Externalities
Chapter 21
Slides by Pamela L. Hall
Western Washington University
©2005, Southwestern
Introduction

Driving an automobile is probably a household’s most
polluting activity
 Efforts since 1970 have greatly reduced typical vehicle emissions
• However, number of miles driven has more than doubled


Offset benefits of controlling emissions
 Net result is only a small reduction in automobile pollutants
Cause of automobile pollution is a major market failure in
presence of an externality (pollution) resulting from missing
markets
 With missing markets, signals in form of market prices do not exist to
reveal consumer preferences for society’s allocation of resources
2
Introduction

If well-defined property rights exist, markets will generally
occur for externalities
 Reduces necessity for mechanisms designed to correct externalitygenerated inefficiencies
• One role for government is to provide a legal system to support welldefined property rights for all of society’s resources

We investigate property rights and consequences of
externalities resulting from ill-defined property rights
 Then broadly classify externalities as either bilateral or multilateral
• Discuss inefficiencies associated with bilateral externalities
• Address enforceable property rights (given Coase Theorem) as a means
for resolving these inefficiencies
3
Introduction

Coase Theorem states
 If a market can be created for an externality, an efficient outcome will
result regardless of how well-defined property rights are allocated

We investigate markets where Coase Theorem does not
hold
 Discuss issue of multilateral externalities
 Evaluate government policies involving quotas, taxes, and fostering
markets for externalities (eliminating missing markets) as tools for
addressing market inefficiencies
• Government agencies develop mechanisms that assign property rights
and regulate agent behavior

Enforcing policies through penalties for noncompliance and dividends for
compliance
 However, government mechanisms may not always result in improving
social welfare
 Such mechanisms can only result in alternative second-best Paretoefficient allocations
4
Introduction

Opportunity cost of allocating resources toward establishing
and maintaining mechanisms may exceed cost of
inefficiency associated with some externalities
 Existence of opportunity cost implies that there are still externalities
at some allocation where social welfare is maximized
• Applied economists are active in estimating costs and benefits of
alternative mechanisms for addressing externalities

Aim in chapter is not to determine least-cost allocation for
removing an externality
 But to understand why ill-defined property rights result in missing
markets for commodities and resulting externalities
• Can determine optimal level of an externality and minimum cost of
achieving a given externality level
5
Externalities Defined



An externality (z) is present whenever some agent’s (say,
A’s) utility or production technology includes commodities
whose amounts are determined by other agents
 Without particular attention to effect on A’s welfare
Definition rules out any market-price affects on agents’ utility
or production, called pecuniary externalities
 Arise when external effect is transmitted through price changes
A pecuniary externality does not cause a market failure
 For example, suppose a new firm enters a market and drives up
rental price of land
• Market for land provides a mechanism by which parties can bid for land

Resulting prices will reflect value of land in its various uses
6
Externalities Defined



Without pecuniary externalities price signals would fail to
sustain an efficient allocation
Consumers relying on firms for supply of commodities are
not externalities
Deliberately affecting welfare of others is not an externality
 For example, deliberate criminal actions against agents are not
externalities

However, waiting for someone who is not particularly
concerned about your welfare is an externality
7
Property Rights

A bundle of entitlements defining an owner’s rights,
privileges, and limitations for use of a resource
 For example, in many cities owning a plot of land may
give you entitlement to build a house but not drill a well

Entitlements vary considerably
 From being very restrictive in a planned community to
essentially no restrictions in some rural areas

A well-defined structure of property rights will
provide incentives for efficient allocation of
resources
8
Property Rights

Following list is one set of well-defined private-property
rights that results in a Pareto-efficient allocation
 Universality
• All resources are privately owned and all entitlements completely
specified
 Exclusivity
• All benefits and costs from owning and employing resources accrue to
owner
 Transferability
• All property rights are transferable from one owner to another in a
voluntary exchange
 Enforceability
• Property rights are secure from involuntary seizure or encroachment by
others
9
Property Rights

Previously we implicitly assumed well-defined property
rights existed
 We demonstrated that perfectly competitive markets yield an efficient
price system for resource allocation
• Such a system is where producers maximize their profits and
households maximize their utility


