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Chapter5_WelfareEconomicsandExternalities.pdf
Chapter 5: Welfare Economics and Externalities from Microeconomics: Markets, Methods & Models by Douglas Curtis and Ian Irvine is available under a Creative Commons Attribution-NonCommercial- ShareAlike 3.0 Unported license. © Lyryx Learning Inc.
Chapter 5
Welfare economics and externalities
In this chapter we will explore:
5.1 Equity and efficiency
5.2 Consumer and producer surplus
5.3 Efficient market outcomes
5.4 Taxation surplus and efficiency
5.5 Market failures – externalities
5.6 Other market failures
5.7 Environment and climate change
5.8 Equity, justice and efficiency
5.1 Equity and efficiency
In modern mixed economies, markets and governments together determine the output produced
and also who benefits from that output. In this chapter we explore a very broad question that
forms the core of welfare economics: Are markets a good way to allocate scarce resources in
view of the fact that they not only give rise to inequality and poverty, but also fail to capture
the impacts of productive activity on non-market participants? Mining impacts the environment,
traffic results in road fatalities, alcohol and tobacco cause premature deaths and prescription pills
are abused. These products all generate secondary impacts beyond their stated objective. We
frequently call these external effects. The analysis of markets in this larger sense involves not
just positive economics; appropriate policy is additionally a normative issue because policies can
impact the various participants in different ways and to different degrees. Welfare economics,
therefore, deals with both normative and positive issues.
Welfare economics assesses how well the economy allocates its scarce resources in accordance
with the goals of efficiency and equity.
117
118 Welfare economics and externalities
Political parties on the left and right disagree on how well a market economy works. Canada’s
New Democratic Party emphasizes the market’s failings and the need for government interven-
tion, while the Progressive Conservative Party believes, broadly, that the market fosters choice,
incentives, and efficiency. What lies behind this disagreement? The two principal factors are ef-
ficiency and equity. Efficiency addresses the question of how well the economy’s resources are
used and allocated. In contrast, equity deals with how society’s goods and rewards are, and should
be, distributed among its different members, and how the associated costs should be apportioned.
Equity deals with how society’s goods and rewards are, and should be, distributed among its
different members, and how the associated costs should be apportioned.
Efficiency addresses the question of how well the economy’s resources are used and allocated.
Equity is also concerned with how different generations share an economy’s productive capabili-
ties: more investment today makes for a more productive economy tomorrow, but more greenhouse
gases today will reduce environmental quality tomorrow. These are inter-generational questions.
Climate change caused by global warming forms one of the biggest challenges for humankind at
the present time. As we shall see in this chapter, economics has much to say about appropriate
policies to combat warming. Whether pollution-abatement policies should be implemented today
or twenty years from now involves considerations of equity between generations. Our first task is
to develop an analytical tool which will prove vital in assessing and computing welfare benefits
and costs – economic surplus.
5.2 Consumer and producer surplus
An understanding of economic efficiency is greatly facilitated as a result of understanding two
related measures: consumer surplus and producer surplus. Consumer surplus relates to the demand
side of the market, producer surplus to the supply side. Producer surplus is also termed supplier
surplus. These measures can be understood with the help of a standard example, the market for
city apartments.
Table 5.1 and Figure 5.1 describe the hypothetical data. We imagine first a series of city-based
students who are in the market for a standardized downtown apartment. These individuals are not
identical; they value the apartment differently. For example, Alex enjoys comfort and therefore
places a higher value on a unit than Brian. Brian, in turn, values it more highly than Cathy or Don.
Evan and Frank would prefer to spend their money on entertainment, and so on. These valuations
are represented in the middle column of Table 5.1, and also in Figure 5.1 with the highest valuations
closest to the origin. The valuations reflect the willingness to pay of each consumer.
5.2. Consumer and producer surplus 119
Demand
Individual Demand valuation Surplus
Alex 900 400
Brian 800 300
Cathy 700 200
Don 600 100
Evan 500 0
Frank 400 0
Supply
Individual Reservation value Surplus
Gladys 300 200
Heward 350 150
Ian 400 100
Jeff 450 50
Kirin 500 0
Lynn 550 0
Table 5.1: Consumer and supplier surpluses
120 Welfare economics and externalities
$900 Alex
Brian
Cathy
Don
Frank
$300 Gladys
Heward Ian
Jeff
Lynn Evan
Kirin
Rent
Quantity
Equilibrium price=$500.
Figure 5.1: The apartment market
Demanders and suppliers are ranked in order of the value they place on an
apartment. The market equilibrium is where the marginal demand value of
Evan equals the marginal supply value of Kirin at $500. Five apartments
are rented in equilibrium.
On the supply side we imagine the market as being made up of different individuals or owners,
who are willing to put their apartments on the market for different prices. Gladys will accept less
rent than Heward, who in turn will accept less than Ian. The minimum prices that the suppliers are
willing to accept are called reservation prices or values, and these are given in the lower part of
Table 5.1. Unless the market price is greater than their reservation price, suppliers will hold back.
By definition, as stated in Chapter 3, the demand curve is made up of the valuations placed on the
good by the various demanders. Likewise, the reservation values of the suppliers form the supply
curve. If Alex is willing to pay $900, then that is his demand price; if Heward is willing to put his
apartment on the market for $350, he is by definition willing to supply it for that price. Figure 5.1
therefore describes the demand and supply curves in this market. The steps reflect the willingness
to pay of the buyers and the reservation valuations or prices of the suppliers.
In this example, the equilibrium price for apartments will be $500. Let us see why. At that
price the value placed on the marginal unit supplied by Kirin equals Evan’s willingness to pay.
Five apartments will be rented. A sixth apartment will not be rented because Lynne will let her
apartment only if the price reaches $550. But the sixth potential demander is willing to pay only
$400. Note that, as usual, there is just a single price in the market. Each renter pays $500, and
therefore each supplier also receives $500.
The consumer and supplier surpluses can now be computed. Note that, while Don is willing to
pay $600, he actually pays $500. His consumer surplus is therefore $100. In Figure 5.1, we can
see that each consumer’s surplus is the distance between the market price and the individual’s
valuation. These values are given in the final column of the top half of Table 5.1.
5.2. Consumer and producer surplus 121
Consumer surplus is the excess of consumer willingness to pay over the market price.
Using the same reasoning, we can compute each supplier’s surplus, which is the excess of the
amount obtained for the rented apartment over the reservation price. For example, Heward obtains
a surplus on the supply side of $150, while Jeff gets $50. Heward is willing to put his apartment on
the market for $350, but gets the equilibrium price/rent of $500 for it. Hence his surplus is $150.
Supplier or producer surplus is the excess of market price over the reservation price of the
supplier.
It should now be clear why these measures are called surpluses. The suppliers and demanders are
all willing to participate in this market because they earn this surplus. It is a measure of their gain
from being involved in the trading.
Computing the surpluses
The sum of each participant’s surplus in the final column of Table 5.1 defines the total surplus in
the market. Hence, on the demand side a total surplus arises of $1000 and on the supply side a
value of $500.
