Market | Market Failure 1
Externalities
A consumption externality is a situation where a consumer cares directly about another agent’s consumption or
production of a particular good,An externality can be positive or negative:
1,Negative,Loud mobile phone use in public places.
2,Positive,Pipe smoking in enclosed public places.
A production externality is a situation where a flrm’s production possibility set is directly in uenced by the
consumption or production decisions of another agent,Again,some examples:
1,Negative,Toxic waste dumping reduces flshing yields.
2,Positive,University lecturer who gives course notes to other tutors.
Externalities arise when there are missing markets,That is,there is no price for a particular good.
Market | Market Failure 2
An Example
Consider two consumers,One is a smoker and one is a fanatical anti-smoker,Clean air is a good for the latter
consumer,but smoke (the absence of clean air) is a good for the former,Money is a good for both.
......
.
......
.
......
.
......
.
......
.
......
.
......
.
......
.
......
.
......
.
......
.
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
....
.........................................................................................................................................................................................................
...........................................................................................................................................................................................................
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
....
...........
...........
...........
...........
...........
...........
...........
...........
...........
...........
......
...........
...........
...........
...........
...........
...........
...........
...........
...........
...........
.......
.....
.....
......
......
......
......
.......
.......
.....
......
......
.......
..
................
.........................
....
.............................
................
..
.......
......
......
.....
......
.......
.......
......
......
......
......
.....
.
...............
.............
..
......
.....
.....
...............
.............
..
......
.....
.....
A
Bs
m
!
!0
x
x0
Suppose both consumers start with an equal amount of money m,In the absence of a market for clean air the
endowment is either at ! | if smoking is illegal,or !0 | if smoking is legal,Why?
Neither of these points are Pareto e–cient,The flrst welfare theorem fails due to the missing market.
If there were a market for clean air,the consumers could trade money for smoke (or money for clean air) until they
arrived at a point like x or x0,The prices are given by the slope of the budget constraints.
These points are Pareto e–cient | the flrst welfare theorem is recovered by providing appropriate property rights.
Market | Market Failure 3
The Coase Theorem
Notice that the amount of the externality produced at the e–cient point depended on how property rights were
assigned,If the smoker started with the property rights,more smoke is generated at the e–cient allocation.
With quasi-linear preferences,it does not matter which consumer starts with property rights | the same amount of
the externality is produced at the e–cient allocation,Consider the last example:
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
....
...........................................................................................................................................................................................................
...........................................................................................................................................................................................................
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
....
...........................................................................................................................................................................................................
....................
..............
.........
.......
.....
......
.....
......
.......
.......
......
......
......
.
......
......
......
......
.......
.......
.....
......
.....
.......
........
..............
..................
....
....................
..............
.........
.....
.....
.....
.......
.......
......
......
......
......
......
......
......
......
.......
.......
.....
.....
.......
..........
...............
................
A
Bs
m
x
0x
s?
Recall that quasi-linear preferences have indifierence curves that are parallel translates of each other.
s? smoke is produced whatever property rights are assigned,Only m varies between e–cient allocations.
This is the Coase theorem | the e–cient externality level is independent of the initial distribution.
Market | Market Failure 4
Production Externalities
Suppose there are two flrms,one producing electricity,e,and one producing flsh f,The electricity flrm dumps toxic
waste w in the sea,reducing flsh yields,Costs are ce(e;w)= c(e)?w(1?w) and cf(f;w)= c(f)+w2 respectively.
Hence proflts are given respectively by:
…e = pee?c(e)+w(1?w) and …f = pff?c(f)?w2
Since the electricity flrm alone chooses w it will keep producing waste (which reduces cost) until no more proflts can
be made from doing so,The beneflt increases until w =0:5 and decreases thereafter.
At w? =0:5 the marginal beneflt of waste is equal to its marginal cost (zero),Both flrms set MR = MC to derive
optimal e? and f? | pe = c0(e?) and pf = c0(f?).
Is this e–cient? No,The electricity flrm is producing too much waste,damaging the flshing flrm.
Market | Market Failure 5
Internalising Externalities
To see this ine–ciency,consider a merged flrm producing both electricity and flsh.
Proflts are given by … = pee+pff?c(e)?c(f)+w(1?w)?w2.
How much waste would such a flrm produce? Proflts are maximised by choosing waste,w,so that the marginal
beneflt to electricity production equals the marginal cost to flsh production.
This occurs when MB = MC or 1?2w =2w,That is,when w0 =0:25,Notice this is less than w?.
.......,......,......,......,....
......
