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 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.)

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• 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 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

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-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)...

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 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

*

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.

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.

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

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

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

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.

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.

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.

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

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!