However, we do not always think of demand and supply functions in terms of the steps illustrated in
Figure 5.1. Usually there are so many participants in the market that the differences in reservation
prices on the supply side and willingness to pay on the demand side are exceedingly small, and so
the demand and supply curves are drawn as continuous lines. So let us see how to compute the
surpluses where the forms of the demand and supply curves are known. Let the equations for the
curves be given by
Demand: P = 1000−100Q
Supply: P = 250+50Q
To find the market equilibrium, the two functions are equated and solved:
1000−100Q = 250+50Q ⇒ 1000−250 = 50Q+100Q ⇒ 750 = 150Q
Therefore,
122 Welfare economics and externalities
Q = 750/150 = 5.
At a quantity traded of five units, we can find the corresponding price by substituting it into the
demand or supply function; the resulting equilibrium price is $500. In this example we have
deliberately used two functions that yield the same equilibrium as the apartment example, and
these functions are illustrated in Figure 5.2.
$900
A $1000
Demand$300 $250
C
Supply
Rent
Quantity
$500 B E
Equilibrium price=$500.
Figure 5.2: Measuring surplus
With the linear demand and supply curves that assume the good is divisible
the consumer surplus is AEB and the supplier surplus is BEC. This exceeds
the surplus computed as the sum of rectangular areas beneath the bars and
above the price. The same reasoning carries over to producer surplus.
The consumer surplus (CS) is the difference between the demand curve and the equilibrium price
(ABE), and is computed by using the standard formula for the area of a triangle—half the base
multiplied by the perpendicular height, and this yields a value of $1250.
CS = (Demand value−price) = area ABE
= (1/2)×5×$500 = $1250
The suppliers’ surplus is the area BEC. This is computed as:
PS = (price− reservation value) = area BEC
= (1/2)×5×$250 = $625
5.3. Efficient market outcomes 123
Before progressing it is useful to note that the numerical values we obtain here differ slightly from
the values in Table 5.1. The reason is straightforward to see: the area under the demand curve
is slightly greater than the sum of the several rectangular areas, each associated with one market
participant. This is equally true on the supply side.
The total surplus that arises in the market is the sum of producer and consumer surpluses.
5.3 Efficient market outcomes
The definition of the surplus measures is straightforward: Once we have the demand and supply
curves, the area between each one and the equilibrium price can be calculated. With straight-line
functions, these areas involve triangles. But where does the notion of market efficiency enter? Let
us pursue the example.
In addition to these city apartments, there are many others in the suburbs that do not have the
desirable “proximity to downtown” characteristic. There are also many more demanders in the
market for living space than the number who rented at $500 in the city. Who are these other
individuals? Clearly they place a lower value on city apartments than the individuals who are
willing to pay at least $500.
The equilibrium price of $500 in Figure 5.1 has two implications. First, individuals who place a
lower value on a city apartment must seek accommodation elsewhere. Second, suppliers who have
a reservation price above the equilibrium price will not participate. This implies that an efficient
market maximizes the sum of producer and consumer surpluses. Here is why.
An efficient market maximizes the sum of producer and consumer surpluses.
Instead of a freely functioning market, imagine that the city government rents all apartments from
suppliers at the price of $500 per unit, but decides to allocate the apartments to tenants in a lottery
(we can imagine the government getting the money to pay for the apartments from tax revenue).
By doing this, many demanders who place a low value on a city apartment would end up living in
one, and other individuals, who were not so fortunate in the lottery, would not obtain an apartment,
even if they valued one highly. Suppose, then, that Frank gets an apartment in the lottery and Cathy
does not. This outcome would not be efficient, because there are further gains in surplus to be had.
Frank and Cathy can now strike a private deal so that both gain.
If Frank agrees to sublet to Cathy at a price between their respective valuations of $400 and $700—
say $600—he will gain $200 and she will gain $100. This is because Frank values the apartment
only at $400, but now obtains $600. Cathy values it at $700 but pays only $600. The random
allocation of apartments, therefore, is not efficient, because further gains from trade are possible.
124 Welfare economics and externalities
In contrast, the market mechanism, in which suppliers and demanders freely trade, leaves no scope
for additional trades that would improve the well-being of participants.
It is frequently useful to characterize market equilibrium in terms of the behaviour of marginal
participants—the very last buyer and the very last supplier, or the very last unit supplied and
demanded. In addition, we will continue with the assumption that the supply curve represents the
full cost of each unit of production. It follows that, at the equilibrium, the value placed on the last
unit purchased (as reflected in the demand curve) equals the cost of supplying that unit. If one
more unit were traded, we can see from Figure 5.2 that the value placed on that additional unit (as
represented by the demand curve) would be less than its cost of production. This would be a poor
use of society’s resources. Phrased another way, resources would not be used efficiently unless the
cost of the last unit equaled the value placed on it.
Before applying the concept of efficiency, and the surpluses it embodies, students should note
that we have invoked some assumptions. For example, if individual incomes change, the corre-
sponding market demand curve changes, and any market equilibrium will then depend on the new
distribution of incomes.
5.4 Taxation, surplus and efficiency
Despite enormous public interest in taxation and its impact on the economy, it is one of the least
understood areas of public policy. In this section we will show how an understanding of two
fundamental tools of analysis—elasticities and economic surplus—provides powerful insights into
the field of taxation.
We begin with the simplest of cases, the federal government’s goods and services tax (GST) or
the provincial governments’ sales taxes (PST). These taxes combined vary by province, but we
suppose that a typical rate is 13 percent. Note that this is a percentage, or ad valorem, tax, not a
specific tax of so many dollars per unit traded. Figure 5.3 illustrates the supply and demand curves
for some commodity. In the absence of taxes, the equilibrium E0 is defined by the combination
(P0,Q0).
5.4. Taxation, surplus and efficiency 125
F
S
St B
D
Price
Quantity
P0 E0
Q0
Pt Et
Qt
Pts A
Tax wedge
Figure 5.3: The efficiency cost of taxation
The tax shifts S to St and reduces the quantity traded from Q0 to Qt . At Qt the demand value placed on an additional unit exceeds the supply valuation
by EtA. Since the tax keeps output at this lower level, the economy can-
not take advantage of the additional potential surplus between Qt and Q0.
Excess burden = deadweight loss = AEtE0.
A 13-percent tax is now imposed, and the new supply curve St lies 13 percent above the no-tax
supply S. A tax wedge is therefore imposed between the price the consumer must pay and the
price that the supplier receives. The new equilibrium is Et , and the new market price is at Pt . The
price received by the supplier is lower than that paid by the buyer by the amount of the tax wedge.
The post-tax supply price is denoted by Pts.
There are two burdens associated with this tax. The first is the revenue burden, the amount of tax
revenue paid by the market participants and received by the government. On each of the Qt units
sold, the government receives the amount (Pt −Pts). Therefore, tax revenue is the amount PtEtAPts. As illustrated in Chapter 4, the degree to which the market price Pt rises above the no-tax price P0 depends on the supply and demand elasticities.
A tax wedge is the difference between the consumer and producer prices.
The revenue burden is the amount of tax revenue raised by a tax.
The second burden of the tax is called the excess burden. The concepts of consumer and producer
surpluses help us comprehend this. The effect of the tax has been to reduce consumer surplus
by PtEtE0P0. This is the reduction in the pre-tax surplus given by the triangle P0BE0. By the
same reasoning, supplier surplus is reduced by the amount P0E0APts; prior to the tax it was P0E0F.
