Microeconomics 2
John Hey
Last 2 weeks of teaching
• Today: lecture 33 on Public Goods.
• Tomorrow: lecture 34 on Asymmetric Information.
• Next Monday: last 11 questions on first specimen
examination paper.
• Next Tuesday: Question and Answer session.
Please send me your queries and questions in
advance.
• In the two meetings next term I will go through the
second specimen paper.
• I will tell you the material strengthening the exam.
Lecture 33: Public Goods
• A public good is one that everyone can consume
simultaneously; one person’s consumption of it does
not reduce the consumption of others.
• For example: a public park, a television channel,
clean air, national defense.
• There are not many examples of pure public goods,
but we shall here assume one of them.
• We can have “all or nothing” public goods.
• And also variable-level public goods.
•
I don’t like the analysis of Public Goods.
Why I do not like the economic study of public goods
• Economic analysis seems totally negative:
• It shows that private provision of public goods is either nonexistent or inadequate, because people free-ride on others and
(have incentives to) hide their true preferences for the good.
• Methods (which could be used by the state) to incentivise people
to reveal their true preferences (such as voting or the GrovesClarke mechanism) have deep flaws.
• We almost certainly end up with public/State provision. (What the
state ‘should do’ takes us into Social Choice and the problems of
aggregating preferences.)
• Is this surprising?
• Note there are very few examples of the private provision of
public goods. (?? Clubs, closed societies of various forms.)
A pretend experiment
• Every one of you can contribute £10 or
nothing.
• I will count up the contributions and I will
add an equal amount to the total
contributed: this is the public fund.
• This public fund will be distributed equally
to all of you.
• Let us play this – but pretend it is for real.
• When I ask you, you should put up your
hands if you want to contribute £10.
Two examples
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First example:
Suppose there are 200 students here and 30 of them contribute £10
and the other 170 nothing.
The public fund is thus £600 = £300 from the students and £300 from
me.
Every student gets £3.
But note that the 30 students who contributed £10 end up £7 worse off
than when they started, while the 170 who contributed nothing end up
£3 better off than when they started.
Second example:
Suppose there are 200 students here and 70 of them contribute £10
and the other 130 nothing.
The public fund is thus £1400 = £700 from the students and £700 from
me.
Every student gets £7.
But note that the 70 students who contributed £10 end up £3 worse off
than when they started, while the 130 who contributed nothing end up
£7 better off than when they started.
Two more (extreme) examples
• Third example:
• Suppose there are 200 students here and all of them
contribute £10.
• The public fund is thus £4000 = £2000 from the students
and £2000 from me.
• Every student gets £20.
• So they are all £10 better off than at the beginning.
• Fourth example:
• Suppose there are 200 students here and all of them
contribute nothing.
• The public fund is thus zero.
• Every student gets nothing – but no-one has paid anything.
• Let us do it (but not for real).
The Public Good problem
the table shows the payoffs relative to the starting position (200 students)
Me
A: Contribute zero
A
B
Each of 199 others
A
B
(£19.90,£9.90)
(£0,£0)
(-£9.90,£0.10)
(£10.00,£10.00)
B: Contribute £10
Overview of the problem
(suppose 100 people)
• Everyone is invited to contribute to the public
good. Total contributions are doubled and
divided equally amongst the members of society.
• Every £1 more that I contribute I get back 2p but
I have spent £1 so I am a 98p out of pocket.
• But if everyone contributes £1 more everyone is
£1 better off (taking into account the
contribution).
• Similarly for every £1 less that I contribute I lose
2p and so I save 98p.
• If everyone contributes £1 less then everyone is
£1 worse off.
Connection with public goods
• We have portrayed the above problem as an all-ornothing problem for the individual but it is variable in
total.
• As we have seen, if contributions are voluntary, then
everyone would prefer everyone else to pay and it might
not get provided at all.
• Depends upon the provision rules.
• Let us look more at a variable-level public good.
• This is where individuals can contribute varying
amounts. But let us take a more general problem – with
two goods - instead of just having money.
