Customer‘s safety is the future trend of the foodservice and hospitality industry

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Externalities II

Part 1. Missing Markets

Economics 313

A Market Solution to Externalities

Slide 2

 We saw that market behaviour can in principle be “corrected” to account for the fact that externalities are affecting members of society not directly involved in a trade

 Prices can be made to reflect external costs and benefits by the imposition of corrective taxes or subsidies

 Alternatively, a benevolent government could intervene directly to mandate efficient levels of production or consumption (or to produce goods and services itself)

 An third option is to “create the missing market”

A Market Solution to Externalities

Slide 3

 This solution focusses directly on the issue at hand: with externalities market prices fail to capture the full costs and benefits of an action.

 Effectively there is a missing market for the spillover.

 If beneficiaries of a positive externality had to pay to gain access to the benefit, the producer would have the ability and incentive to produce efficiently. Similarly, if the damage from a negative externality came with a price for the damage caused, agents would account for the total cost of their actions.

A Market Solution to Externalities

Slide 4

 How can “markets” be a policy solution? Economists place great faith in the ability and willingness of agents to find ways to capture surplus. So if a market could exist, wouldn’t it do so? What is the role for policy?

 Maybe, and maybe not. This question brings up another fundamental aspect of markets that we have mostly left unmentioned: markets do not exist in a vacuum, but require institutional support.

 A key requirement is that “property rights” are well-defined, and enforceable. In economies of any complexity, defining, clarifying and enforcing property rights depends on government.

Property as a “bundle of rights”

Slide 5

 Adheres to the property, not the owner. Certain types of property come with specific rights. Impersonal.

 Adheres to the property, not the owner. Certain types of property come with specific rights. Impersonal..

 Laws define the boundaries on these rights. Typically, the right to “use and abuse”, transfer, lend, mortgage, exclude others from, etc.

 Laws and the courts interpreting these laws also assign these rights

A Market Solution to Externalities

Slide 6

 If markets don’t exist without property rights, a potential policy response to an externality is to create it by assigning property rights.

 But a simple declaration by government is neither necessary nor sufficient for property rights to function.

 For example, in many situations of direct barter, parties respect the rights of each other as the basis of negotiation. Perhaps this is due to “the shadow of the law” but these bargains seem to occur in societies without active enforcement.

A Market Solution to Externalities

Slide 7

 On the other hand, property rights need to be enforceable, and to be worth enforcing.

 Thinking about externalities as “unpriced exchanges” as opposed to spillovers, and focus on the underlying allocation of “rights” rather than costs of benefits being imposed on third parties, the situation looks more symmetric than the way we have considered it so far.

 This insight brings takes us to the so-called Coase Theorem

-- end of part 1 --

Externalities II

2. The Coase “Theorem”

Economics 313

Coase and Pigou

Slide 10

 In a series of papers in the late 1950s, Ronald Coase challenged the standard interpretation of externalities and rejects the view the Pigouvian taxes were in general the appropriate policy response

 His framing was simple but controversial. As usual, he starts with an extreme case valuable for clarity not realism.

 This reference case has been labelled the Coase Theorem. Various versions of this have been formalized, but Coase himself certainly didn’t see it as a statement about reality.

Rights and obligations

Slide 11

 His first insight was hinted at above: rights and obligations have a “reciprocity” downplayed in the usual approach. If I impose a cost on you by my action, and then a court decides that I owe you a duty of compensation, then your preferences and choice will impose a cost on me.

 This reciprocity exists in any exchange, where true symmetry only exists when the parties have equal rights. More generally, the assignment of rights alters the balance of potential gains.

 Added to this is the standard economists view that parties will negotiate to extract gains from exchange

The Coase Theorem

Slide 12

 Coase, R. (1960). The Problem of Social Cost. The Journal of Law & Economics, 3, 1-44.

 A simple example of neighbouring property owners, a grain farmer and a cattle rancher, where increases in the number of cattle impose a cost on the farmer.