126 Welfare economics and externalities
Consumers and suppliers have therefore seen a reduction in their well-being that is measured by
these dollar amounts. Nonetheless, the government has additional revenues amounting to PtEtAPts,
and this tax imposition therefore represents a transfer from the consumers and suppliers in the
marketplace to the government. Ultimately, the citizens should benefit from this revenue when it
is used by the government, and it is therefore not considered to be a net loss of surplus.
However, there remains a part of the surplus loss that is not transferred, the triangular area EtE0A.
This component is called the excess burden, for the reason that it represents the component of the
economic surplus that is not transferred to the government in the form of tax revenue. It is also
called the deadweight loss, DWL.
The excess burden, or deadweight loss, of a tax is the component of consumer and producer
surpluses forming a net loss to the whole economy.
The intuition behind this concept is not difficult. At the output Qt , the value placed by consumers
on the last unit supplied is Pt (=Et), while the production cost of that last unit is Pts (= A). But
the potential surplus (Pt −Pts) associated with producing an additional unit cannot be realized, because the tax dictates that the production equilibrium is at Qt rather than any higher output.
Thus, if output could be increased from Qt to Q0, a surplus of value over cost would be realized
on every additional unit equal to the vertical distance between the demand and supply functions D
and S. Therefore, the loss associated with the tax is the area EtE0A.
In public policy debates, this excess burden is rarely discussed. The reason is that notions of
consumer and producer surpluses are not well understood by non-economists, despite the fact that
the value of lost surpluses can be very large. Numerous studies have attempted to estimate the
excess burden associated with raising an additional dollar from the tax system. They rarely find
that the excess burden is less than 25 percent. This is a sobering finding. It tells us that if the
government wished to implement a new program by raising additional tax revenue, the benefits of
the new program should be 25 percent greater than the amount expended on it!
The impact of taxes and other influences that result in an inefficient use of the economy’s resources
are frequently called distortions. The examples we have developed in this chapter indicate that
distortions can describe either an inefficient output being produced, as in the taxation example, or
an inefficient allocation of a given output, as in the case of apartments being allocated by lottery.
A distortion in resource allocation means that production is not at an efficient output, or a given
output is not efficiently allocated.
5.4. Taxation, surplus and efficiency 127
Elasticities and the excess burden
We suggested above that elasticities are important in determining the size of the deadweight loss
of a tax. Going back to Figure 5.3, suppose that the demand curve through E0 were more elastic
(with the same supply curve, for simplicity). The post-tax equilibrium Et would now yield a lower
Qt value and a price between Pt and P0. The resulting tax revenue raised and the magnitude of the
excess burden would differ because of the new elasticity.
A wage tax
A final example will illustrate how the concerns of economists over the magnitude of the DWL are
distinct from the concerns expressed in much of the public debate over taxes. Figure 5.4 illustrates
the demand and supply for a certain type of labour. On the demand side, the analysis is simplified
by assuming that the demand for labour is horizontal, indicating that the gross wage rate is fixed,
regardless of the employment level. On the supply side, the upward slope indicates that individuals
supply more labour if the wage is higher. The equilibrium E0 reflects that L0 units of labour are
supplied at the gross, that is, pre-tax wage W0.
S
Wt Dt
W0 D
Wage
Labour
E0
L0
B
Et
Lt
Wage tax
Excess burden = deadweight loss = BE0Et
Figure 5.4: Taxation and labour supply
The demand for labour is horizontal at W0. A tax on labour reduces the
wage paid to Wt . The loss in supplier surplus is the area W0E0EtWt . The
government takes W0BEtWt in tax revenue, leaving BE0Et as the DWL of
the wage tax.
An income tax is now imposed. If this is, say, 20 percent, then the net wage falls to 80 percent
of the gross wage in this example, given the horizontal demand curve. The new equilibrium Et is
defined by the combination (Wt ,Lt). Less labour is supplied because the net wage is lower. The
128 Welfare economics and externalities
government generates tax revenue of (W0−Wt ) on each of the Lt units of labour now supplied, and this is the area W0BEtWt . The loss in surplus to the suppliers is W0E0EtWt , and therefore the DWL
is the triangle BE0Et . Clearly the magnitude of the DWL depends upon the supply elasticity.
Whereas the DWL consequence of the wage tax is important for economists, public debate is more
often focused on the reduction in labour supply and production. Of course, these two issues are
not independent. A larger reduction in labour supply is generally accompanied by a bigger excess
burden.
5.5 Market failures – externalities
The consumer and producer surplus concepts we have developed are extremely powerful tools of
analysis, but the world is not always quite as straightforward as simple models indicate. For ex-
ample, many suppliers generate pollutants that adversely affect the health of the population, or
damage the environment, or both. The term externality is used to denote such impacts. External-
ities impact individuals who are not participants in the market in question, and the effects of the
externalities may not be captured in the market price. For example, electricity-generating plants
that use coal reduce air quality, which, in turn, adversely impacts individuals who suffer from
asthma or other lung ailments. While this is an example of a negative externality, externalities can
also be positive.
An externality is a benefit or cost falling on people other than those involved in the activity’s
market. It can create a difference between private costs or values and social costs or values.
We will now show why markets characterized by externalities are not efficient, and also show how
these externalities might be corrected or reduced. The essence of an externality is that it creates a
divergence between private costs/benefits and social costs/benefits. If a steel producer pollutes the
air, and the steel buyer pays only the costs incurred by the producer, then the buyer is not paying
the full “social” cost of the product. The problem is illustrated in Figure 5.5.
5.5. Market failures – externalities 129
R
S (Private supply cost)
K
S f (Full social supply cost) U
D
Price
Quantity of electricity
P0 E0
Q0
P∗ E∗
A
V
Q∗
Figure 5.5: Negative externalities and inefficiency
A negative externality is associated with this good. S measures private costs,
whereas S f measures the full social cost. The socially optimal output is Q ∗,
not the market outcome Q0. Beyond Q ∗ the real cost exceeds the demand
value; therefore Q0 is not an efficient output. A tax that increases P to P ∗
and reduces output is one solution to the externality.
Negative externalities
In Figure 5.5, the supply curve S represents the cost to the supplier, whereas S f (the full cost)
reflects, in addition, the cost of bad air to the population. Of course, we are assuming that this
external cost is ascertainable, in order to be able to characterize S f accurately. Note also that this
illustration assumes that, as power output increases, the external cost per unit rises, because the
difference between the two supply curves increases with output. This implies that low levels of
pollution do less damage: Perhaps the population has a natural tolerance for low levels, but higher
levels cannot be tolerated easily and so the cost is greater.
Despite the externality, an efficient level of production can still be defined. It is given by Q∗, not
Q0. To see why, consider the impact of reducing output by one unit from Q0. At Q0 the willingness
of buyers to pay for the marginal unit supplied is E0. The (private) supply cost is also E0. But from
a societal standpoint there is a pollution/health cost of AE0 associated with that unit of production.
The full cost, as represented by S f , exceeds the buyer’s valuation. Accordingly, if the last unit of
output produced is cut, society gains by the amount AE0, because the cut in output reduces the
excess of true cost over value.