.
......
.
......
.
......
.
....
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
...
............................................................................................................................................
......
......
......
......
......
......
......
.....
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
.....
......
......
......
......
......
......
......
......0
MC
w
w0 = 14 w? = 12
MBe = MCf
MBe MCf
One solution to externalities is to internalise them in this way,This will result in a socially optimal (e–cient)
amount of the externality,Here it is impossible to make one flrm better ofi without making the other worse ofi.
Market | Market Failure 6
Tragedy of the Commons
Consider an economy by the ocean,Each agent is a flsherman,They can buy a boat at cost c and go flshing.
If there are b boats at sea the total value of flsh caught is f(b),More boats means more flsh,but at a decreasing
rate | overcrowding reduces the number of flsh each flsherman catches.
Each flsherman takes home flsh to a value of f(b)=b,This is average beneflt,and it is decreasing,A new flsherman
would go to sea if the value of flsh they would get exceeds the cost of a boat,f(b)=b > c.
Hence,an equilibrium is reached when f(b?)=b? = c,No flsherman would join or leave the market.
The government would maximise social welfare which is the total value minus the total cost.
max
b
f(b)?cb =) f0(bs)= c
Is there over-flshing or under-flshing relative to the social optimum? Recall that f0(b) is marginal beneflt.
(E–ciency occurs,as usual,when marginal beneflt equates to marginal cost).
Market | Market Failure 7
Pigouvian Taxes
Recall average revenue (demand) and marginal revenue,MR lies below AR and is downward sloping when AR is
decreasing,This is analogous to average and marginal beneflts in the current model,Cost is a constant c.
.
.
.
.
.
.
.
......
.
......
.
......
.
......
.
....
......
.
......
.
......
.
......
.
.....
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
.....
..........................................................................................................................................
.....................................................................................................................................
......
......
......
......
......
......
......
......
......
......
......
......
....
......
......
......
......
......
......
......
......
.
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
....
.......
.......
.......
.......
.......
.......
.......
.......
..0
f(b)
b
c
f(b)=bf0(b)
b?bs
The social optimum,bs,is smaller than the equilibrium value,b?,There is over-flshing.
How can this be prevented? There are many possibilities:
1,Property Rights,Sell the sea to one agent,they will act just like the government.
2,Quota,Only allow bs boats on the sea,and enforce by law.
3,Pigouvian Tax,A tax on boats t to increase the cost to c+t,Now flsherman will buy the socially optimal
number of boats,A Pigouvian tax is a tax to correct an externality,t is given by the dotted line.
Market | Market Failure 8
Public Goods
A public good is a good that is provided in the same amount to all consumers if it is provided at all.
A pure public good is non-excludable and non-rival,Once provided it is impossible to prevent agents from
consuming it,Moreover,one agents consumption of the good does not reduce the amount available to other agents.
1,Excludable Rival,Regular private goods,like apples and bananas.
2,Non-Excludable Rival,Free-for-all goods,like the roads.
3,Excludable Non-Rival,Goods like satellite TV and mobile phone networks.
4,Non-Excludable Non-Rival,Pure public goods like BBC World Service radio.
When should a particular public good be provided? When the beneflt exceeds the cost,If the beneflt to each
consumer is b1 and b2 and the cost is c then a good should be provided if b1 +b2? c.
If both b1 < c and b2 < c then neither consumer would buy the good individually,Even when b1? c and b2? c
provision is not guaranteed,due to the problem of free riding.
Market | Market Failure 9
Free Riding
Consider the following,Each player has bi < c,but bi > c=2,Hence the good should be provided,Each player
chooses whether to pay (contribute toward the public good) or not,Free riding results.
Pay Don’t
Pay b2?c=2
b1?c=2
b2
b1?c
Don’t b2?c
b1
0
0
.
This is the Prisoners’ Dilemma again,The only equilibrium is for both players to not pay.
When both agents have bi > c,they could still attempt to free ride by waiting for the other to purchase the good.
Then there is a coordination problem,Both player might claim that they do not value the public good.
Can the true valuations of the agents be revealed?
Market | Market Failure 10
E–cient Provision
How much of a public good,g,should be provided?
Suppose there are two goods,a private good and a public good,Two agents have income m1 and m2 and spend it
on private goods worth x1 and x2 and the public good which costs c(g).
To achieve a Pareto e–cient allocation,flx agent 2’s utility at u2 and maximise u1:
maxx
1;x2;g
u1(x1;g) such that u2(x2;g)= u2 and x1 +x2 +c(g)= m1 +m2
The solution lies where jMRS1j+jMRS2j= MC(g),The sum of the marginal rates of substitution between the
private and public goods is equal to the marginal cost of the public good.