 Coase shows that, if all other markets are perfectly competitive, an efficient allocation of resources will occur, independently of the assignment of rights

 Very simple: if the farmer can sue for damages, the cattle rancher will only add cattle that, at the margin, earn more in the cattle market than the cost of the harm they create. If the rancher has the right to run cattle, the farmer will pay them to reduce the number of cattle, an offer that will be accepted so long as the value of damage exceeds the profit from the cattle

The Coase Theorem

Transaction Costs

Slide 14

 In this view, the problem of externalities is due to the inability of parties to bargain effectively to come to an efficient allocation

 “Transaction costs” as Coase defines them are the costs of identifying counterparties, negotiating terms, and enforcing the resulting contracts

 These are all impossible unless rights are clearly specified. This is the ground for government policy.

Transaction Costs

Slide 15

Source: Cooter and Ulen, Law and Economics, 6th edition p. 91. https://lawcat.berkeley.edu/record/1127400/files/04-Ch1_AnIntroductiontoLawandEconomics.pdf

The Coase Theorem: qualifications

Slide 16

 The focus remains on efficiency, in keeping with our approach. Other aspects may matter.

 For example, the Coase Theorem does not say that the outcome is invariant to the assignment of property rights, just that it will be efficient

 Coase spends most of the cited paper giving examples of how transaction costs matter. Even in the context of well defined property rights, legal institutions have implications for the size of transaction costs and so the feasible set of solutions to bargaining.

 This idea is fundamental to the field of “Law and Economics” and are explored in detail in Economics 308

-- end of part 2 --

Externalities II

Part 3. Bargaining in Markets

Economics 313

A Market Solution to Externalities

Slide 19

 One interpretation of the Coase Theorem is that externalities are an illusion: if all agents are (constrained) optimizers, the solution must be efficient.

 Transaction Costs are just costs, and so they must be accounted for in evaluating efficiency. If the gains from reallocations are positive they will occur; if they are not, because of high transaction costs, they won’t, and moreover should not

 This view ignores the just mentioned role of policy in grounding property rights and more generally affecting the extent of transaction costs.

A Market Solution to Externalities

Slide 20

 Taking the role of government seriously suggests another solution to externalities: define property rights and support markets to transact exchanges.

 Imagine again the case of a market externality we looked at last week.

 Assume property rights are clearly defined: producers have the right to produce and consumers are free to consumer

Negative Externalities Example

Slide 21

 Production: we have 10 identical producers of 𝑥𝑥 & 𝑦𝑦

 Consumption: we have 100 identical consumers of 𝑥𝑥 & 𝑦𝑦  Each consumer 𝑖𝑖 has quasi-linear utility and receives and equal

share in firm output as a dividend (this gives them income)

 Externality: there are 10 individuals for whom 𝑥𝑥 is a pure “bad”. These would each trade two unit of 𝑦𝑦 to have the production of 𝑦𝑦 reduced by one unit

Negative Externalities Example: Equilibrium

Slide 22

 Market demand for 𝑥𝑥

� 𝑖𝑖

𝑥𝑥𝐷𝐷 = 100 − 𝑝𝑝𝑥𝑥 𝑝𝑝𝑦𝑦

 Market supply of 𝑥𝑥

� 𝑖𝑖

𝑥𝑥𝑗𝑗 𝑆𝑆 =

𝑝𝑝𝑥𝑥 𝑝𝑝𝑦𝑦

 Set Supply equal to Demand  𝑥𝑥𝐷𝐷 = 𝑥𝑥𝑆𝑆 → 100 − 𝑝𝑝𝑥𝑥

𝑝𝑝𝑦𝑦 = 𝑝𝑝𝑥𝑥

𝑝𝑝𝑦𝑦 → 𝑝𝑝𝑥𝑥

𝑝𝑝𝑦𝑦 = 50

 Given 𝑝𝑝𝑥𝑥 𝑝𝑝𝑦𝑦

= 50, there 𝑥𝑥𝐸𝐸 = 50

Negative Externalities Example: Equilibrium

Slide 23

 Now think about the individuals for whom x is a bad  Per person Marginal External Cost (MEC) = 2

