ANSWERS TO TUTORIAL 7: WLEFARE, PUBLIC GOODS AND EXTERNALITIES
Alberto Behar
Question 1)
a) Definitions of public good vary:
 Katz & Rosen: Good that is non-rival in consumption (note why this is tantamount to saying
marginal cost is zero). If not strictly non-rival, then an impure public good. They only see
the excludability issue as relevenat to whether these public goods can be provided privately
or not.
 Varian: Good that must be provided in the same amount to all the affected consumers
(marginal cost of providing to an extra consumer is 0)
 I prefer the interpretation that pure public goods are both non-excludable and non-rival (and
impure ones are either non-excludable or non-rival). Eg watching cable TV is definitely
non-rival but is excludable and therefore is not a pure public good
Regardless of your ultimate choice of definition (some definitions are more useful sometimes than
others), you should consider whether roads are non-rival and non-excludable in general and in this
example. The rivalry can be argued either way and the non-excludability problem is solved by the
new technology. Eg: one could conclude roads are rival in consumption (traffic jams) and that they
are now excludable and therefore no longer public goods. In contrast, Kats & Rosen might argue
roads are still non-rival and that the excludability only means it could be profitable for a private
firm to build roads like these.
b) To reduce congestion (note link to a), air pollution, noise pollution, encourage exercise etc Note
most of these arguments fall under externalities arguments ie this is a Pigouvian tax. Note the
revenue argument, if seen as being generated to allow for maintenance or funding of a new road,
could be seen as addressing a public goods problem.
c) The diagram here is supposed to compare marginal social costs and benefits of the quantity of
cars using the road, explaining how these differ from private costs/benefits, comparing and
contrasting private from socially optimal levels. You would discuss the potential role of the
Pigouvian tax and the appropriate rate, showing how, if too high, social benefits outweigh costs.
Standard welfare analysis would fit here. You could also consider it from a tax revenue angle,
where the tax is brining in too little overall revenue.
2) See diagram overleaf. Assume Sven has endowment S of the right to smoke while the total
amount of money (X) is shared between the two in some way (xS and xA). The labels on the corners
represent Sven and Arsene’s consumption in green and blue respectively. Note that, for money, X =
xS+xA while, for smoke, sS=sA. As we move down the graph, Sven is worse off because he smokes
less and Arsene is better off because he (passive) smokes less, or alternatively consumes more clean
air, not because Sven smoking less means Arsene is smoking more.
a) We are on the top line because Sven has the right to smoke and therefore “owns” the air.
After trade, ie Arsene paying Sven to smoke less, we reach the pareto efficient point on the
contract curve corresponding to the initial endowment. Both are better off.
b) By preventing trade, the government prevents them from trading to in a mutually beneficial
way to a pareto efficient point, so it is not pareto efficient/optimal1 as both could be made
1
Note that it is technically possible to have indifference curves that do make points at the edges or even corners of the
box pareto efficient, but this gets a little complicated so don’t worry.
better off. (Note the move from the initial to new endowment is not pareto imprioving
either, as Sven is worse off). The ban definitely prevents social welfare being maximised as
it is not a pareto efficient point, but we can’t say anything about whether social welfare is
being increased or decreased: one person gains and another loses from the move from the
initial endowment (or the free-exchange equilibrium) to the new endowment/equilibrium
and we have no way of comparing their relative utilities. Compare this answer to the case
where the right to clean air is given to the non-smoking Arsene but Sven can buy the right to
smoke.
Arsene
S,0; S,X
Endowment when Sven has right (could be anywhere on this line)
S,X; 0,0
Optimal point (could be anywhere on contract
curve)
Smoke
e
Endowment when smoking banned (could be anywhere on this line)
Money
0,0; 0,X
Sven
0,X; 0,0
3) I must apologise but this question is actually far harder than I thought and not particularly
helpful. Please don’t worry about it in its current form and instead consider what would be the case
if the benefit was certain (ie not 50%). Also assume that both of them going to feed the dog does
not improve the chances of his stopping as he can only be fed once. Do it before looking at the
answers!
a) If either one of them goes, the cost of making him stop barking is £3 while the benefit is the
sum of Laurel and Hardy’s expected benefit, which is 2*(2+e)=(4+2e), where e is some
unknown greater than or equal to zero. Assume it is 0. It is efficient for the dog to stop
barking if this benefit is at least 3. Even with e=0, the benefit is 4, so it is efficient. (It is
never optimal for both to go, although this can be better than none going if e>1).
b) The theorem says that, regardless of who/what has the right to bark (in this case the dog, as
opposed to the right to silence owned by the neighbours), the efficient level of barking will
take place (in this case the levels are either zero or some positive amount). If the benefit is
less than 3, then the dog keeps barking. If the benefit is more than 3, the theorem predicts
the barking will stop.
c) However, the Coase theorem ignores communication/co-ordination costs.
Hardy
Stay
Feed dog
Laurel
Stay
0,0
2+e,-1+e
Feed dog
-1+e,2+e
-1+e,-1+e
There are 2 cases:
 For e<1, note that is strictly dominant for each player to stay, with the result that the dog
barks even though this is not an efficient outcome (free-riding)
 For e>1, it is strictly dominant for each player to feed the dog, which is better than the
case where just 1 person does it (the exact opposite to free riding)
In neither case do we have the socially optimal outcome.
d) It can be either. It is a public good in the sense that consumption of quiet is non-rival (Laurel
enjoying quiet doesn’t mean hardy can’t) and that the marginal cost of one person enjoying
quiet is zero once the other one is consuming it. It is an externality in the sense that the
dog’s consumption of barking affects the others negatively (has an extra social cost of 4+e)
and that the analysis is similar to the smoking example, where the pollution is noise instead
of smoke. Note that the lines between public goods and externalities are generally fuzzy
according to some definitions.
4) Brief outline:
 intro
 Statement of first welfare theorem including assumptions, in other words that
competitive equilibrium is pareto efficient
 Relevant ways assumption can break down, particularly missing markets ie
externalities or public goods and imperfect competition
 Case for regulating monopoly (brief)
 How the externalities/public goods optimal conditions compare to the case of private
goods (eg sum of MRS=MRT in general equilibrium setting or comparison of
private and social costs/benefits in partial equilibrium setting)
 Ways government intervention can fix the problem, eg tax, regulation etc
 Discussion of other ways problem can be addressed
 (note one could argue that, even if the assumptions don’t break down, there may be
an efficiency case for intervention)
 Possibly that nature of intervention can have distributional consequences eg who has
right (to smoke vs to clean air) and who gets taxed
 Note there can be roles for government in making sure the assumptions hold if they
break down or more traditional intervention without making the assumptions hold
 Conclusion that addresses the question directly