If this were not the case both agents could be made better ofi by a change in the amount of provision.
If preferences were quasi-linear,ui(xi;g)= xi +vi(g),then the equation simplifles,Replacing MRS with marginal
utilities for the public good,dv1=dg +dv2=dg = dc=dg.
Market | Market Failure 11
Voting and Demand Revelation
All this relies upon agents revealing their true valuations for the public good,Would they?
Recall agents would like to free ride,They would like the good to be provided but they would rather not pay for it.
Private provision of the public good is therefore unlikely to take place,Voting for a particular level of the public
good might be a way to reveal the preferences of individuals,But remember:
Agent 1 Agent 2 Agent 3
a b c
b c a
c a b
If a,b and c represent difierent levels of the public good,then there is majority who prefer a to b,a majority who
prefer b to c and a majority who prefer c to a,Social preferences are not transitive.
More generally,even when transitivity is imposed on a voting system,the level of public good provision voted for is
the median preferred level | which is not necessarily the e–cient level.
Valuation mis-representation to manipulate the vote remains an issue,How can true valuations be revealed?
Market | Market Failure 12
A Revelation Mechanism
There is a solution,Revelation mechanisms,Suppose there are n agents,each with a true valuation for the public
good of ui,Each will pay a commonly known share si of the cost c if the good is provided.
Their net valuations are vi = ui?sic,Consider the following mechanism:
1,Each agent is asked their net valuation vi,They report a valuation bi which may or may not be their true
valuation,(They can misrepresent their preferences if they wish).
2,The public good is provided ifPni=1 bi?0,If the reported valuations add to more than zero the good is
provided | this would be e–cient if everyone told the truth.
3,Each agent receives a side-payment equal to the sum of the other agents’ reported valuations (Pj6=i bj).
Each agent will tell the truth,The incentive to do so is provided by the side-payments at the end,Given that each
agent tells the truth the public good will be provided e–ciently,This mechanism is expensive,however.
There are cheaper alternatives,The Clarke tax is similar but only gives side-payments to pivotal agents.
As an exercise,show why no agent has an incentive to report bi 6= vi in the above mechanism.
Externalities
A consumption externality is a situation where a consumer cares directly about another agent’s consumption or
production of a particular good,An externality can be positive or negative:
1,Negative,Loud mobile phone use in public places.
2,Positive,Pipe smoking in enclosed public places.
A production externality is a situation where a flrm’s production possibility set is directly in uenced by the
consumption or production decisions of another agent,Again,some examples:
1,Negative,Toxic waste dumping reduces flshing yields.
2,Positive,University lecturer who gives course notes to other tutors.
Externalities arise when there are missing markets,That is,there is no price for a particular good.
Market | Market Failure 2
An Example
Consider two consumers,One is a smoker and one is a fanatical anti-smoker,Clean air is a good for the latter
consumer,but smoke (the absence of clean air) is a good for the former,Money is a good for both.
......
.
......
.
......
.
......
.
......
.
......
.
......
.
......
.
......
.
......
.
......
.
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
....
.........................................................................................................................................................................................................
...........................................................................................................................................................................................................
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
....
...........
...........
...........
...........
...........
...........
...........
...........
...........
...........
......
...........
...........
...........
...........
...........
...........
...........
...........
...........
...........
.......
.....
.....
......
......
......
......
.......
.......
.....
......
......
.......
..
................
.........................
....
.............................
................
..
.......
......
......
.....
......
.......
.......
......
......
......
......
.....
.
...............
.............
..
......
.....
.....
...............
.............
..
......
.....
.....
A
Bs
m
!
!0
x
x0
Suppose both consumers start with an equal amount of money m,In the absence of a market for clean air the
endowment is either at ! | if smoking is illegal,or !0 | if smoking is legal,Why?
Neither of these points are Pareto e–cient,The flrst welfare theorem fails due to the missing market.
If there were a market for clean air,the consumers could trade money for smoke (or money for clean air) until they
arrived at a point like x or x0,The prices are given by the slope of the budget constraints.
These points are Pareto e–cient | the flrst welfare theorem is recovered by providing appropriate property rights.
Market | Market Failure 3
The Coase Theorem
Notice that the amount of the externality produced at the e–cient point depended on how property rights were
assigned,If the smoker started with the property rights,more smoke is generated at the e–cient allocation.