 There are 10 people for whom x has a MEC of 2

 Every x produced → total external costs is 20 units of utility

 This tells us that the marginal social cost (MSC) = 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑖𝑖𝑀𝑀𝑀𝑀 𝑃𝑃𝑀𝑀𝑖𝑖𝑟𝑟𝑀𝑀𝑟𝑟𝑟𝑟 𝐶𝐶𝑜𝑜𝑜𝑜𝑟𝑟 + 20

Negative Externalities Example: Equilibrium

Slide 24

 At 𝑥𝑥 = 50 𝑀𝑀𝑃𝑃𝐶𝐶 = 𝑀𝑀𝑀𝑀𝑀𝑀, but 𝑀𝑀𝑀𝑀𝐶𝐶 = 𝑀𝑀𝑃𝑃𝐶𝐶 + 20, so 𝑀𝑀𝑀𝑀𝐶𝐶 > 𝑀𝑀𝑀𝑀𝑀𝑀 and thus PPIs exist

𝑝𝑝𝑥𝑥 𝑝𝑝𝑦𝑦

x50

MEC

𝑥𝑥𝑆𝑆 (MPC)

𝑀𝑀𝑀𝑀𝐶𝐶 = 𝑀𝑀𝑃𝑃𝐶𝐶 + 𝑀𝑀𝑀𝑀𝐶𝐶

𝑀𝑀𝑀𝑀𝐶𝐶

𝑥𝑥𝐷𝐷 (MSB)

DWL

Externalities Example: Coase

Slide 25

 Now assume that “non-market participants” can costlessly negotiate

𝑝𝑝𝑥𝑥 𝑝𝑝𝑦𝑦

x50

MPC

𝑀𝑀𝑀𝑀𝐶𝐶

MSB

Externalities Example: Coase

Slide 26

 Property rights owned by the market participants → those who are harmed by x will need to pay producers and consumers to ↓ x

𝑝𝑝𝑥𝑥 𝑝𝑝𝑦𝑦

x50

MPC

𝑀𝑀𝑀𝑀𝐶𝐶

MSB

We need to calculate the willingness to pay (WTP) of those harmed by x and the willingness to accept (WTA) of those who benefit from x

If WTP> WTA, then negotiations will allow ↓ x from 50 to 40.

Externalities Example: Coase

Slide 27

 Those who are harmed by x will pay market participants to voluntarily reduce x from 50 to 40

 Reducing x from 50 to 40 will be an actual Pareto Improvement

𝑝𝑝𝑥𝑥 𝑝𝑝𝑦𝑦

x50

MPC

𝑀𝑀𝑀𝑀𝐶𝐶

MSB

Assume each unit of x has MEC of 2 units of y per person → in other words each person harmed is WTP up to 2y to reduce x by 1 unit.

Assume there are 10 people affected outside the market. This implies a social WTP for 20y for a reduction of 1 x

Externalities Example: Coase

Slide 28

 In total the WTP to reduce x from 50 to 40 is 200y  The WTP is the green parallelogram (remember the difference

between MSC and MPC is just MEC)

𝑝𝑝𝑥𝑥 𝑝𝑝𝑦𝑦

x50

MPC

𝑀𝑀𝑀𝑀𝐶𝐶

MSB

To figure the WTA of the market participants, we need to make assumptions about what happens at the market level if x falls

Important: these negotiations are going to move the market out of the competitive equilibrium

