Market Failures: Open-Access
Resources, Externalities and Public
Goods/Bads
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Key Questions
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What are the different reasons that markets often fail to provide
efficient levels of environmental protection?
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What do these reasons imply about the relationships between the
free market and efficient levels of protection?
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Sources of Market Failure
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Open Access Resources
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Externalities
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Public Goods/Bads
These are overlapping concepts and they are all connected to the idea
that markets for environmental goods have incomplete property rights.
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Open-Access Resources
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The “Tragedy of the Commons”
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More than one party has the right to use the resource.
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High seas fisheries
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Pastures
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Free-access roads
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Departure from typical private good considered in competitive
equilibrium.
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Benefits or costs of use are not exclusive to the individual.
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As a result, there are social costs or benefits not accounted for in
a consumer or firm decision to use it.
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Example: Open-Access Fishery
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Efficient Outcome — total profits (value) in the industry are
maximized at Y ∗ , where the M C (slope of the T C curve) is equal
to the M R or price (slope of the T R curve).
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Open-Access Outcome — fishermen continue to harvest as long
as profits are positive leading to equilibrium harvest at YOA .
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Example: Open-Access Fishery
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There is too much effort exerted by fishermen because they fail to
take into account the effect their choice to fish has on the costs of
other fishermen, a problem caused by the fact that no one (or
everyone) owns the rights to the fishery and cannot force those
who want access to pay the social cost of its use.
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We often talk about efficient markets in which firms earn zero
profits at the competitive equilibrium. What’s different about the
open-access outcome that leads to inefficiency?
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Marginal profits versus total profits
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Costs of firms are not directly impacted by output choices of
others in competitive markets.
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Externalities
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An externality is when the actions of one individual (or firm)
directly impact the well-being of others without their permission.
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Alternatively, when the choices of one individual (or firm)
directly enter the utility or production function of others.
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Examples:
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Negative — power plant’s decision to pollute directly impacts
well-being of individuals through its effect on their health.
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Positive — the fact that many others use Microsoft Word makes
the product more valuable to you because you can collaborate.
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Externalities
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Externalities
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Steel mill fails to account for the costs it imposes on laundry by
emitting smoke.
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This leads them to produce too much smoke from society’s
perspective.
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We know that production efficiency dictates that the M RT equal
the price ratio of the two goods.
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The M RT acknowledges these external costs because it captures
the rate at which the economy can shift production from laundry
to steel — including the negative impact that an additional
production unit of steel has on laundry output via the smoke
externality.
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Pecuniary Externalities
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When the choices of individuals (or firms) impact others through
their effects on prices
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When my favorite musician becomes famous there is a negative
pecuniary externality imparted to me because the price of
concert tickets goes up
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Pecuniary externalities are not a source of inefficiency — the
increase in the price of tickets in the previous example reflects an
increase in the social value of the tickets
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Public Goods/Bads
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Both open-access and externalities have a common feature —
they cause inefficiency because outcomes for some individuals or
firms depend on the actions of others and these others fail to
account for these effects
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Public goods/bads are another way of thinking about these issues
in a way that identifies the key characteristics of goods that lead
to these types of problems
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Properties of Public Goods
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Non-Excludable — with private goods, if you own the good you
can stop others from using it without your permission. Not so
with non-excludable goods.
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Non-Rival — with private goods your use of a good means that
there is less for others to use. Not so with non-rival goods.
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Public Goods/Bads
Rival
Non-Rival
Excludable
Good: Coffee
Bad: Household Garbage
Good: Proprietary Software
Bad: Computer Virus
Non-Excludable
Good: Open-Access Fishery
Bad: Neighbor’s leaves
Good: National Defense
Bad: Global Warming
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Inefficiency of Private Provision of
Public Goods/Bads
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Non-Excludable — destroys the ability of the owner of a
good/bad to secure the appropriate level of compensation in
exchange for the good.
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Non-Rival — means that every unit of a good produced has the
potential to benefit everyone, but an individual takes into
account only his own benefit when deciding how much to
purchase/produce.
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Efficient Provision of Public Goods
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Recall that Pareto optimality requires that M RS = M RT , where
these are define over the public good (G) and a bundle of all
other goods (x).
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For non-rival goods, this condition changes a bit because all
individuals i can consume every unit of G. So the optimal level of
provision, G∗ , is given by:
X
M RSi (G∗ ) = M RT (G∗ )
i
Suppose, instead, that the LHS was greater than the RHS. Then,
collectively, consumers would be willing to give up more of x to
get an extra unit of G than it costs (in terms of lost output of x)
for producers to produce that extra unit of G. Therefore, society
could generate a Pareto improvement by doing so.
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Efficient Provision of Public Goods
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We can also use marginal willingness to pay (MWTP) curves to
define efficiency in public goods provision. MWTP is equivalent
to MRS when what the individual is giving up is denominated in
currency units instead of other goods.