Given their respective resource constraints and current state of technology
Presence of externalities violates assumption of well-defined
property rights
 For example, building a cabin that blocks neighbor’s view of lake
results in a cost that accrues to neighbor

With externalities, household preferences for commodities
are not defined solely over bundle of commodities that it has
ability to choose
10
Property Rights


Assumption of firms freely choosing inputs is also
violated with presence of production externalities
Generally, consumption or production externalities
exist when agents (households and firms) are
directly affected by actions (external effects) of
other agents
 Examples are
• Presence of other vehicles on a congested highway (negative
externality)
• Sight of a neighbor’s flower garden (positive externality)
11
Property Rights


When externalities exist, perfectly competitive equilibrium
does not correspond with a Pareto-optimal allocation
A common property exists when no individual agent has
property entitlements
 Agent cannot employ resource for individual gain
• In a communist economy, all society’s resources are considered
common property

In a centrally planned socialist economy, state (government) has property
entitlements and controls property (resource) allocation for common good of
society
• In a free-market economy, property entitlements are vested privately
with individual agents

Leading to private property as dominant form of property rights
12
Bilateral Externalities

Where one agent’s utility or profit is affected by
another agent’s actions
 Agents could be two firms with their production
technologies linked
• Firms could be producing either same or different outputs

For example, firms could be a chemical plant and a kayak rental
company located on the same river
 Alternatively, agents could be two households or one firm
and a household
• For example, two households living in a duplex where one
household enjoys loud music
13
Bilateral Externalities


For expository purposes, we will assume agents are firms
 With one firm experiencing a negative externality from the other
Rather than well-defined property rights, assume Firm 1’s
short-run total cost function is a function of marketable
output q1 and a nonmarket output (externality) z, STC1(q1, z)
 For example, q1 could be production of steel and z the associated
river water pollution

Assuming Stage II of production for q1, associated marginal
cost curve, ∂STC1/∂q1 = SMC1 > 0
 Has a positive slope, ∂SMC1/∂q1 > 0
• For externality z, ∂STC1/∂z < 0

Increasing z will decrease cost of production
 Represents a marginal benefit to firm
14
Bilateral Externalities
Define marginal benefit as marginal benefit
of the externality (MBE)
 MBE = -∂STC1/∂Z > 0
 Associated MBE curve is illustrated in Figure
21.1, given Law of Diminishing Marginal
Returns
 As z increases, MBE declines
 Given a missing market for z, there is no positive

market price for z
• A profit-maximizing firm would produce where
∂STC1/∂z = 0
15
Figure 21.1 Negative externality
16
Bilateral Externalities

An increase in costs with no associated change in revenue will decrease profit
 Level of z that minimizes costs is ∂STC1/∂z = 0

Assume firm 2’s short-run total cost function is directly affected by firm 1’s
nonmarket output z, STC2(q2, z)
 q2 denotes Firm 2’s marketable output, kayak rentals


Firm 2’s cost of producing q2 is directly affected by amount of z firm 1 produces
A negative externality implies ∂STC2/∂z > 0
 An increase in z increases STC2 and depresses profit
• Partial ∂STC2/∂z > 0 is called marginal social cost (MSC) of externality


Illustrated in Figure 21.1
Positive slope associated with MSC indicates
 As z increases, marginal social cost increases
• ∂MSC/∂z > 0 and ∂2MSC/∂z2 > 0
 Firm 2’s costs are increased by an increase in z at an increasing rate
• For example, the river may be able to assimilate initial increases in water pollution, so MSC of
water pollution for kayaking is low

However, as water pollution increases, capacity of river for assimilating pollution may be exceeded,
resulting in marginal cost for the kayak firm increasing at an increasing rate
17
Bilateral Externalities

Positive slope associated with MSC indicates
 As z increases, marginal social cost increases
• ∂MSC/∂z > 0 and ∂2MSC/∂z2 > 0
 Firm 2’s costs are increased by an increase in z
at an increasing rate
• For example, river may be able to assimilate initial
increases in water pollution

MSC of water pollution for kayaking is low
 However, as water pollution increases, capacity of river
for assimilating pollution may be exceeded
 Resulting in marginal cost for kayak firm increasing at an
increasing rate
18
Independent Decision Making