Applying this logic to each unit of output between Q0 and Q ∗, it is evident that society can increase
its well-being by the dollar amount equal to the area E∗AE0, as a result of reducing production.
130 Welfare economics and externalities
Next, consider the consequences of reducing output further from Q∗. Note that pollution is being
created here, and environmentalists frequently advocate that pollution should be reduced to zero.
However, an efficient outcome may not involve a zero level of pollution! If the production of power
were reduced below Q∗, the loss in value to buyers, as a result of not being able to purchase the
good, would exceed the full cost of its production.
If the government decreed that, instead of producing Q∗, no pollution would be tolerated, then soci-
ety would forgo the possibility of earning the total real surplus equal to the area UE∗K. Economists
do not advocate such a zero-pollution policy; rather, we advocate a policy that permits a “tolera-
ble” pollution level – one that still results in net benefits to society. In this particular example, the
total cost of the tolerated pollution equals the area between the private and full supply functions,
KE∗VR.
As a matter of policy, how is this market influenced to produce the amount Q∗ rather than Q0?
One option would be for the government to intervene directly with production quotas for each
firm. An alternative would be to impose a corrective tax on the good whose production causes the
externality: With an appropriate increase in the price, consumers will demand a reduced quantity.
In Figure 5.5 a tax equal to the dollar value VE∗ would shift the supply curve upward by that
amount and result in the quantity Q∗ being traded.
A corrective tax seeks to direct the market towards a more efficient output.
We are now venturing into the field of environmental policy, and this is explored in the following
section. The key conclusion of the foregoing analysis is that an efficient working of the market
continues to have meaning in the presence of externalities. An efficient output level still maximizes
economic surplus where surplus is correctly defined.
Positive externalities
Externalities of the positive kind enable individuals or producers to get a type of ‘free ride’ on
the efforts of others. Real world examples abound: When a large segment of the population is
inoculated against disease, the remaining individuals benefit on account of the reduced probability
of transmission.
A less well recognized example is the benefit derived by many Canadian firms from research and
development (R&D) undertaken in the United States. Professor Dan Treffler of the University of
Toronto has documented the positive spillover effects in detail. Canadian firms, and firms in many
other economies, learn from the research efforts of U.S. firms that invest heavily in R&D. In the
same vein, universities and research institutes open up new fields of knowledge, with the result
that society at large, and sometimes the corporate sector, gain from this enhanced understanding
of science, the environment, or social behaviours.
5.5. Market failures – externalities 131
The free market may not cope any better with these positive externalities than it does with nega-
tive externalities, and government intervention may be beneficial. For example, firms that invest
heavily in research and development would not undertake such investment if competitors could
have a complete free ride and appropriate the fruits. This is why patent laws exist, as we shall see
later in discussing Canada’s competition policy. These laws prevent competitors from copying the
product development of firms that invest in R&D. If such protection were not in place, firms would
not allocate sufficient resources to R&D, which is a real engine of economic growth. In essence,
the economy’s research-directed resources would not be appropriately rewarded, and thus too little
research would take place.
While patent protection is one form of corrective action, subsidies are another. We illustrated
above that an appropriately formulated tax on a good that creates negative externalities can reduce
demand for that good, and thereby reduce pollution. A subsidy can be thought of as a negative tax.
Consider the example in Figure 5.6.
S
D (Private value)
D f (Full social value)
Price
Quantity
P0
Q0 Q ∗
P∗
Figure 5.6: Positive externalities - the market for flu shots
The value to society of vaccinations exceeds the value to individuals: the
greater the number of individuals vaccinated, the lower is the probability of
others contracting the virus. D f reflects this additional value. Consequently,
the social optimum is Q∗ which exceeds Q0.
Individuals have a demand for flu shots given by D. This reflects their private valuation – their
personal willingness to pay. But the social value of flu shots is greater. When a given number
of individuals are inoculated, the probability that others will be infected falls. Additionally, with
higher rates of inoculation, the health system will incur fewer costs in treating the infected. There-
fore, the value to society of any quantity of flu shots is greater than the sum of the values that
individuals place on them.
Let D f reflects the full social value of any quantity of flu shots. If S is the supply curve, the socially
132 Welfare economics and externalities
optimal, efficient, market outcome is Q∗. How can we influence the market to move from Q0 to
Q∗? One solution is a subsidy that would reduce the price from P0 to P ∗. Rather than shifting the
supply curve upwards, as a tax does, the subsidy would shift the supply downward, sufficiently
to intersect D at the output Q∗. In some real world examples, the value of the positive externality
is so great that the government may decide to drive the price to zero, and thereby provide the
inoculation at a zero price. For example, children typically get their MMR shots (measles, mumps,
and rubella) free of charge.
5.6 Other market failures
There are other ways in which markets can fail to reflect accurately the social value or social cost
of economic activity. Profit seeking monopolies, which restrict output in order to increase profits,
create inefficient markets, and we will see why in the chapter on monopoly. Or the market may
not deal very well with what are called public goods. These are goods, like radio and television
service, national defence, or health information: with such goods and services many individuals
can be supplied with the same good at the same total cost as one individual. We will address this
problem in our chapter on government. And, of course, there are international externalities that
cannot be corrected by national governments because the interests of adjoining states may differ:
One economy may wish to see cheap coal-based electricity being supplied to its consumers, even
if this means acid rain or reduced air quality in a neighbouring state. Markets may fail to supply
an “efficient” amount of a good or service in all of these situations. Global warming is perhaps the
best, and most extreme, example of international externalities and market failure.
5.7 Environmental policy and climate change
The 2007 recipients for the Nobel Peace Prize were the United Nation’s Intergovernmental Panel
on Climate Change (IPCC), and Al Gore, former vice president of the United States. The Nobel
committee cited the winners “for their efforts to build up and disseminate greater knowledge about
man-made climate change, and to lay the foundations for the measures that are needed to counteract
such change.” While Al Gore is best known for his efforts to bring awareness of climate change to
the world, through his book and associated movie (An Inconvenient Truth), the IPCC is composed
of a large, international group of scientists that has worked for many years in developing a greater
understanding of the role of human activity in global warming. Reports on the extent and causes
of the externality that we call global warming are now plentiful. The IPCC has produced several
reports at this point; a major study was undertaken in the UK under the leadership of former World
Bank Chief Economist Sir Nicholas Stern. Countless scientific papers have been published on the
subject.
5.7. Environmental policy and climate change 133
Greenhouse gases
The emission of greenhouse gases (GHGs) is associated with a wide variety of economic activities
such as coal-based power generation, oil-burning motors, wood-burning stoves, etc. The most
common GHG is carbon dioxide. The gases, upon emission, circulate in the earth’s atmosphere
and, if their build-up is excessive, prevent sufficient radiant heat from escaping. The result is a slow
warming of the earth’s surface and air temperatures. It is envisaged that such temperature increases
will, in the long term, increase water temperatures, possibly cause glacial melting, with the result
that water levels worldwide may rise. In addition to the possibility of higher water levels (which
the IPCC estimates will be about one foot by the end of the 21st century), oceans may become
more acidic, weather patterns may change and weather events may become more variable and
severe. The changes will be latitude-specific and vary by economy and continent, and ultimately
will impact the agricultural production abilities of certain economies.