Externalities Example: Coase

Slide 29

 Assume for the sake of argument that market participants reach a deal with each other and they decide that no matter what happens 𝑝𝑝𝑥𝑥 𝑝𝑝𝑦𝑦

will remain at 50

𝑝𝑝𝑥𝑥 𝑝𝑝𝑦𝑦

x50

MPC

𝑀𝑀𝑀𝑀𝐶𝐶

MSB

What is the WTA of consumers? In other words, what do they need to be paid to reduce x from 50 to 40 given that

𝑝𝑝𝑥𝑥 𝑝𝑝𝑦𝑦

= 50

Because we have quasi- linear utility functions we can ignore income effects and consumer surplus will equal WTA

Externalities Example: Coase

Slide 30

 At 𝑝𝑝𝑥𝑥 𝑝𝑝𝑦𝑦

= 50, consumers want to consumer 50 units of x, so

consumer surplus is the blue triangle

𝑝𝑝𝑥𝑥 𝑝𝑝𝑦𝑦

x50

MPC

𝑀𝑀𝑀𝑀𝐶𝐶

MSB

Externalities Example: Coase

Slide 31

 At 𝑝𝑝𝑥𝑥 𝑝𝑝𝑦𝑦

= 50, consumers want to consumer 50 units of x, so

consumer surplus is the blue triangle

𝑝𝑝𝑥𝑥 𝑝𝑝𝑦𝑦

x50

MPC

𝑀𝑀𝑀𝑀𝐶𝐶

MSB

But if you are restricted to only by x=40, the consumer surplus is given only by the red outlined area

Externalities Example: Coase

Slide 32

 Thus in order to accept reducing your consumption of x from 50 to 40 units, consumers of x need to be paid the area in orange

𝑝𝑝𝑥𝑥 𝑝𝑝𝑦𝑦

x50

MPC

𝑀𝑀𝑀𝑀𝐶𝐶

MSB

This gives us a dollar measure of their willingness to accept (WTA) reducing their consumption from 50 to 40 x

Externalities Example: Coase

Slide 33

 Now what do producers need to be paid to accept this deal?  Producer surplus is given by the area above given by the blue triangle

𝑝𝑝𝑥𝑥 𝑝𝑝𝑦𝑦

x50

MPC

𝑀𝑀𝑀𝑀𝐶𝐶

MSB

Externalities Example: Coase

Slide 34

 Now what do producers need to be paid to accept this deal?  Producer surplus is given by the area above given by the blue triangle

𝑝𝑝𝑥𝑥 𝑝𝑝𝑦𝑦

x50

MPC

𝑀𝑀𝑀𝑀𝐶𝐶

MSB

By reducing their sales from 40 to 50 in this deal, producers would lose the area in green in profit

Externalities Example: Coase

Slide 35

 Remember those harmed are WTP at most the area of the green trapezoid

𝑝𝑝𝑥𝑥 𝑝𝑝𝑦𝑦

x50

MPC

𝑀𝑀𝑀𝑀𝐶𝐶

MSB

Externalities Example: Coase

Slide 36

 Remember those harmed are WTP at most the area of the green trapezoid

𝑝𝑝𝑥𝑥 𝑝𝑝𝑦𝑦

x50

MPC

𝑀𝑀𝑀𝑀𝐶𝐶

MSB

Consumers need to be paid at least the area of the orange triangle (lost consumer surplus)

Externalities Example: Coase

Slide 37

 Remember those harmed are WTP at most the area of the green trapezoid

𝑝𝑝𝑥𝑥 𝑝𝑝𝑦𝑦

x50

MPC

𝑀𝑀𝑀𝑀𝐶𝐶

MSB

Consumers need to be paid at least the area of the orange triangle (lost consumer surplus)

Producers need to be paid at least the area of the darker green triangle (lost profit)

Externalities Example: Coase

Slide 38

 With costless negotiation, the efficient level of 40 is produced. The total surplus to the market participants is the blue area….

MPC

𝑀𝑀𝑀𝑀𝐶𝐶

MSB

𝑝𝑝𝑥𝑥 𝑝𝑝𝑦𝑦

𝑥𝑥50

Externalities Example: Coase

Slide 39

 Of which the green shaded area is a transfer from the externally affected parties….