In its profit maximization, firm 1 has control over
both q1 and z
 p1 is per-unit price firm 1 receives for its output, q1
Since z is a nonmarket output, there is no
associated market price
 F.O.C.s are
• ∂1/∂q1 = p1 – SMB1(q1, z) = 0

Discussed in Chapter 9 and illustrated in Figure 21.1
• ∂1/∂z = -∂STC1(q1, z)/∂z = 0

Establishes cost-minimizing level of z as a necessary condition for
profit maximization
19
Independent Decision Making

Level of externality z should be adjusted to point where
additional reduction in cost of generating an additional unit
of z is zero
 Solving F.O.C.s simultaneously for z and q1 results in their optimal
levels zP and qP1
• Figure 21.1 illustrates this optimal solution


zP is associated with -∂STC1/∂z = MBE = 0 and qP1 with SMC1 = p1
For its profit maximization, firm 2 only has control over its
output, q2, but production of q2 is influenced by externality z,
so
 p2 is per-unit price of q2
• F.O.C. is


∂2/∂q2 = p2 – SMC2(q2, z) = 0
Establishes price equaling marginal cost as a condition for profit
maximization
20
Independent Decision Making

Externality results from firm 2 having no control
over z, which affects its production
 Firm 1 controls level of z and has no incentive to

consider effect z has on firm 2’s production
When firm 2’s additional social cost, MSC, associated
with firm 1’s pollution, z, is not considered by firm 1, an
inefficient high level of pollution may result
• At zP in Figure 21.1, MSC > MBE

Decreasing z will subtract more from cost than from benefits
 Not considering additional social costs or benefits from an
externality generally results in an inefficient allocation of
resources
21
Dependent (Joint) Decision
Making


Internalizing social costs of a negative externality into
agent’s decisions
 Results in a Pareto-efficient allocation of resources
Internalization of social costs results in firm 1 taking into
consideration impact its production decisions have on firm
2’s production possibilities
 With this consideration, output z is no longer an externality
• All effects of z are now internalized into firm 1’s production decisions


Accomplished by maximizing joint profit of the two firms ( = 1 + 2)
Equivalent to two firms merging to form one firm that produces marketable
outputs q1 and q2, with associated prices p1 and p2, along with nonmarket
output z
 With joint action, there is no longer an externality
 Additional social costs are now internalized within this one firm
22
Dependent (Joint) Decision
Making

Mathematically, joint profit maximization is

F.O.C.s are
 ∂/∂q1 = p1 – SMCJ1(q1, z) = 0
 ∂/q2 = p2 – SMCJ2(q2, z) = 0
 ∂/∂z = -∂STC1(q1,z)/∂z - ∂STC2(q2, z)/ ∂z = 0
• SMCJj is short-run marginal joint cost of producing qj, j = 1, 2

First two F.O.C.s are same as when firms act privately
 A perfectly competitive firm equates price to marginal cost
 Under joint action, optimal levels of q1 and q2, (qJ1 and qJ2) are where
price is equated with marginal cost
• For a negative externality, qJ1 < qP1, given z increases costs for
producing q2
23
Dependent (Joint) Decision
Making

Last F.O.C. differs from independent conditions where firms
act privately
 Now optimal levels of q1, q2, and z depend on effect z has on firm 2’s
costs


Figure 21.1 illustrates optimal levels of z and q1
Instead of setting ∂STC1/∂z equal to zero, joint production
sets -STC1/∂z equal to marginal social cost
 -∂STC1(q1, z)/∂z = ∂STC2(q2, z)/ ∂z
 MBEJ = MSC
• MBEJ is marginal joint benefit of externality from joint production of q1
and q2
• Joint action will result in firm 1 decreasing level of z below point where
MBE = 0
• Marginal social cost derived from firm 2 is now internalized into decision
process
24
Dependent (Joint) Decision
Making

Difference between private and joint optimal solution is illustrated in
Figure 21.1
 Optimal level of z decreases, from zP to zJ, along with a decrease in the

optimal level of output, from qP1 to qJ1
Firm 1’s short-run marginal cost of producing q1 shifts to the left, from SMC1
to SMCJ1
• Given increased cost of internalizing production of z
• Similarly, firm 1’s marginal benefit of externality shifts to left, to MBEJ, given
decrease in q1
 Through internalization, firm 1 pays a cost for producing z
• At Pareto-efficient level of z, zJ, amount firm 1 is willing to pay for producing an
additional unit of z is equal to firm 2’s additional costs associated with this
additional unit of z

