possible solutions

The divergence in outcomes (number of boat) arises because when individual fishermen enter the market, they do not take into account the negative effects their actions have on the quantity of fish caught by everyone else. This behavior produces a negative externality, that ensures that in equilibrium too many boat are operating on the lake. Government intervention is necessary to prevent the inefficient outcome.

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Remedies for Externalities

1 Pigouvian corrective taxes. 2 Quotas / Permits. 3 Regulation: assign property rights over the common pool resource. 4 Coasian bargaining solution

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Taxes and quotas

The policy maker intervenes in the market in order to achieve an efficient allocation, through: 1 Impose a tax per boat, t: internalises the externality by making each fisherman bear the full cost of his/her actions on society. Individual fisherman will now fish until the following equation is satisfied: π = F (B∗) − c − t = w 2 Set a quota: limits the total number of boats that can operate per day to be equal to B0. Which is the limit of this policy?

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Graphically

Revenue per boat

w + c + t Tax w + c Total cost per boat

F(B)+BF'(B) F(B)

BO B* Number of boat

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Regulation: Property rights

The policy maker assigns property rights over the common pool resource → it becomes a private good to one specific fisherman (fisherman 1), that becomes ”ownership” of the fish stock. Fisherman 1 wants to maximise his profit.

I Each boat costs c to hire, I Each skipper costs w (equal to what the person earns in paid employment). Now the First Welfare Theorem should apply and an efficient allocation should be obtained through private trade.

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Decision: Fisherman 1’s problem

What is the optimal number of boats?

Optimisation problem Fisherman 1 should therefore choose the number of boats, B, that maximises his π: Total number of boat that maximises his π:

MaxB [F (B) − c − w] This is equal to the condition for a social optimum: the number of boats at the optimal price p∗ is where B(p∗) = B0, which is the same as the optimal tax (Pigouvian tax) the government could have chosen.

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Property rights’ Price (1)

Fisherman 1 is entitled to sell the right to fish for a day to others at price p.

Optimisation problem Fisherman 1 should therefore choose the number of boats, B, that maximises his π:

MaxppB(p) st: F (B(p)) − c − p ≥ w

Maxp[B(p)(F (B(p)) − c − w] = MaxB [F (B) − c − w] This is exactly the problem that defined socially optimal number of boats.

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Property rights’ Price (2)

Why might fisherman 1 prefer to issue licences (property rights) to other fishermen?

Optimisation problem

If c1 > c

MaxB B[F (B) − c1 − w] With the assignment of property rights, the fishermen can bargain (Coase Theorem)

I It is only necessary perfect information - individuals need to know each other?s technology for an efficient outcome to be attained.

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Coase bargaining solution

Coase Theorem In a competitive economy with complete information and zero transaction costs, the allocation of resources will be efficient and invariant with respect to legal rules of entitlement.

The government must ensure that the property rights are both well-defined and enforceable, then the economic agents may resolve externality problems themselves without the need for government intervention → Legal rules of entitlement or property rights determine ownership in the economy. If there was a property right anyone suffering an externality would be paid compensation. The compensation is a price for the externality. Competitive trading will ensure the correct price emerges and efficiency is achieved. Why does ”pollution” occur? 28/33 Introduction Externality Tragedy of the commons Government Intervention Conclusion

Limitation of Coase Theorem

Lack of clear property rights. Transaction costs in reaching compensation agreements. Potential thinness of the market implying bilateral bargaining and potential inefficiency with incomplete information. Potential monopoly power.

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Missing market

In the absence of property rights there is a ”missing” market. Legal enforcement costs money → we will not be able to truly achieve the Pareto optimum. To prevent ”the tragedy of commons” governments assign fishermen quotas entitling them to catch some quantity of fish each period: the restriction has to be on total output (fishes) and not on inputs (boats).

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Conclusion

Externalities are a feature of economic activity. The existence of externalities can lead to inefficiency when the conditions of the Coase theorem do not apply. Pigouvian taxes can reduce the inefficiency but require excessive differentiation. Marketable licenses can also help and have simpler administration. All solutions require the same information for implementation.

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Food for thought

How can one determine the efficient level of provision of a Common pool/property resources? Which are the conditions under the Coase theorem leads a Pareto efficient allocation? Comment Education is often viewed as a good with positive externalities. a. Explain how education might produce positive external effect. b. Suggest a positive action of the government to induce the market for education to perform more efficiently.

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Readings

Hindriks and Myles (2013), Intermediate Public Economics, Ch. 8. Varian (2014), Intermediate Microeconomics: A Modern Approach (Ninth Edition), Ch. 36. Hardin, G. (1968). The Tragedy of the Commons.

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