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The efficiency condition requires that we sum MWTP for each
unit of the public good to derive total marginal benefits of
provision.
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Efficient Provision of Public Goods
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Private Provision of Public Goods
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Suppose we have N identical individuals with income w and
preferences given by
U = u(x, G)
where G is the total amount of a pure public good supplied,
defined as
G = Ḡ + g
where Ḡ is the amount supplied by all other individuals and g is
an individual’s personal contribution. If units of x and g are
chosen so that prices are equal to unity, then the budget
constraint is:
w =x+g
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Private Provision of Public Goods
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We can rewrite the utility function substituting in the definition
of G and the budget constraint.
U = u(w − g, g + Ḡ)
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Now, if w is fixed, we can think of an individual’s optimal choice
of g (and x) based on indifference curves defined over g and Ḡ.
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The indifference curves are increasing in Ḡ and U-shaped in g.
The reason is that when G is low enough, the individual is willing
to give up a lot of x to get more G. So, for a given level of Ḡ,
raising g and lowering x raises utility. But when Ḡ or g is high
enough, x is the scarce good so reducing x further reduces utility.
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Private Provision of Public Goods
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Private Provision of Public Goods
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For a fixed level of Ḡ, the optimal choice of g is the point of
tangency between the indifference curve and the horizontal line
at Ḡ.
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As Ḡ increases, the optimal level of g falls because the individual
can rely more on the provision of others.
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This is true as long as x is a normal good because higher Ḡ is
equivalent to an increase in income; less must be spent on g to
obtain the same level of G. Thus, expenditures on x will rise with
Ḡ if x is a normal good. The straight downward-sloping line in
the diagram indicates this relationship.
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Private Provision of Public Goods
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Since everyone is the same, they choose the same level of g.
Therefore:
Ḡ = (n − 1)g
The straight upward-sloping line in the diagram indicates this
relationship.
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So the point (N ) where these two lines intersect is the
equilibrium level public goods (ḠN , gN ).
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Private Provision of Public Goods
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Efficient Provision of Public Goods
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What is the efficient level of G in this model?
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The problem with the private-provision equilibrium is that each
individual optimally lowers their level of g when others provide
more Ḡ — they fail to realize the effect of their choice of g on G,
an externality.
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Now suppose that we assume that if one individual raises g,
others will do the same, so that individuals understand that:
Ḡ = (n − 1)g
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Efficient Provision of Public Goods
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Again, the upward-sloping line in the diagram indicates this
relationship.
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In this case, the individual would choose g ∗ , the point of
tangency between her indifference curve and this line (E). This is
the efficient level of provision because M RS = n − 1. That is, the
individual realizes that reducing g reduces the well-being of the
n − 1 other individuals.
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Private Provision of Public Goods
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Work an example of public goods
provision
U = x1/2 G1/2
w =x+g
G = Ḡ + g
Substituting the budget and public goods constraints into the utility
fn gives
U = (w − g)1/2 (Ḡ + g)1/2
Solving for Ḡ allows us to explore the shape of an indifference curve
in Ḡ − g space.
Ḡ = U02 /(w − g) − g
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Work an example of public goods
provision
Ḡ = U02 /(w − g) − g
Let U0 = 40, w = 10.
G_bar
16
U_0
14
12
10
8
6
4
2
4
6
8
g
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Work an example of public goods
provision
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Private provision: find highest, feasible indifference curve
assuming Ḡ is fixed — where dU/dg = 0.
dU
= −1/2(w−g ∗ )−1/2 (g ∗ +Ḡ)1/2 +1/2(w−g ∗ )1/2 (g ∗ +Ḡ)−1/2 = 0
dg
1/2
(w − g ∗ )1/2
(g ∗ + Ḡ)1/2
=
1/2
(w − g ∗ )1/2
(g ∗ + Ḡ)1/2
(w − g ∗ ) = (g ∗ + Ḡ)
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We know that, because all players are identical, Ḡ = (n − 1)g ∗ so
(w − g ∗ ) = (g ∗ + (n − 1)g ∗ )
g ∗ = w/(n + 1), G∗ = nw/(n + 1)
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Work an example of public goods
provision
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Now let’s compare this to the efficient provision. Now, each
individual realizes that Ḡ = (n − 1)g when choosing his
contribution.
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Substitute in for Ḡ in the utility function
U = (w − g)1/2 (g + (n − 1)g)1/2 = (w − g)1/2 (ng)1/2
dU
= −1/2(w − g ∗ )−1/2 (ng ∗ )1/2 + n/2(w − g ∗ )1/2 (ng ∗ )−1/2 = 0
dg
n/2
(w − g ∗ )1/2
(ng ∗ )1/2
=
1/2
(ng ∗ )1/2
(w − g ∗ )1/2
ng ∗ = n(w − g ∗ )
g ∗ = w, G∗ = nw
so efficient provision is n + 1 times as large as private provision.
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Public Goods Games: Isaac et al (1984)
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