MPC

𝑀𝑀𝑀𝑀𝐶𝐶

MSB

𝑝𝑝𝑥𝑥 𝑝𝑝𝑦𝑦

𝑥𝑥50

The surplus to the market participants is greater that the total social surplus because of the (efficient) external costs.

Externalities Example: Coase

Slide 40

 Now imagine that the “property right” is held by those experiencing the externality.

 Then before negotiation, no 𝑥𝑥 would be produced 𝑝𝑝𝑥𝑥 𝑝𝑝𝑦𝑦

MPC

𝑀𝑀𝑀𝑀𝐶𝐶

MSB

Externalities Example: Coase

Slide 41

 Total potential consumer and producer surplus is given by the lined blue area if they could increase production to 50

𝑝𝑝𝑥𝑥 𝑝𝑝𝑦𝑦

𝑥𝑥50

MPC

𝑀𝑀𝑀𝑀𝐶𝐶

MSB

Externalities Example: Coase

Slide 42

 However, this surplus is insufficient to compensate those who hold the rights – green is bigger than blue at these units)

𝑝𝑝𝑥𝑥 𝑝𝑝𝑦𝑦

𝑥𝑥50

MPC

𝑀𝑀𝑀𝑀𝐶𝐶

MSB

Externalities Example: Coase

Slide 43

 They would be willing however be willing to compensate the parties enough at the margin for the next unit of 𝑥𝑥 up to 40

𝑝𝑝𝑥𝑥 𝑝𝑝𝑦𝑦

𝑥𝑥50

MPC

𝑀𝑀𝑀𝑀𝐶𝐶

MSB

Externalities Example: Coase

Slide 44

 Beyond 40, the market participants are unwilling to compensate the right holder

MPC

𝑀𝑀𝑀𝑀𝐶𝐶

MSB

The red arrow is the max WTP (above production cost) to consume the associated unit. Not sufficient to cover the external cost of 2

𝑝𝑝𝑥𝑥 𝑝𝑝𝑦𝑦

𝑥𝑥50

Externalities Example: Coase

Slide 45

 Once again, without transaction costs, the efficient level of output will be produced.

MPC

𝑀𝑀𝑀𝑀𝐶𝐶

MSB

𝑝𝑝𝑥𝑥 𝑝𝑝𝑦𝑦

𝑥𝑥50

The total compensation is the area in green.

The total social surplus then would be give by the blue area (the benefits beyond the social cost)

Externalities Example: Coase

Slide 46

 So we see that no matter who holds the “property rights” negotiation leads to an efficient outcome, in this case, the same unique Pareto Efficient level of 40 units

 Who gets the surplus does matter. When the market participants “own” the rights, they can be compensated for the inefficient units, so get the same surplus as they would at 50, but some in the form of payments from the external parties

 When the external parties hold the rights, they “sell” the right to produce up the first 40 units, and are perfectly compensated for the damage. The market participants get less surplus.

Property Rights Are A Form of Wealth

Slide 47

 In the absence of transactions costs, the parties can always reach the socially efficient outcome no matter who owns the property rights  The socially optimal amount will be produced

 However, who owns the property rights will determine the gains from any particular transaction

 Who owns property rights does not matter for efficiency

 But who owns the property rights matters for equity

When can defining property rights work?

Slide 48

 The Coase Theorem only works if  Transaction costs are negligible  Property rights are well defined

 In the example above when we assumed that there were no transaction costs, we assumed the 10 parties harmed could arrange the required transfers.

 Suppose instead a firm that pollutes affects a community of 2000 residents

 It will take a lot of energy and time to negotiate with all the residents – transaction costs will be huge (and of course, property rights may be ill-defined)

-- end of part 3 --

Externalities II

Part 4. Tradable Permits

Economics 313

The Tragedy of the Commons

Slide 51

 One externality problem that seems likely to benefit from property rights is the Tragedy of the Commons that we talked about last week.

