20
Public goods (and private ones) Public goods (and private ones) From Efficient markets From Efficient markets to Market Failure
Public goods (and private ones)Public goods (and private ones)
From Efficient marketsFrom Efficient markets
to
Market Failure
One moreOne more
• In 2008, ,• US Army had more than 1 million soldiers. 543,000 were active duty.
US N h d b t 460 000 il Ab t• US Navy had about 460,000 sailors. About 335,000 were active duty.
• USMC had about 198,000 marines.USMC had about 198,000 marines.• US Air Force had about 400,000 personnel. About 330,000 were active duty.
• US Coast Guard had about 40,000 active duty personnel. – WHAT ARE ALL THESE PEOPLE DOINGWHAT ARE ALL THESE PEOPLE DOING
OutlineOutline
• Public and Private goodsPublic and Private goods
• MarketsP i t d ilib i– Private goods equilibrium
– Public goods equilibrium
• Solution– Voluntary participation
– Privatize.
– Tax
Public and Private goodsPublic and Private goods
Public GoodsPrivate Goods Public Goods
Non Rival
If I li t t th di
Private Goods
Rival in consumptionIf you eat the apple I can not eat it
If I listen to the radio waves so can you
Non ExcludableExcludable
If you produce the radio wave you can’t stop anyone from listening
If you have the apple you can prevent me from having it.
Pure private goods havePure private goods have additional properties (divisibility, transferability)
Excludable Non‐Excludable
Rival Consumption goods Fishing grounds
Non Rival Scrambled radio Clean Air
Excludable Non‐Excludable
Ri l Wild S l 2010 Wild S l i 1980
Scarcity creates Rivalry
Rival Wild Salmon 2010 Wild Salmon in 1980
Non Rival Wild Salmon in 1600
Excludable Non‐Excludable
Technology creates excludability
Rival Range in the US West1800s
Range in the US West1860s
Non Rival Digital Radio 2010 Radio in 1930
Demand for private goodsDemand for private goods
• At quantity demanded – Marginal willingness to pay=price
• Total demand at a given price is the sum of individual demandsdemands. – this comes out of the rivalry. If want to satisfy the demand of two people I have to produce enough for each of them.If price is $1 and x want 4 apples and Y wants 3 I have to– If price is $1 and x want 4 apples and Y wants 3 I have to have 7 apples to sell.
• Logic differentf ll $ f d d– If X is willing to pay $1 for one jazz radio station and Y is willing to pay $2 for one jazz radio station I can satisfy each of them with 1 radio station
Private demand600
500D(1)
400
D(2)
D(3)
300
D(4)
D(10)
100
200 D(20)
0
0 50 100 150 200 250 300 350 400 450 500
Demand for Public Good5000
Demand for Public Good4000
4500D(1)
D(2)
3000
3500
D(3)
2000
2500D(4)
D(10)
1000
1500D(20)
0
500
0 10 20 30 40 50 600 10 20 30 40 50 60
Private demand sum across Public demand sum up
600 D(1)
D(2)
p
600
D(1)
400
500D(3)
D(4)
D(10) 400
500D(2)
D(3)
D(4)
D(10)
(20)
300
D(20)
300
D(20)
200 200
0
100
0 50 100 150 200
0
100
0 50 100 150 2000 50 100 150 200 0 50 100 150 200
Problems with these goodsProblems with these goods
• The non rival means that there is usually aThe non rival means that there is usually a high ‘social’ willingness to pay (sum of each person’s the marginal willingness to pay)person s the marginal willingness to pay)
• But the non excludable get in the way.
Wh b i di id l i l S h• Why because individuals are rational. So they want to get stuff at least cost
• Why pay for something if someone else will
Provision of public goods 1. Voluntary
• Population of n individuals, all identical
M U(G ) h G i bli d i• Max U(G,c) where G is public goods c is consumption sbjt to g+c≤Y where G=G‐i+g
( )– U(G, c) =Gα +c
• Voluntary contributions optimize!
• Under private provision, G is a constant
Private provision is inefficient
• G is a constant and individual contributions are falling with n.
• What should we do?
• Total utility is nGα so we want to max nGα –Gy
– Not transparent but G is increasing in n. (and so is g)
α=0.1
0.2
0.25
2000
2500
0.151500
al con
tribution
public goo
d G
g
0.05
0.1
500
1000
Individu
Total g
00
1 10 100 1000 10000
Population
SolutionsSolutions
• Taxation!Taxation!– That solves the voluntary part but not the efficient level pbslevel pbs
• Preference elicitationSurvey– Survey
– Voting
M h i d i– Mechanism design
Ask people who they are
• Remember
• Now assume αi is distributed between
Cl l th• Clearly then
• Marginal willingness to pay
• So if you expect everyone else to contribute you will say the lowest possible feasible
Voting• There is going to be a vote on the size of the public good.public good.
• Given our assumptions, individuals will vote for what ever option is closest to theirfor what ever option is closest to their preferred G
Fi d th t th t h th di f• Find the voter that has the median preference
(half the population wants a smaller G and half a bigger one).
VotingVoting
• Recall that the efficient solution would be toRecall that the efficient solution would be to sum individual demand – With a distribution of preferences, that would be p ,integrating over the preferences.
• If the mean demand and the median demand are the same then voting will produce the efficient outcome (but only then).
• What would like to do is to elicit individual preferences and then integrate
Mechanism designMechanism design• Suppose we implement the following scheme
T ll th t (1) th i t ib ti ill– Tell everyone that (1) their contribution g will depend on the average of everyone else reports (2) the choice of G will depend on the average ( ) p greport.
– (1) implies what you say does not affect what you ( )pay => everyone has a (weak) incentive to be
honest.(2) implies that if everyone is honest then we get– (2) implies that if everyone is honest, then we get the efficient outcome.
• More on this in EC 106, 118, 131, 132.