With quasi-linear preferences,it does not matter which consumer starts with property rights | the same amount of
the externality is produced at the e–cient allocation,Consider the last example:
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
....
...........................................................................................................................................................................................................
...........................................................................................................................................................................................................
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
....
...........................................................................................................................................................................................................
....................
..............
.........
.......
.....
......
.....
......
.......
.......
......
......
......
.
......
......
......
......
.......
.......
.....
......
.....
.......
........
..............
..................
....
....................
..............
.........
.....
.....
.....
.......
.......
......
......
......
......
......
......
......
......
.......
.......
.....
.....
.......
..........
...............
................
A
Bs
m
x
0x
s?
Recall that quasi-linear preferences have indifierence curves that are parallel translates of each other.
s? smoke is produced whatever property rights are assigned,Only m varies between e–cient allocations.
This is the Coase theorem | the e–cient externality level is independent of the initial distribution.
Market | Market Failure 4
Production Externalities
Suppose there are two flrms,one producing electricity,e,and one producing flsh f,The electricity flrm dumps toxic
waste w in the sea,reducing flsh yields,Costs are ce(e;w)= c(e)?w(1?w) and cf(f;w)= c(f)+w2 respectively.
Hence proflts are given respectively by:
…e = pee?c(e)+w(1?w) and …f = pff?c(f)?w2
Since the electricity flrm alone chooses w it will keep producing waste (which reduces cost) until no more proflts can
be made from doing so,The beneflt increases until w =0:5 and decreases thereafter.
At w? =0:5 the marginal beneflt of waste is equal to its marginal cost (zero),Both flrms set MR = MC to derive
optimal e? and f? | pe = c0(e?) and pf = c0(f?).
Is this e–cient? No,The electricity flrm is producing too much waste,damaging the flshing flrm.
Market | Market Failure 5
Internalising Externalities
To see this ine–ciency,consider a merged flrm producing both electricity and flsh.
Proflts are given by … = pee+pff?c(e)?c(f)+w(1?w)?w2.
How much waste would such a flrm produce? Proflts are maximised by choosing waste,w,so that the marginal
beneflt to electricity production equals the marginal cost to flsh production.
This occurs when MB = MC or 1?2w =2w,That is,when w0 =0:25,Notice this is less than w?.
.......,......,......,......,....
......
.
......
.
......
.
......
.
....
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
...
............................................................................................................................................
......
......
......
......
......
......
......
.....
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
.....
......
......
......
......
......
......
......
......0
MC
w
w0 = 14 w? = 12
MBe = MCf
MBe MCf
One solution to externalities is to internalise them in this way,This will result in a socially optimal (e–cient)
amount of the externality,Here it is impossible to make one flrm better ofi without making the other worse ofi.
Market | Market Failure 6
Tragedy of the Commons
Consider an economy by the ocean,Each agent is a flsherman,They can buy a boat at cost c and go flshing.
If there are b boats at sea the total value of flsh caught is f(b),More boats means more flsh,but at a decreasing
rate | overcrowding reduces the number of flsh each flsherman catches.
Each flsherman takes home flsh to a value of f(b)=b,This is average beneflt,and it is decreasing,A new flsherman
would go to sea if the value of flsh they would get exceeds the cost of a boat,f(b)=b > c.
Hence,an equilibrium is reached when f(b?)=b? = c,No flsherman would join or leave the market.
The government would maximise social welfare which is the total value minus the total cost.
max
b
f(b)?cb =) f0(bs)= c
Is there over-flshing or under-flshing relative to the social optimum? Recall that f0(b) is marginal beneflt.
(E–ciency occurs,as usual,when marginal beneflt equates to marginal cost).
Market | Market Failure 7
Pigouvian Taxes
Recall average revenue (demand) and marginal revenue,MR lies below AR and is downward sloping when AR is
decreasing,This is analogous to average and marginal beneflts in the current model,Cost is a constant c.
.
.
.
.
.
.
.
......
.
......
.
......
.
......
.
....
......
.
......
.
......
.
......
.
.....
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
.....
..........................................................................................................................................
.....................................................................................................................................
......
......
......
......
......
......
......
......
......
......
......
......
....
......
......
......
......
......
......
......
......
.
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
....
.......
.......
.......
.......
.......
.......
.......
.......
..0
f(b)
b
c
f(b)=bf0(b)
b?bs
The social optimum,bs,is smaller than the equilibrium value,b?,There is over-flshing.
How can this be prevented? There are many possibilities:
1,Property Rights,Sell the sea to one agent,they will act just like the government.