Greenhouse gases that accumulate excessively in the earth’s atmosphere prevent heat from es-
caping and lead to global warming.
While most scientific findings and predictions are subject to a degree of uncertainty, there is little
disagreement in the scientific community on the very long-term impact of increasing GHGs in the
atmosphere. There is some skepticism as to whether the generally higher temperatures experienced
in recent decades are completely attributable to anthropogenic activity since the industrial revolu-
tion, or whether they also reflect a natural cycle in the earth’s temperature. But scientists agree
that a continuance of the recent rate of GHG emissions will ultimately lead to serious climatic
problems. And since GHG emissions are strongly correlated with economic growth, the very high
rate of economic growth in many large-population economies such as China and India mean that
GHGs could accumulate at a faster rate than considered likely in the 1990s.
This is an area where economic, atmospheric and environmental models are used to make predic-
tions. We have just one earth and humankind has never witnessed current GHG emission patterns
and trends. Consequently the methodology of this science is strongly model based. Scientists at-
tempt to infer something about the relationship between temperature and climate on the one hand
and carbon dioxide concentrations in the atmosphere on the other, using historical data. Data values
are inferred by examining ice cores and tree rings from eons past. Accordingly, there is a degree
of uncertainty regarding the precise impact of GHG concentrations on water levels, temperatures,
and extreme weather events.
The consensus is that, in the presence of such uncertainty, a wise strategy would involve controls
on the further buildup of gases, unless the cost of such a policy was prohibitive.
134 Welfare economics and externalities
GHGs as a common property
A critical characteristic of GHGs is that they are what we call in economics a ‘common property’:
every citizen in the world ‘owns’ them, every citizen has equal access to them, and it matters little
where these GHGs originate. Consequently, if economy A reduces its GHG emissions, economy
B may simply increase their emissions rather than incur the cost of reducing its emissions also.
Hence, economy A’s behaviour goes unrewarded. This is the crux of international agreements – or
disagreements. Since GHGs are a common property, in order for A to have the incentive to reduce
emissions, it needs to know that B will act correspondingly.
The Kyoto Protocol
The world’s first major response to climate concerns came in the form of the United Nations–
sponsored Earth Summit in Rio de Janeiro in 1992. This was followed by the signing of the
Kyoto Protocol in 1997, in which a group of countries committed themselves to reducing their
GHG emissions relative to their 1990 emissions levels by the year 2012. Canada’s Parliament
subsequently ratified the Kyoto Protocol, and thereby agreed to meet Canada’s target of a 6 percent
reduction in GHGs relative to the amount emitted in 1990.
On a per-capita basis, Canada is one of the world’s largest contributors to global warming, even
though Canada’s percentage of the total is just 2 percent. Many of the world’s major economies
refrained from signing the Protocol—most notably China, the United States, and India. Canada’s
emissions in 1990 amounted to approximately 600 giga tonnes (Gt) of carbon dioxide; but by the
time we ratified the treaty in 2002, emissions were about 25% above that level. Hence the signing
was somewhat meaningless, in that Canada had virtually a zero possibility of attaining its target.
The target date of 2012 has come and gone; and the leaders of the world economy, at their meeting
in Copenhagen failed to come up with a new agreement that would have greater force. In 2012 the
Rio+20 summit was held – in Rio once again, with the objective of devising a means of reducing
GHG emissions.
The central challenge in this area is that developed economies are those primarily responsible for
the buildup of GHGs in the post industrial revolution era. Developing economies, however, do not
accept that the developed economies should be free to continue to emit GHGs at current levels,
while the developing economies should be required to limit theirs at a much lower level.
To compound difficulties, there exists strong skepticism in some economies regarding the urgency
to implement limits on the growth in emissions.
5.7. Environmental policy and climate change 135
Canada’s GHG emissions
An excellent summary source of data on Canada’s emissions and performance during the period
1990-2010 is available on Environment Canada’s web site. See:
Environment Canada – National Inventory Report – GHG sources and sinks in Canada 1990-2010.
Canada, like many economies, has become more efficient in its use of energy (the main source of
GHGs) in recent decades—its use of energy per unit of total output has declined steadily. On a per
capita basis Canada’s emissions amounted to 23.5 tonnes in 2005, and dropped to 20.3 by 2010.
This improvement in efficiency means that Canada’s GDP is now less energy intensive. The quest
for increased efficiency is endless, if economic growth is to continue at rates that will satisfy the
world’s citizens and more broadly the impoverished world. The critical challenge is to produce
more output while using not just less energy per unit of output, but to use less energy in total
While Canada’s energy intensity (GHGs per unit of output) has dropped by a very substantial
amount – 27% between 1990 and 2010 – overall emissions increased by almost 20%. Further-
more, while developed economies have increased their efficiency, it is the world’s efficiency that
is ultimately critical. By outsourcing much our its manufacturing sector to China, Canada and
the West have offloaded some of their most GHG-intensive activities. But GHGs are a common
property resource.
Canada’s GHG emissions also have a regional aspect: the production of oil and gas, which has
created considerable wealth for all Canadians (and contributed to the appreciation of the Cana-
dian dollar in the last decade), is both energy intensive and concentrated in a limited number of
provinces (Alberta, Saskatchewan and more recently Newfoundland and Labrador).
GHG Measurement
GHG atmospheric concentrations are measured in parts per million (ppm). Current levels in the
atmosphere are below 400 ppm, and long-term levels above 500 could lead to serious economic
and social disruption. In the immediate pre-industrial revolution era concentrations were in the
250 ppm range. Hence 500 ppm represents the ‘doubling’ factor that is so frequently discussed in
the media.
GHGs are augmented by the annual additions to the stock already in the atmosphere, and at the
same time they decay—though very slowly. GHG-reduction strategies that propose an immediate
reduction in emissions are more costly than those aimed at a more gradual reduction. For example,
a slower investment strategy would permit in-place production and transportation equipment to
reach the end of its economic life rather than be scrapped and replaced ‘prematurely’. Policies that
focus upon longer term replacement are therefore less costly.
136 Welfare economics and externalities
While not all economists and policy makers agree on the time scale for attacking the problem, most
agree that, the longer major GHG reduction is postponed, the greater the efforts will have to be in
the long term—because GHGs will build up more rapidly in the near term.
A critical question in controlling GHG emissions relates to the cost of their control: how much of
annual growth might need to be sacrificed in order to get emissions onto a sustainable path? Again
estimates vary. The Stern Review proposed that, with an increase in technological capabilities, a
strategy that focuses on the relative near-term implementation of GHG reduction measures might
cost “only” a few percentage points of the value of world output. If correct, this may not be an
inordinate price to pay for risk avoidance in the longer term.
Nonetheless, such a reduction will require particular economic policies, and specific sectors will
be impacted more than others.
Economic policies for climate change
There are three main ways in which polluters can be controlled. One involves issuing direct con-
trols; the other two involve incentives—in the form of pollution taxes, or on tradable “permits” to
pollute.
