Public goods (and private ones)
Public goods (and private ones)
From Efficient markets From
Efficient markets
to Market Failure
One more
One more
• In 2008, ,
•
US Army had more than 1 million soldiers. 543,000 were active duty. •
US N
US Navy had about 460,000 sailors. About h d b t 460 000 il
Ab t
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 DOING
WHAT ARE ALL THESE PEOPLE DOING
Outline
• Public and Private goods
Public and Private goods
• Markets
– Private goods equilibrium
Pi t
d
ilib i
– Public goods equilibrium
• Solution
– Voluntary participation
– Privatize.
– Tax
Public and Private goods
Public and Private goods
Private Goods
Private
Goods
Rival in consumption
If you eat the apple I can not eat it
Excludable
If you have the apple you can prevent me from having it.
Pure private goods have Pure
private goods have
additional properties (divisibility, transferability)
Public Goods
Public
Goods
Non Rival
If I listen to the radio waves so If
I li t t th
di
can you
Non Excludable
If you produce the radio wave you can’t stop anyone from listening
Rival
Non Rival
Excludable
Non‐Excludable
Consumption goods
Fishing grounds
Scrambled radio
Clean Air
Scarcity creates Rivalry
Ri l
Rival
Excludable
Non‐Excludable
Wild S l
Wild Salmon
2010
Wild S l
Wild Salmon
i 1980
in 1980
Non Rival
Wild Salmon in 1600
Technology creates excludability
Rival
Non Rival
Excludable
Non‐Excludable
Range in the US West
1800s
Range in the US West
1860s
Digital Radio 2010
Radio in 1930
Demand for private goods
Demand for private goods
• At quantity demanded – Marginal willingness to pay=price
• Total demand at a given price is the sum of individual demands. demands
– 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 different
– If X is willing to pay $1 for one jazz radio station and Y is f
ll
$ f
d
d
willing to pay $2 for one jazz radio station I can satisfy each of them with 1 radio station
Private demand
600
D(1)
500
D(2)
400
D(3)
D(4)
300
D(10)
D(20)
200
100
0
0
50
100
150
200
250
300
350
400
450
500
5000
Demand for Public Good
Demand for Public Good
4500
D(1)
4000
D(2)
3500
D(3)
3000
D(4)
2500
2000
D(10)
1500
D(20)
1000
500
0
0
10
20
30
40
50
60
Private demand sum across
Public demand sum up
p
D(1)
600
600
D(2)
D(1)
D(3)
500
D(2)
500
D(3)
D(4)
D(4)
D(10)
400
D(10)
400
D(20)
(20)
D(20)
300
300
200
200
100
100
0
0
0
50
100
150
200
0
50
100
150
200
Problems with these goods
Problems with these goods
• The
The non rival means that there is usually a non rival means that there is usually a
high ‘social’ willingness to pay (sum of each person’ss the marginal willingness to pay)
person
the marginal willingness to pay)
• But the non excludable get in the way. • Why because individuals are rational. So they Wh b
i di id l
i
l S h
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
• Max U(G,c) where G is public goods c is M U(G ) h
Gi
bli
d i
consumption sbjt to g+c≤Y where G=G‐i+g
– U(G, c) =G
(
) α +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?
α so we want to max nGα –G
• Total utility is nG
y
– Not transparent but G is increasing in n. (and so is g)
2500
0.25
2000
0.2
G
1500
0.15
g
1000
0.1
500
0.05
0
0
1
10
100
Population
1000
10000
Individual contribution
Total public good
α=0.1
Solutions
• Taxation!
– That solves the voluntary part but not the efficient level pbs
level pbs
• Preference elicitation
– Survey
– Voting
– Mechanism design
M h i d i
Ask people who they are
• Remember
• Now assume αi is distributed between
• Clearly then
Cl l th
• 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 their
for what ever option is closest to their preferred G
• Find the voter that has the median preference
Fi d th
t th t h th
di
f
(half the population wants a smaller G and half a bigger one). Voting
• Recall
Recall that the efficient solution would be to 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 design
Mechanism design
• Suppose we implement the following scheme
– Tell everyone that (1) their contribution g will T ll
th t (1) th i
t ib ti
ill
depend on the average of everyone else reports ( )
(2) the choice of G will depend on the average p
g
report.
– (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.