• So all (both) citizens are deciding between two goods, a
private one and a public one.
• Let us go to Maple (skip the first section)...
The next 9 slides
In black and white, are shamelessly downloaded from
Martin Cripps site at UCL. My thanks to him.
Back to all-or-nothing.
Reveals how clever economists (think they) are.
Clark-Groves Mechanism
This is a process that will get individuals to
truthfully to reveal their preferences for the
public good.
Step 1 : Individuals report their value for the
bridge (the public good) vi
Note : they don’t have to report the truth vi
≠ vi*
Clark-Groves Mechanism
This is a process that will get individuals to
truthfully to reveal their preferences for the
public good.
Step 1 : Individuals report their value for the
bridge vi
Step 2 : Add up the reported values.
Clark-Groves Mechanism
This is a process that will get individuals to
truthfully to reveal their preferences for the
public good.
Step 1 : Individuals report their value for the
bridge vi
Step 2 : Add up the reported values.
Step 3 : If Sum of reported values – Cost of
Bridge > 0 then build the bridge.
Clark-Groves Mechanism
This is a process that will get individuals to
truthfully to reveal their preferences for the
public good.
Step 1 : Individuals report their value for the
bridge vi
Step 2 : Add up the reported values.
Step 3 : If Sum of reported values – Cost of
Bridge > 0 Build Bridge
If Sum of reported values – Cost of
Bridge <0 Do not Build
Clark-Groves Mechanism
Step 1 : Individuals report their value for the bridge
vi
Step 2 : Add up the reported values.
Step 3 : If Sum of reported values – Cost of Bridge
>0 Build Bridge
If Sum of reported values – Cost of Bridge
<0 Don’t Build
Step 4 : If the individual’s value was decisive, i.e.
Sum of Others’ Reports < Cost of Bridge < Sum of
all Reports
Clark-Groves Mechanism
Step 1 : Individuals report their value for the bridge vi
Step 2 : Add up the reported values.
Step 3 : If Sum of reported values – Cost of Bridge >0
Build Bridge
If Sum of reported values – Cost of Bridge <0
Don’t Build
Step 4 : If the individual’s value was decisive, i.e.
Sum of Others’ Reports < Cost of Bridge < Sum of all
Reported values
Charge the individual = Cost of Bridge – Sum of
others’ reported values
Clark-Groves Mechanism
Optimal to tell the truth.
Let U be the sum of the other’s reports and let v
be my value.
If U>Cost:
I don’t care what I say so reporting truthfully
is fine.
Clark-Groves Mechanism
Optimal to tell the truth.
If U+v > Cost > U:
Then any report u such that U+u>Cost (or
u>Cost-U) will get me utility
v – (Cost –U) >0 .
(independent of report!)
But any report u < Cost – U will get me utility
=0.
Clark-Groves Mechanism
Properties:
(1)Optimal to tell the truth
(2)Voter only pays when decisive.
(3)Payments < benefits received
(4)As population grows less of a problem with
excess revenue.
Groves-Clark mechanism – to decide whether an all-or-nothing public should be provided
• Three flatmates – should they get a TV (costing £300)?
• The share of the costs has already been decided and the
only question is whether it should be bought.
Person
Cost share True Reservation value
– stated as such
Net
value
Clarke tax
A
£100
£50
-£50
£0
B
£100
£50
-£50
£0
C
£100
£250
£150
£100
• Note that the sum of reservation values > cost.
• The pivotal person (here C) pays the tax – which would
compensate the others if it were paid. But it cannot be –
as it would destroy the incentive for everyone to reveal
their true reservation values.
Summary
• A public good is a good that can be consumed
simultaneously by more than one individual.
• Whether with an all-or-nothing public good or a
variable public good there are difficulties in
deciding who will/should pay for the good.
• There are clear individual incentives for
individuals to free-ride.
• The Nash Equilibrium is clearly Pareto inferior to
the Social optimum.
• Perhaps we should rely on state/public
provision?
• But what is the State for?!
Lecture 33
• Goodbye!