To see how these different policies operate, consider first Figure 5.7. It is a standard diagram
in environmental economics, and is somewhat similar to our supply and demand curves. On the
horizontal axis is measured the quantity of environmental damage or pollution, and on the vertical
axis its dollar value or cost. The upward-sloping damage curve represents the cost to society of
each additional unit of pollution or gas, and it is therefore called a marginal damage curve. It
is positively sloped to reflect the reality that, at low levels of emissions, the damage of one more
unit is less than at higher levels. In terms of our earlier discussion, this means that an increase in
GHGs of 10 ppm when concentrations are at 300 ppm may be less damaging than a corresponding
increase when concentrations are at 500 ppm.
5.7. Environmental policy and climate change 137
Marginal damage
Marginal abatement cost
Pollution cost
Pollution quantityQ∗
Figure 5.7: The optimal quantity of pollution
Q∗ represents the optimal amount of pollution. More than this would in-
volve additional social costs because damages exceed abatement costs. Co-
versely, less than Q∗ would require an abatement cost that exceeds the re-
duction in damage.
The marginal damage curve reflects the cost to society of an additional unit of pollution.
The second curve is the abatement curve. It reflects the cost of reducing emissions by one unit,
and is therefore called a marginal abatement curve. This curve has a negative slope indicating
that, as we reduce the total quantity of pollution produced, the cost of further unit reductions rises.
This shape corresponds to reality. For example, halving the emissions of pollutants and gases from
automobiles may be achieved by adding a catalytic converter and reducing the amount of lead in
gasoline. But reducing those emissions all the way to zero requires the development of major new
technologies such as electric cars—an enormously more costly undertaking.
The marginal abatement curve reflects the cost to society of reducing the quantity of pollution
by one unit.
If producers are unconstrained in the amount of pollution they produce, they may produce more
than what we will show is the optimal amount – corresponding to Q∗. This amount is optimal in
the sense that at levels greater than Q∗ the damage exceeds the cost of reducing the emissions.
However, reducing emissions by one unit below Q∗ would mean incurring a cost per unit reduction
that exceeds the benefit of that reduction. Another way of illustrating this is to observe that at a
level of pollution above Q∗ the cost of reducing it is less than the damage it inflicts, and therefore
138 Welfare economics and externalities
a net gain accrues to society as a result of the reduction. But to reduce pollution below Q∗ would
involve an abatement cost greater than the reduction in pollution damage and therefore no net gain
to society. This constitutes a first rule in optimal pollution policy.
An optimal quantity of pollution occurs when the marginal cost of abatement equals the marginal
damage.
A second guiding principle emerges by considering a situation in which some firms are relative
‘clean’ and others are ‘dirty’. More specifically, a clean firm A may have already invested in new
equipment that uses less energy per unit of output produced, or emits fewer pollutants per unit
of output. In contrast the dirty firm B uses older dirtier technology. Suppose furthermore that
these two firms form a particular sector of the economy and that the government sets a limit on
total pollution from this sector, and that this limit is less than what the two firms are currently
producing. What is the least costly method to meet the target?
The intuitive answer to this question goes as follows: in order to reduce pollution at least cost to
the sector, calculate what it would cost each firm to reduce pollution from its present level. Then
implement a system so that the firm with the least cost of reduction is the first to act. In this case
the ‘dirty’ firm will likely have a lower cost of abatement since it has not yet upgraded its physical
plant. This leads to a second rule in pollution policy:
With many polluters, the least cost policy to society requires producers with the lowest abatement
costs to act first.
This principle implies that policies which impose the same emission limits on firms may not be
the least costly manner of achieving a target level of pollution. Let us now consider the use of
tradable permits and corrective/carbon taxes as policy instruments. These are market-based
systems aimed at reducing GHGs.
Tradable permits and corrective/carbon taxes are market-based systems aimed at reducing
GHGs.
Incentive mechanism I: tradable permits
A system of tradable permits is frequently called a ‘cap and trade’ system, because it limits or caps
the total permissible emissions, while at the same time allows a market to develop in permits. For
illustrative purposes, consider the hypothetical two-firm sector we developed above, composed of
firms A and B. Firm A has invested in clean technology, firm B has not. Thus it is less costly for
B to reduce emissions than A if further reductions are required. Next suppose that each firm is
allocated by the government a specific number of ‘GHG emission permits’; and that the total of
such permits is less than the amount of emissions at present, and that each firm is emitting more
5.7. Environmental policy and climate change 139
than its permits allow. How can these firms achieve the target set for this sector of the economy?
The answer is that they should be able to engage in mutually beneficial trade: If firm B has a lower
cost of reducing emissions than A, then it may be in A’s interest to pay B to reduce B’s emissions
heavily. This would free up some of B’s emission permits. A in essence is thus buying B’s emission
permits from B.
This solution may be efficient from a resource use perspective: having A reduce emissions might
involve a heavy investment cost for A. But having B reduce emissions might involve a more modest
cost – one that he can more than afford by selling his emission permits to A.
The largest system of tradable permits currently operates in the European Union. It covers more
than 10,000 large energy-using installations. Trading began in 2005. A detailed description of its
operation is contained in Wikipedia. California introduced a similar scheme in November 2012.
See: Wikipedia – European Union Emission Trading Scheme
Incentive mechanism II: taxes
Corrective taxes are frequently called Pigovian taxes, after the economist Arthur Pigou. He advo-
cated taxing activities that cause negative externalities. These taxes have been examined above in
Section 5.4. Corrective taxes of this type can be implemented as part of a tax package reform. For
example, taxpayers are frequently reluctant to see governments take ‘yet more’ of their money, in
the form of new taxes. Such concerns can be addressed by reducing taxes in other sectors of the
economy, in such a way that the package of tax changes maintains a ‘revenue neutral’ impact.
Policy in practice – international
In an ideal world, permits would be traded internationally, and such a system might be of benefit to
developing economies: if the cost of reducing pollution is relatively low in developing economies
because they have few controls in place, then developed economies, for whom the cost of GHG
reduction is high could induce firms in the developing world to undertake cost reductions. Such a
trade would be mutually beneficial. For example, if a developed-economy firm must expend $30 to
reduce GHGs by one tonne, and this can be achieved at a cost of $10 in the developing economy,
then the firm in the developed world could pay up to $20 to the firm in the developing world to
reduce GHGs by one tonne. Both would obviously gain from such an arrangement. This gain
arises because of the common property nature of the gases – it matters not where they originate.
This process is evidently just an extension of the domestic cap-and-trade system described above
under ‘incentive mechanism I’ to the international market. The advantage of internationalizing the
140 Welfare economics and externalities
system is that the differences in the cost of reducing emissions may be very large internationally,
and the scope for gains correspondingly larger.
Policy in practice – domestic large final emitters
Governments frequently focus upon quantities emitted by individual firms, sometimes because
governments are reluctant to introduce carbon taxes or a system of tradable permits. Specifically
the focus is upon firms called large final emitters (LFEs). Frequently, a relatively small number of
producers are responsible for a disproportionate amount of an economy’s total pollution, and limits
are placed on those firms in the belief that significant economy-wide reductions can be achieved
in this manner. A further reason for concentrating on these LFEs is that the monitoring costs are
relatively small compared to the costs associated with monitoring all firms in the economy. It
must be kept in mind that pollution permits may be a legal requirement in some jurisdictions, but
monitoring is still required, because firms could choose to risk polluting without owning a permit.