Note that if firm 2’s cost of producing q2 is independent of z, no externality exists
 Firm 2’s cost associated with z is zero
• Firm 1 will again equate additional cost of producing an additional unit of z to zero
25
Resolving Externality Inefficiency

In February 2002, Oakland County International Airport in
Waterford, Michigan, helped 650 residents to sound insulate
and vibration reinforce their homes against airplane takeoffs
and landings
 Such solutions to externality inefficiencies are possible when
conditions allow agents to negotiate an optimal solution

Providing favorable negotiating conditions is one approach
to mitigating inefficiencies associated with externalities
 Based on these negotiations, a market for externality is then
established

For example, suppose for a negative externality z,
enforceable property rights are established where firm 2 is
assigned rights to production level of z (noise)
 Firm 1 is unable to produce z without firm 2’s approval
26
Resolving Externality Inefficiency

Denote total price (fee) for z units that firm 2
charges firm 1 as Fee
 For profit maximization, firm 2 will determine level of Fee
• Where firm 1 is indifferent between paying Fee to produce z units
of externality or not producing any of the externality
• If firm 2 charges a price below Fee, firm 1 will still produce z units



An increase in Fee will enhance firm 2’s profits without changing
level of z
Increasing Fee transfers some of firm 1’s producer surplus in
production of z to firm 2
Firm 2 will increase Fee to point where all producer surplus from
producing z units is absorbed by Fee
 At this point, firm 1 is indifferent between paying Fee to
produce z units or not producing any z
27
Resolving Externality Inefficiency

Mathematically, this occurs where
 1(q1, z) – Fee = 1(q01, 0)
 p1q1 – STC1(q1, z) – Fee = p1,q01 – STC1(q01, 0)
• q01 represents optimal level of output given z = 0

Firm 2 will then maximize profits subject to level of
Fee where firm 1 is indifferent
 Solving for Fee in the constraint and substituting into
objective function yields
28
Resolving Externality Inefficiency

F.O.C.s are
 ∂2/∂q2 = p2 – SMCJ2 = 0
 ∂2/∂z = -∂STC2(q2, z)/∂z - ∂STC1(q1, z)/∂z = 0 = -MSC + MBEJ = 0
• Optimal levels for q2 and z are same solutions for joint production, zJ and
qJ2

Given this charge, Fee, for producing zJ units of a negative
externality, firm 1’s profit-maximizing problem is
 F.O.C. is
• ∂1/∂q1 = p1 – SMCJ1 = 0


F.O.C.s are identical to F.O.C.s for joint profit maximization
By assigning a property right to z, a market is created for z
 Allows a firm to charge a price for its production of z
• Resulting solution is the same optimal solution obtained under joint
action, zJ
29
Resolving Externality Inefficiency

Coase Theorem
 If trade of an externality can occur (a market exists)
• Bargaining will lead to an efficient outcome no matter how property
•

rights are allocated
Assumes there are no transaction costs associated with bargaining
Any asymmetry in information between buyer and seller can
cause transaction costs
 Will not result in an efficient outcome no matter how property rights
are allocated

Specifically, suppose firm 1 now has property rights to
produce as much of the externality z as it desires
 In absence of any trading, firm 1 will select private level of z, zP
 Firm 2 will offer to pay firm 1 to move from firm 1’s private solution zP
to joint-optimal solution zJ
30
Resolving Externality Inefficiency

Firm 1 will be indifferent between producing an
alternative level of z and receiving S as payment
from firm 2 or producing zP and receiving no
payment
 1(q1, z) + S = 1(qP1, zP)
 p1q1 – STC1(q1, z) + S = p1qP1 – STC1(qP1, zP)
• Firm 2 will then maximize profits, subject to levels of S, where
firm 1 is indifferent
31
Resolving Externality Inefficiency