2,Quota,Only allow bs boats on the sea,and enforce by law.
3,Pigouvian Tax,A tax on boats t to increase the cost to c+t,Now flsherman will buy the socially optimal
number of boats,A Pigouvian tax is a tax to correct an externality,t is given by the dotted line.
Market | Market Failure 8
Public Goods
A public good is a good that is provided in the same amount to all consumers if it is provided at all.
A pure public good is non-excludable and non-rival,Once provided it is impossible to prevent agents from
consuming it,Moreover,one agents consumption of the good does not reduce the amount available to other agents.
1,Excludable Rival,Regular private goods,like apples and bananas.
2,Non-Excludable Rival,Free-for-all goods,like the roads.
3,Excludable Non-Rival,Goods like satellite TV and mobile phone networks.
4,Non-Excludable Non-Rival,Pure public goods like BBC World Service radio.
When should a particular public good be provided? When the beneflt exceeds the cost,If the beneflt to each
consumer is b1 and b2 and the cost is c then a good should be provided if b1 +b2? c.
If both b1 < c and b2 < c then neither consumer would buy the good individually,Even when b1? c and b2? c
provision is not guaranteed,due to the problem of free riding.
Market | Market Failure 9
Free Riding
Consider the following,Each player has bi < c,but bi > c=2,Hence the good should be provided,Each player
chooses whether to pay (contribute toward the public good) or not,Free riding results.
Pay Don’t
Pay b2?c=2
b1?c=2
b2
b1?c
Don’t b2?c
b1
0
0
.
This is the Prisoners’ Dilemma again,The only equilibrium is for both players to not pay.
When both agents have bi > c,they could still attempt to free ride by waiting for the other to purchase the good.
Then there is a coordination problem,Both player might claim that they do not value the public good.
Can the true valuations of the agents be revealed?
Market | Market Failure 10
E–cient Provision
How much of a public good,g,should be provided?
Suppose there are two goods,a private good and a public good,Two agents have income m1 and m2 and spend it
on private goods worth x1 and x2 and the public good which costs c(g).
To achieve a Pareto e–cient allocation,flx agent 2’s utility at u2 and maximise u1:
maxx
1;x2;g
u1(x1;g) such that u2(x2;g)= u2 and x1 +x2 +c(g)= m1 +m2
The solution lies where jMRS1j+jMRS2j= MC(g),The sum of the marginal rates of substitution between the
private and public goods is equal to the marginal cost of the public good.
If this were not the case both agents could be made better ofi by a change in the amount of provision.
If preferences were quasi-linear,ui(xi;g)= xi +vi(g),then the equation simplifles,Replacing MRS with marginal
utilities for the public good,dv1=dg +dv2=dg = dc=dg.
Market | Market Failure 11
Voting and Demand Revelation
All this relies upon agents revealing their true valuations for the public good,Would they?
Recall agents would like to free ride,They would like the good to be provided but they would rather not pay for it.
Private provision of the public good is therefore unlikely to take place,Voting for a particular level of the public
good might be a way to reveal the preferences of individuals,But remember:
Agent 1 Agent 2 Agent 3
a b c
b c a
c a b
If a,b and c represent difierent levels of the public good,then there is majority who prefer a to b,a majority who
prefer b to c and a majority who prefer c to a,Social preferences are not transitive.
More generally,even when transitivity is imposed on a voting system,the level of public good provision voted for is
the median preferred level | which is not necessarily the e–cient level.
Valuation mis-representation to manipulate the vote remains an issue,How can true valuations be revealed?
Market | Market Failure 12
A Revelation Mechanism
There is a solution,Revelation mechanisms,Suppose there are n agents,each with a true valuation for the public
good of ui,Each will pay a commonly known share si of the cost c if the good is provided.
Their net valuations are vi = ui?sic,Consider the following mechanism:
1,Each agent is asked their net valuation vi,They report a valuation bi which may or may not be their true
valuation,(They can misrepresent their preferences if they wish).
2,The public good is provided ifPni=1 bi?0,If the reported valuations add to more than zero the good is
provided | this would be e–cient if everyone told the truth.
3,Each agent receives a side-payment equal to the sum of the other agents’ reported valuations (Pj6=i bj).
Each agent will tell the truth,The incentive to do so is provided by the side-payments at the end,Given that each
agent tells the truth the public good will be provided e–ciently,This mechanism is expensive,however.
There are cheaper alternatives,The Clarke tax is similar but only gives side-payments to pivotal agents.
As an exercise,show why no agent has an incentive to report bi 6= vi in the above mechanism.