 Recall that this is the overuse of a common resource, a good that all individuals can access freely and whose value to the individual consumer decrease as others use it

 Common resources are non-excludable and rival: Non- excludability means that consumers cannot be prevented from using, accessing or consuming the good. Rivalry means that the consumption or use of a good reduces the amount available to others or the value to others

 The Tragedy of the Commons: the phenomenon that a common resource is used more intensively that is socially efficient.

The Tragedy of the Commons

Slide 52

 No single user takes into account the negative externality they imposes on others when they use or access the good

 This leads people to use the common resource too much relative to its socially efficient level

 The externality arises because of the combination of open access and depletion through use

Solutions

Slide 53

 Just a special form of externality: one persons use of the resource directly effects the availability and value of the resource to others.

 So solutions we have discussed can work such as quantity limits, taxes, and property rights and negotiations can work

 However in many situations these solutions are limited (uncertainty, transactions costs, and lack of government information)

Solution: Government or Private Ownership

Slide 54

 In the context of common resources, one solution is to assign a property right. So total ownership is held by either the government or private party. They can set a price for access and resolve the externality

 This essentially deals works by making the resource “excludable” so one party fully internalizes the costs and benefits with the use of the resource

 Another option is to use taxes or quota.

Another Solution: Tradable Permits

Slide 55

 With quotas property rights can still play a role.

 Because the government does not have perfect information, any assignment of quota can result in a misallocation.

Tradable Permits

Slide 56

 Consider a simple market with 2 firms that emit some form of pollution, where the optimal amount of pollution is known, but there is uncertainty about firm costs of abatement

 Creating a market for the externality through tradable permits can result in efficient quantity reduction

 The government can set a cap on the externality produced and issue permits that sum to equal the cap and then allow firms trade the rights to produce the externality among them (also known as “cap-and-trade”)

Tradable Permits: Equal Division

Slide 57

 2 firms in a community that pollute the environment. (To fix ideas you could assume that before the quota, each firm was polluting without bearing a cost, and produced some amount greater that 7 units, for example 20 units each.)

 The government has decided that 14 units of pollution must be abated and that each firm must cut pollution by 7 units

 The total cost of pollution abatement:

𝑇𝑇𝐶𝐶𝐴𝐴 = 1 4 𝑅𝑅2 for firm A, and 𝑇𝑇𝐶𝐶𝑀𝑀 = 1

8 𝑅𝑅2 for firm B

 𝑅𝑅 is the quantity of abatement.

Tradable Permits: Equal Division

Slide 58

 Is this solution cost efficient? No, because the marginal cost of abating 7 units is not the same for all firms.

 The marginal cost of pollution abatement for firm A (the partial derivative of TC with respect to R) is

𝑀𝑀𝐶𝐶𝐴𝐴 = 1 2 𝑅𝑅

and the marginal cost of pollution abatement for firm B is

𝑀𝑀𝐶𝐶𝐵𝐵 = 1 4 𝑅𝑅

Evaluating at 𝑅𝑅 = 7, 𝑀𝑀𝐶𝐶𝐴𝐴 = 3.5 for firm A, 𝑀𝑀𝐶𝐶𝑀𝑀 = 1.75 for firm B.

=> we can abate the same amount of pollution with lower total cost by shifting abatement to the lower cost abater.

Tradable Permits: Reallocation

Slide 59

 For example, firm B can abate one more unit and A can abate one less unit and cost savings are

11 8

= 1.375

 This is because firm A and B have total costs of 147/8 if each of them abates 7 units

 They have total costs of 136/8 if A abates 6 units and B abates 8 units

 The total cost of abatement is lower if they can trade the “right” to pollute

The Planner’s Problem

Slide 60

 If the solution is not cost efficient, how much pollution should each firm abate at the cost efficient outcome?