Revenues from taxes and permits
Taxes and tradable permits differ in that taxes generate revenue for the government from polluting
producers, whereas permits may not generate revenue, or may generate less revenue. If the gov-
ernment simply allocates permits initially to all polluters, free of charge, and allows a market to
develop, such a process generates no revenue to the government. While economists may advocate
an auction of permits in the start-up phase of a tradable permits market, such a mechanism may
run into political objections.
Setting taxes at the appropriate level requires knowledge of the cost and damage functions associ-
ated with GHGs.
Despite the monitoring costs and the incomplete information that governments typically have about
pollution activities, there exist a number of fruitful tools for reducing pollutants and GHGs. Permits
and taxes are market based and are efficient when sufficient information is available. In contrast,
direct controls may be fruitful in specific instances. In formulating pollution policy it must be kept
in mind that governments rarely have every bit of the information they require; pollution policy is
no exception.
5.8 Equity, justice, and efficiency
Our discussion of environmental challenges in the modern era illustrates starkly the tradeoffs that
we face inter-generationally: disregarding the impacts of today’s behaviour can impact future
5.8. Equity, justice, and efficiency 141
generations. Clearly there is a question here of equity.
Economists use several separate notions of equity in formulating policy: horizontal equity, ver-
tical equity, and inter-generational equity. Horizontal equity dictates, for example, that people
who have the same income should pay the same tax, while the principle of vertical equity dic-
tates that people with more income should pay more tax, and perhaps a higher rate of tax. Inter-
generational equity requires that the interests of different cohorts of individuals—both those alive
today and those not yet born—should be balanced by ethical principles.
Horizontal equity is the equal treatment of similar individuals.
Vertical equity is the different treatment of different people in order to reduce the consequences
of these innate differences.
Intergenerational equity requires a balancing of the interests and well-being of different gener-
ations and cohorts.
Horizontal equity rules out discrimination between people whose economic characteristics and
performance are similar. Vertical equity is more strongly normative. Most people agree that hor-
izontal equity is a good thing. In contrast, the extent to which resources should be redistributed
from the “haves” to the “have-nots” to increase vertical equity is an issue on which it would be
difficult to find a high degree of agreement.
People have different innate abilities, different capacities, and different wealth. These differences
mean people earn different incomes in a market economy. They also affect the pattern of consumer
demand. Brazil, with a very unequal distribution of income and wealth, has a high demand for
luxuries such as domestic help. In more egalitarian Denmark, few can afford servants. Different
endowments of ability, capital, and wealth thus imply different demand curves and determine dif-
ferent equilibrium prices and quantities. In principle, by varying the distribution of earnings, we
could influence the outcomes in many of the economy’s markets.
This is an important observation, because it means that we can have many different efficient out-
comes in each of the economy’s markets when considered in isolation. The position of a demand
curve in any market may depend upon how incomes and resources are distributed in the economy.
Accordingly, when it is proposed that the demand curve represents the “value” placed on a good or
service, we should really think of this value as a measure of willingness to pay, given the current
distribution of income.
For example, the demand curve for luxury autos would shift downward if a higher tax rate were
imposed on those individuals at the top end of the income distribution. Yet the auto market could
be efficient with either a low or high set of income taxes. Let us pursue this example further in
order to understand more fully that the implementation of a degree of redistribution from rich to
poor involves an equity–efficiency trade-off.
142 Welfare economics and externalities
John Rawls, a Harvard philosopher who died recently, has been one of the most influential
proponents of redistribution in modern times. He argued that much of the income difference
we observe between individuals arises on account of their inherited abilities, social status, or
good fortune. Only secondarily, he proposes, are income differences due to similar individu-
als making different work choices.
If this view is accurate, he challenges us to think today of a set of societal rules we would
adopt, not knowing our economic status or ability in a world that would begin tomorrow! He
proposes that, in such an experiment, we could collectively adopt a set of rules favouring the
less fortunate, in particular those at the very bottom of the income heap.
Application Box 5.1: Equity, ability, luck, and taxes
Equity versus efficiency
Figure 5.8 describes the market for high-skill labour. With no income taxes, the equilibrium labour
supply and wage rate are given by (L0,W0). If a tax is now imposed that reduces the gross wage W0 to Wt1, the consequence is that less labour is supplied and there is a net loss in surplus equal to
the dollar amount E0E1A. This is the efficiency loss associated with raising government revenue
equal to W0AE1Wt1. Depending on how this money is spent, society may be willing to trade off
some efficiency losses in return for redistributive gains.
Wt2 Dt2
Wt1 Dt1
W0 D0
S
Wage
Labour
E2
L2
E1
L1
E0
L0
AB Initial wage tax
Final wage tax
Figure 5.8: Equity versus efficiency in the labour market
Doubling the wage tax on labour from (W0 −Wt1) to (W0 −Wt2) increases the DWL from AE0E1 to BE0E2. The DWL more than doubles – in this
case it quadruples when the tax doubles.
5.8. Equity, justice, and efficiency 143
Let us continue with the illustration: suppose the tax is increased further so as to reduce the net
wage to Wt2. The DWL is now BE0E2, much larger than before. Whether we should take this
extra step in sacrificing more efficiency for redistributive gains is an ethical or normative issue.
The citizens of some economies, most notably in Scandinavia, appear more willing than the citi-
zens of the United States to make efficiency sacrifices in return for other objectives. Canada lies
between these extremes, and our major political parties can be placed clearly on a spectrum of
willingness to trade equity and efficiency. A vital role for the economist, therefore, is to clarify the
nature and extent of the trade-offs. The field of public economics views this as a centrepiece in its
investigations.
144 Key Terms
KEY TERMS
Efficiency addresses the question of how well the economy’s resources are used and allocated.
Equity deals with how society’s goods and rewards are, and should be, distributed among its
different members, and how the associated costs should be apportioned.
Consumer surplus is the excess of consumer willingness to pay over the market price.
Supplier or producer surplus is the excess of market price over the reservation price of the
supplier.
Efficient market: maximizes the sum of producer and consumer surpluses.
Tax wedge is the difference between the consumer and producer prices.
Revenue burden is the amount of tax revenue raised by a tax.
Excess burden of a tax is the component of consumer and producer surpluses forming a net
loss to the whole economy.
Deadweight loss of a tax is the component of consumer and producer surpluses forming a net
loss to the whole economy.
Distortion in resource allocation means that production is not at an efficient output, or a given
output is not efficiently allocated.
Externality is a benefit or cost falling on people other than those involved in the activity’s
market. It can create a difference between private costs or values and social costs or values.
Corrective tax seeks to direct the market towards a more efficient output.
Greenhouse gases that accumulate excessively in the earth’s atmosphere prevent heat from
escaping and lead to global warming.
Marginal damage curve reflects the cost to society of an additional unit of pollution.
Marginal abatement curve reflects the cost to society of reducing the quantity of pollution
by one unit.
Tradable permits and corrective/carbon taxes are market-based systems aimed at reducing
GHGs.
Key Terms 145
Horizontal equity is the equal treatment of similar individuals.
Vertical equity is the different treatment of different people in order to reduce the conse-
quences of these innate differences.