Solving for S in the constraint and substituting into
objective function yields

F.O.C.s are
 ∂2/∂q2 = p2 – SMCJ2 = 0
 ∂2/∂z = -∂STC2(q2, z)/∂z - ∂STC1(q1, z)/∂z = 0
• Again, optimal levels for q2 and z are the same as in joint
production, zJ and qJ2
32
Resolving Externality Inefficiency

Firm 1’s profit-maximizing problem is

F.O.C. is
 ∂1/∂q1 = p1 – SMCJ1 = 0
• Exactly the same optimal result as when property rights are controlled by
firm 2 or with joint production

Given well-defined property rights and that agents can
bargain with essentially zero transaction costs, resulting
solution will be Pareto efficient
 In practice, it is rare to find externalities with these characteristics
 Normally, a profit incentive exists to either internalize the externality
by merging or establish a market for the externality
• Thus, market forces tend to remove any possible existence of a bilateral
externality
33
Resolving Externality Inefficiency

There are distributional effects that depend on assignment of property
rights
 Property rights are a form of initial endowments, which do have market value

For example, even though Coase Theorem states that optimal levels of
z, q1, and q2 remain unaffected by property rights assignment
 Resulting profit levels of firms are affected
 When an agent is bestowed property right, its benefits will not decrease
• Potential exists for enhancing benefits
 Greater control over property rights improves bargaining power of an agent
and, hence, potential rewards

• Distribution of benefits can change with assignment of property rights
A market with well-defined property rights and essentially zero
transaction costs will provide a Pareto-optimal allocation
 Any improvement in social welfare is dependent on equity impacts of
resulting allocation
34
Multilateral Externalities

Decreasing automobile emissions can have a
major impact on air quality and on asthma in
children
 This example illustrates multilateral externalities
• Far more common than bilateral externalities

Numerous agents create transaction costs
associated with ill-defined property rights
 Obstruct market from internalizing externalities
 Coase Theorem no longer holds under these transaction
costs
• Efforts to internalize these externalities may require some type of
government intervention into markets
35
Government Policies

Government actions to mitigate inefficient exploitation of resources have
taken a number of forms
 One policy is to instill some form of private-property rights on a commonproperty resource
• For example, in western U.S., common- property problem of livestock overgrazing
was addressed by issuing grazing permits




Ranchers who own grazing permits are allowed to use public rangeland for a set fee
Original grazing permits issued by state and federal agencies were freely given to
ranchers
 Common property of public lands was transferred to private ownership
Without a permit, one could not use public land for its major usegrazing
 Permits acquired a market value through their incorporation into land value of
ranch holding permits
Policy of granting private-property rights to common property may result
in improving economic efficiency
 However, it raises equity issues in terms of enhancing ranchers’
endowments at expense of other agents
36
Permit System


Trading of emission permits represents a
government management tool for a common
property
Government controls resource and establishes
barriers to prevent agents from exacting resource
unless licensed by the government
 For example, government may issue a permit to extract
a certain quantity and/or size of a resource
• Fishing and hunting licenses are examples
37
Permit System

A permit system can also be employed for reducing a firm’s
undesirable emissions that adversely affect air and water
quality
 Prior to generating a negative externality firm would be required to
obtain a permit
• Number of permits can be limited to achieve some target level

Allocation of permits transfers certain property rights to
permit holder
 In the case of a hunting permit, hunter pays for this transfer of
property right

In terms of firms generating some negative externality, they
may be issued permits at or below their historical emissions
level
 Given they possess a history of quasi-property rights to emission
releases
38
Permit System




Permits that can be traded (called marketable permits),
create a market for permits with an associated equilibrium
price
If a firm’s marginal cost of reducing emissions is greater
than market price for a permit to release emissions
 It would minimize cost by purchasing permit and releasing emissions
If its marginal cost is less than market price, it would
minimize cost by selling permits and reducing its emissions
In equilibrium, each firm’s marginal cost of reducing
emissions would be equal to market price for permits
39
Permit System

Specifically, let’s consider two firms engaged in
generating a negative externality
 Let z1 and z2 represent emission levels of firm 1 and firm