𝑀𝑀𝐶𝐶𝐴𝐴 = 𝑀𝑀𝐶𝐶𝐵𝐵 ½ 𝑅𝑅𝐴𝐴 = ¼ 𝑅𝑅𝐵𝐵. 𝑅𝑅𝑀𝑀 = 2 𝑅𝑅𝐴𝐴

𝑅𝑅𝐴𝐴 + 𝑅𝑅𝐵𝐵 = 14 𝑅𝑅𝐴𝐴 + 2𝑅𝑅𝐴𝐴 = 14

→ 𝑅𝑅𝐴𝐴 = 14 3

= 4.67, and 𝑅𝑅𝑀𝑀 = 28/3 = 9.33

We need that all firms’ marginal costs of abatement are the same and that the total amount abated adds up to 14.

Tradable Permits: Cost Saving

Slide 61

Remember: 𝑇𝑇𝐶𝐶𝐴𝐴 = 1 4 𝑅𝑅2 for firm A, and 𝑇𝑇𝐶𝐶𝐵𝐵 = 1

8 𝑅𝑅2

 Total costs with 7 units per firm: 49 4

+ 49 8

= 18.375

 Total cost if cost efficient: ⁄14 3

4 +

⁄28 3 2

8 = 16.333

 Cost savings: 18.375 – 16.333 = 2.042

Tradable Permits

Slide 62

 Suppose now that firms can trade pollution permits

 If each firm must abate 7 units of pollution, what is the maximum firm A would be willing to pay firm B to cut 2 additional units of pollution so that firm A could cut its pollution by only 5 units?

 What is the minimum payment from firm A to firm B to compensate B for the increase its abatement by 2 units?

Tradable Permits: Gains from trade

Slide 63

 To get a measure of how much firm A would be willing to pay firm B we can compute firm A’s cost savings when being able to pollute two more units. Subtracting the cost of abating 5 units from the cost of abating 7 units give a saving of:

49/4 − 25/4 = 24/4 = 6

 To get a measure of by how much firm B needs to be compensated subtract from cost of abating 9 units the cost of abating 7 units.

81/8 − 49/8 = 32/8 = 4

 Since 4 < 6, both firms will be better off if firm A can pollute 2 additional units and firm B cuts pollution by 2 additional units and receives a payment from firm A of more than 4 and less than 6 dollars

Tradable Permits: the market

Slide 64

 Suppose the government sets a cap of 14 and gives each firm enough permits to pollute by 7 units less than they currently do, but allows them to trade these rights.

 If there is a competitive market for pollution abatement, what would be the price for each unit a firm abates beyond its 7th unit?

 Let 𝑥𝑥 be the additional amount beyond 7 units by which a firm is considering cutting pollution if it gets paid 𝑝𝑝 for each additional unit of pollution abated

 Let 𝑐𝑐(𝑞𝑞) be the total cost of cutting pollution by 𝑞𝑞 units

Tradable Permits: the market

Slide 65

 For a firm to buy a permit from another firm to pollute more, the firm solves the following problem:

Cost of abating 7 units

Cost of abating 7 units minus how much you pay someone else to abate for you.

How much you pay someone else to abate

max 𝑥𝑥

𝑐𝑐 7 − 𝑐𝑐 7 − 𝑥𝑥 − 𝑝𝑝𝑥𝑥

In words: maximize the difference between the cost saving from abating 𝑥𝑥 units less and the payment to the other firms who will now abate 𝑥𝑥 units more

Tradable Permits: the market

Slide 66

 Profits are maximized when 𝑐𝑐′ 7 − 𝑥𝑥 = 𝑝𝑝

 That is, the cost savings of the last unit not abated needs to be equal to the price that the firm has to pay the other firm for abating the last unit on its behalf

