microeconomics 2 john hey. last 2 weeks of teaching today: lecture 33 on public goods. tomorrow:...
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Microeconomics 2
John Hey
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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.
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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.
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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 non-
existent 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 Groves-Clarke 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.)
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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.
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Two examples• 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.
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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).
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The Public Good problemthe table shows the payoffs relative to the starting position (200 students)
Each of 199 othersA B
MeA (£0,£0) (£19.90,£9.90)
B (-£9.90,£0.10) (£10.00,£10.00)
A: Contribute zero B: Contribute £10
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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.
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Connection with public goods
• We have portrayed the above problem as an all-or-nothing 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)...
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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.
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Clark-Groves MechanismThis 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
*
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Clark-Groves MechanismThis 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.
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Clark-Groves MechanismThis 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.
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Clark-Groves MechanismThis 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
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Clark-Groves MechanismStep 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
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Clark-Groves MechanismStep 1 : Individuals report their value for the bridge v i
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
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Clark-Groves MechanismOptimal 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.
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Clark-Groves MechanismOptimal 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.
To ensure I get this positive utility should then report truthfully.
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Clark-Groves MechanismProperties:
(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.
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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.
• 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.
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
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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?!
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Lecture 33
• Goodbye!