2, respectively, with associated short-run total cost
functions STC1(q1, z1) and STC2(q2, z2)
Assume target level of total emissions (zJ) is established,
so zJ = z1 + z2
• Determine minimum cost of achieving emissions level zJ by
 TC is total cost of reduced emissions
40
Permit System

Lagrangian is

F.O.C.s are
41
Permit System

Minimum-cost condition of achieving a zJ level of
emissions is MBEJ1 = MBEJ2 = J
 Firms’ short-run marginal benefits of emissions are set

equal to J
In this case, Lagrange multiplier is marginal social cost of
combined emissions by two firms, J = ∂TC/∂z
• Setting this equal to each firm’s MBEJ yields minimum cost of
establishing a zJ level of emissions


Illustrated in Figure 21.2
Target level zJ is obtained at minimum cost with firm
1 and firm 2 generating zJ1 and zJ2 emissions,
respectively
42
Figure 21.2 Minimum cost of
achieving a given emission level
43
Permit System



Establishing a marketable permit system achieves this
minimum social cost of emissions
Let pz represent per-unit equilibrium price of a permit and z01
and z02 initial level of permits for firms 1 and 2, respectively
 z J = z 01 + z 02
With j = 1, 2, representing either of the firms, each firm will
maximize profits as follows
 When z0j - zj < 0, firm is using more permits than it was allocated
• It will acquire additional permits in amount of (zj - z0j) at per-unit price of
pz
 If z0j – zj > 0, firm is not using all of its permit allocation
• Will sell (z0j - zj) at per-unit price of pz
44
Permit System

F.O.C.s are
 ∂j/∂qj = pj – SMCJj(qj, zj) = 0
• Discussed in Chapter 9
 ∂j/∂zj = -∂STCj(qj, zj)/ ∂zj – pz = 0 = MBEJj – pz = 0, j = 1, 2
• Each firm equates their marginal benefit of emissions to pz

A major limitation of this marketable permit system exists when spatial
distribution of externality generated by all firms is not uniform
 If agents who are being affected by externalities are not uniformly affected by each
firm
• Permit system will result in some agents receiving even more of the externality
• For example, assume households of type A are only affected by firm 1’s emissions and
households of type B only by firm 2’s emissions


As illustrated in Figure 21.3, firm 1 sells permits to firm 2
Thus, from initial emission levels (z01,z02) emissions for type A households are
reduced at expense of type B households, who receive a higher emissions level
 Although emissions level is now generated at a minimum cost, distribution of resulting
emissions are not optimal
45
Figure 21.3 Minimum cost of achieving a
given emission level with marketable permits
46
Taxes and Standards (Quotas)

If general knowledge exists about which firms can efficiently
reduce a negative externality relative to other firms
 Direct taxes or standards may be employed
• Direct taxes on negative externalities have the theoretical foundation of
the agent receiving an inefficient price for negative externality it is
generating

With ill-defined property rights firms would receive a zero
price for generation of emissions
 An efficient price would be a tax equivalent to marginal social cost of
negative externality
• Profit-maximizing problem for firm j is

j is a per-unit tax for firm j on negative externality, z
47
Taxes and Standards (Quotas)

Potentially, firms with differing production capabilities for efficiently
reducing negative externality would face different tax levels
 On a practical level, tax would generally be the same for firms with like
production technologies within same industry and causing similar harm to
other agents

Assuming a constant tax level across two firms, , F.O.C.s are
 ∂j/∂qj = pj – SMCJj(qj, zj) = 0
• Discussed in Chapter 9
 ∂j/∂zj = -∂STCj(qj, zj)/∂zj -  = 0 = MBEJj -  = 0, j = 1, 2

• Firm j equates its marginal benefit of emission to 
Equating tax  to MSCj will yield an efficient level of emissions
generation by each firm, zJj
• Illustrated in Figure 21.4
48
Figure 21.4 Pigouvian tax on
emissions
49
Taxes and Standards (Quotas)

As illustrated in Figure 21.1, if there is only one agent being affected by
firm j’s emissions, then  = ∂STC2/∂zj
 Given well-defined property rights, Coase Theorem would apply
• No government-established price for market would be required for efficiency
• However, as number of agents increase, even with well-defined property rights