Intergenerational equity requires a balancing of the interests and well-being of different
generations and cohorts.
146 Exercises
EXERCISES FOR CHAPTER 5
Exercise 5.1. Four teenagers live on your street. Each is willing to shovel snow from one driveway
each day. Their “willingness to shovel” valuations (supply) are: Jean, $10; Kevin, $9; Liam, $7;
Margaret, $5. Several households are interested in having their driveways shoveled, and their
willingness to pay values (demand) are: Jones, $8; Kirpinsky, $4; Lafleur, $7.50; Murray, $6.
(a) Draw the implied supply and demand curves as step functions.
(b) How many driveways will be shoveled in equilibrium?
(c) Compute the maximum possible sum for the consumer and supplier surpluses.
(d) If a new (wealthy) family arrives on the block, that is willing to pay $12 to have their drive-
way cleared, recompute the answers to parts (a), (b), and (c).
Exercise 5.2. Consider a market where supply and demand are given by P = 10 and P = 34−Q respectively.
(a) Illustrate the market geometrically, and compute the equilibrium quantity.
(b) Impose a tax of $2 per unit on the good so that the supply curve is now P = 12. Calculate the new equilibrium quantity, and illustrate it in your diagram.
(c) Calculate the tax revenue generated, and also the deadweight loss.
Exercise 5.3. Redo Exercise 5.2 with the demand curve replaced by P = 26− (2/3)Q.
(a) Is this new demand curve more or less elastic than the original at the equilibrium?
(b) What do you note about the relative magnitudes of the DWL and tax revenue estimates here,
relative to the previous question?
Exercise 5.4. Next, consider an example of DWL in the labour market. Suppose the demand for
labour is given by the fixed gross wage W = $16. The supply is given by W = 0.8L.
(a) Illustrate the market geometrically.
(b) Calculate the equilibrium amount of labour supplied, and the supplier surplus.
(c) Suppose a wage tax that reduces the wage to W = $12 is imposed. By how much is the supplier’s surplus reduced at the new equilibrium?
Exercise 5.5. Governments are in the business of providing information to potential buyers. The
first serious provision of information on the health consequences of tobacco use appeared in the
United States Report of the Surgeon General in 1964.
Exercises 147
(a) How would you represent this intervention in a supply and demand for tobacco diagram?
(b) Did this intervention “correct” the existing market demand?
Exercise 5.6. In deciding to drive a car in the rush hour, you think about the cost of gas and the
time of the trip.
(a) Do you slow down other people by driving?
(b) Is this an externality, given that you yourself are suffering from slow traffic?
Exercise 5.7. Suppose that our local power station burns coal to generate electricity. The demand
and supply functions for electricity are given by P = 12− 0.5Q and P = 2+ 0.5Q, respectively. However, for each unit of electricity generated, there is an externality. When we factor this into the
supply side of the market, the real social cost is increased, and the supply curve is P = 3+0.5Q.
(a) Find the free market equilibrium and illustrate it geometrically.
(b) Calculate the efficient (i.e. socially optimal) level of production.
Exercise 5.8. Evan rides his mountain bike down Whistler each summer weekend. The utility
value he places on each kilometre ridden is given by P = 4− 0.02Q, where Q is the number of kilometres. He incurs a cost of $2 per kilometre in lift fees and bike depreciation.
(a) How many kilometres will he ride each weekend? [Hint: Think of this “value” equation as
demand, and this “cost” equation as a (horizontal) supply.]
(b) But Evan frequently ends up in the local hospital with pulled muscles and broken bones. On
average, this cost to the Canadian taxpayer is $0.50 per kilometre ridden. From a societal
viewpoint, what is the efficient number of kilometres that Evan should ride each weekend?
Exercise 5.9. Your local dry cleaner, Bleached Brite, is willing to launder shirts at its cost of $1.00
per shirt. The neighbourhood demand for this service is P = 5−0.005Q.
(a) Illustrate and compute the market equilibrium.
(b) Suppose that, for each shirt, Bleached Brite emits chemicals into the local environment that
cause $0.25 damage per shirt. This means the full cost of each shirt is $1.25. Calculate the
socially optimal number of shirts to be cleaned.
Exercise 5.10. The supply curve for agricultural labour is given by W = 6+0.1L, where W is the wage (price per unit) and L the quantity traded. Employers are willing to pay a wage of $12 to all
workers who are willing to work at that wage; hence the demand curve is W = 12.
(a) Illustrate the market equilibrium, and compute the equilibrium wage (price) and quantity of
labour employed.
148 Exercises
(b) Compute the supplier surplus at this equilibrium.
Exercise 5.11. The demand for ice cream is given by P = 24−Q and the supply curve by P = 4.
(a) Illustrate the market equilibrium, and compute the equilibrium price and quantity.
(b) Calculate the consumer surplus at the equilibrium.
(c) As a result of higher milk prices to dairy farmers the supply conditions change to P = 6. Compute the new quantity traded, and calculate the loss in consumer surplus.
Exercise 5.12. Two firms A and B, making up a sector of the economy, emit pollution (pol) and
have marginal abatement costs: MAA = 24− pol and MAB = 24−(1/2)pol. So the total abatement curve for this sector is given by MA = 24− (1/3)pol. The marginal damage function is constant at a value of $12 per unit of pollution emitted: MD = $12.
(a) Draw the MD and market-level MA curves and establish the efficient level of pollution for
this economy.
Exercise 5.13. In Exercise 5.12, if each firm is permitted to emit half of the efficient level of
pollution, illustrate your answer in a diagram which contains the MAA and MAB curves.
(a) With each firm producing this amount of pollution, how much would it cost each one to
reduce pollution by one unit?
(b) If these two firms can freely trade the right to pollute, how many units will they (profitably)
trade?
Exercise 5.14. Once again, in Exercise 5.13, suppose that the government’s policy is to allow
firms to pollute provided that they purchase a permit valued at $10 per unit emitted (rather than
allocating a pollution quota to each firm).
(a) How many units of pollution rights would be purchased and by the two participants in this
market?
Exercise 5.15. The market demand for vaccine XYZ is given by P = 36−Q and the supply con- ditions are P = 20. There is a positive externality associated with being vaccinated, and the real societal value is known and given by P = 36− (1/2)Q.
(a) What is the market solution to this supply and demand problem?
(b) What is the socially optimal number of vaccinations?
(c) If we decide to give the supplier a given dollar amount per vaccination supplied in order to
reduce price and therefore increase the number of vaccinations to the social optimum, what
would be the dollar value of that per-unit subsidy?
Exercises 149
Exercise 5.16. In Exercise 5.15, suppose that we give buyers the subsidy instead of giving it to the
suppliers. By how much would the demand curve have to shift upward in order that the socially
optimal quantity is realized?
Exercise 5.17. The demand and supply curves in a regular market (no externalities) are given by
P = 42−Q and P = 0.2Q.
(a) Solve for the equilibrium price and quantity.
(b) A percentage tax of 100% is now levied on each unit supplied. Hence the form of the new
supply curve P = 0.4Q. Find the new market price and quantity.
(c) How much per unit is the supplier paid?
(d) Compute the producer and consumer surpluses after the imposition of the tax and also the
DWL.