Tradable Permits: the market

Slide 67

Consider the problem of firm A facing the price 𝑝𝑝 that buys 𝑥𝑥𝐴𝐴 permits to reduce less than the allocation of 7. It wants to minimize the total cost of abatement:

min 𝑥𝑥𝐴𝐴

1 4

7 − 𝑥𝑥𝐴𝐴 2 + 𝑝𝑝𝑥𝑥𝐴𝐴

 FOC 1 2

7 − 𝑥𝑥𝐴𝐴 = 𝑝𝑝

So 𝑥𝑥𝐴𝐴 = 7 − 2𝑝𝑝

Tradable Permits: the market

Slide 68

Similarly for firm B facing the price 𝑝𝑝 that buys 𝑥𝑥𝐵𝐵 permits to add to the allocation of 7 and reduce abatement

min 𝑥𝑥𝐵𝐵

1 8

(7 − 𝑥𝑥𝐵𝐵)2+ 𝑝𝑝𝑥𝑥𝐵𝐵

 FOC 1 4

7 − 𝑥𝑥𝐵𝐵 = 𝑝𝑝

So 𝑥𝑥𝐵𝐵 = 7 − 4𝑝𝑝

Tradable Permits: the market

Slide 69

But the market needs to clear, so 𝑥𝑥𝐴𝐴 + 𝑥𝑥𝐵𝐵 = 0

𝑥𝑥𝐵𝐵 = −𝑥𝑥𝐴𝐴

7 − 4𝑝𝑝 = 2𝑝𝑝 − 7

So the market clearing price is

𝑝𝑝 = 14 6

= 7 3

Thus: 𝑥𝑥𝐴𝐴 = 7 3

and 𝑥𝑥𝐵𝐵 = − 7 3

Tradable Permits: the market

Slide 70

Firm A buys permits and abates less, and Firm B sells permits and abates more:

𝑥𝑥𝐴𝐴 = 7 − 2𝑝𝑝 = 7 − 14 3

= 7 3

and

𝑥𝑥𝐵𝐵 = 7 − 4𝑝𝑝 = 7 − 28 3

= − 7 3

Tradable Permits: Firm output

Slide 71

 Firm A uses its permits to abate 7 − 7/3 = 14/3 units. Firm B only has enough permits to abate 7 + 7/3 = 28/3 units.

 Total payments to firm B are (7/3) ∗ (7/3) = 49/9

 Firm A saves 49/4 – (14/3)2/4 – 49/9 = 1.361

 Firm B gains 49/9 – [(28/3)2/8 − 49/8] = .68056

 Total benefits are 2.042 same as cost savings when joint costs are minimized with respect to the abatement constraint → permits are cost efficient

Pro and Cons of Tradeable Permits

Slide 72

 Permits have the advantage that they achieve cost efficiency, because the marginal cost of abatement will be equalized across firms with charges and permits.

 Permits the government must decide on the number of permits to allocate

 Permits combine the certainty of how much pollution will be abated with cost efficiency.

-- end of part 4 --

Externalities II

Part 5. Summary

Economics 313

Ostrom and Common Resources

Slide 75

 While private property rights and tradable permits are one system to manage common pool resources, efficient management of resources can occur in other systems

 Nobel prize winner Elinor Ostrom and her student Susan Crawford have provided a method of analyzing tenure systems

 They propose that these systems must give responsibility to certain participant under certain rules, which are well defined and understood, and there must be the “or else” condition

Societies have often found solutions

Slide 76

What I Expect You To Know

Slide 77

 Understand the Coase Theorem and discuss under what assumptions it works

 Be able to identify willingness to pay or accept on the graphs we have discussed and social benefits and costs and private costs and benefits

What I Expect You To Know

Slide 78

 What is the tragedy of the commons and under what situations it arises and be able to give examples

 Ways to deal with the tragedy of the commons

 How tradable permits work and what they are and be able to solve a problem with two firms

 Be able to solve a problem that involves two firms trading permits for the amount each abates and the price of a permit

 Private property systems or federal government solutions are not the only way to solve the common pool problem