Transaction costs of determining who are being affected by a negative externality
increases
A government mechanism design in form of an emissions tax may be
socially desirable
 Such a tax, equivalent to MSC, is called a Pigouvian tax, after Arthur Pigou
• Assuming general knowledge exists of which firms can efficiently reduce a
negative externality relative to other firms


Pigouvian taxes directly associated possible spatial MSC would not have spatial
distribution limitation associated with a permit system
Aside from the problem of acquiring this general knowledge for implementation
 Pigouvian taxes are a Lindahl taxface same limitations
 Agents facing a higher tax rate relative to others may not respond well to
tax-discriminating nature of Pigouvian taxes
50
Taxes and Standards (Quotas)

Major problem with a Pigouvian tax
 Indirect method of reducing a negative externality versus direct method of
setting some quota (called emissions standard)
• Setting emissions standards directly reduces level of a negative externality to
some stated level


In contrast, a tax requires firms to consider effect of tax on their profits
In a dynamic setting where MSC is continuously changing, adjusting
emissions standards to these changes will yield a direct short-run
response of establishing desired emissions level
 Whereas changing tax rate may not
• Short-run MBE curve may be rather inelastic to change in a tax

Results in less than desired reduction in emissions
• Desired level of emissions may not be obtained until long run

By then MSC may have changed
 Illustrated in Figure 21.5
51
Taxes and Standards (Quotas)

An upward shift in MSC curve to MSC', indicating a higher
marginal social cost at all levels of emissions, warrants a
reduction in emissions from z0 to z"
 Changing emissions standards from z0 to z" will directly produce this
desired effect
• Firm’s response is not dependent on elasticity of MBEJ curve
• However, effect of emissions from a tax change does depend on
elasticity of MBEJ curve


In short run, an increase in tax from 0 to “ results in a decrease in
emissions from z0 to z'
 Only in long run will emissions fall to z"
System of taxes requires additional knowledge concerning
long- and short-run response of firms’ emissions to tax
changes
52
Figure 21.5 Standards versus taxes with
long-run and short-run adjustments
53
Taxes and Standards (Quotas)

An example of taxes versus standards is maintaining air
quality within an air basin (such as Los Angeles)
 Changing weather conditions will affect air quality on a daily basis
• An inversion layer, where ambient air temperatures increase with
altitude, traps air pollution within basin

Potentially resulting in poor air quality
• Announcing stricter emissions standards when such weather conditions
occur would directly mitigate the problem


Announcing an increase in emissions taxes may not have such immediate
effects
In contrast, when MSC curve is relatively static (doesn’t shift), a tax will
minimize firms’ cost relative to a standard
 An example is water quality where socially desirable level of affluent
remains relatively constant
54
Taxes and Standards (Quotas)

One of the F.O.C.s for two firms maximizing profits given a
negative externality tax is
 -∂STC1(q1, z1)/∂z1 = -∂STC2(q2, z2)/∂z2 = 
 MBEJ1 = MBEJ2 = 
• Demonstrated in Figure 21.6 for two firms located relatively close to
each other



MSC is the same regardless of which firm changes its affluent level
As indicated in the figure, cost-minimizing levels of affluents
are z1J and z2J for firms 1 and 2, respectively
 Only if MBEJ' for both firms is the same will z1J = z2J
Taxation offers a lower cost for reducing a given level of
affluent compared to setting the same emissions standard
for both firms
55
Figure 21.6 Minimum cost of achieving a
given affluent level with a Pigouvian tax
56
Firms’ Preference

Firms’ preference for emissions standards versus taxes
 Depends on which mechanism yields a higher profit for a given level
of emissions
• For example, if emissions standards directly limit total output, firms may
prefer such standards to a Pigouvian tax

As indicated in Figure 21.7, standards may provide a cartel
situation, which can result in improved profit
 Prior to any standards, let perfectly competitive equilibrium price and
output be (pe, qe)
• With imposition of standards, socially optimal output declines to qs and
price increases to ps

Results in a net gain in producer surplus of pepsAC - DCB
• Alternatively, imposition of a tax that reduces output price to p' with the
same output, qs, results in a loss in producer surplus of p'peBD

Firms have incentives to support emissions standards versus Pigouvian
taxes
57
Figure 21.7 Producer surplus for
standards versus taxes
58