Transcript Presentation 2. Demand and provison of public goods

The Demand for Public Goods
Frederick University
2014
Definition
Public Goods have two attributes :
• Non-excludability -If they have been
provided to one consumer it is
difficult/impossible to stop another from
enjoying it too.
• Non-rivalry - The amount of the good
enjoyed by one consumer has no affect on
the amount enjoyed by another consumer
CONSEQUENCES
Non-excludability:
•
Very difficult for the private sector to provide it and
make a profit.
Non-rivalry:
•
Do not want to exclude people as it is inefficient
(The marginal cost of them getting the good is zero and
they get positive benefit.)
The Free Rider Problem
The fundamental problem of all public
goods is that consumers will try to have
someone else to pay for the provision of
public goods
This is called the free-rider problem.
The Demand for Private Goods
• The market demand for a private good is derived
through the horizontal summation of the
individual demand curves
• Example:
• There are two buyers of widgets (private goods):
Anna and Bob
• Their individual demand curves present the
quantities of widgets that they are willing and
able to buy at each price of widgets
The Demand for Private Goods
•
•
•
•
•
Anna’s demand for widgets is given by:
QA = 5 – 0.5P
Bob’s demand for widgets is given by:
QB = 6 – P
The market demand for widgets = Anna’s
demand + Bob’s demand = QA + QB =
• = 5 – 0.5P + 6 – P = 11 – 1.5P
The Demand for Private Goods
P
Anna's demand
P
Bob's demand
P
9
Market demand
8
8
8
7
7
7
6
6
6
5
5
5
4
4
3
3
2
2
2
1
1
1
0
0
4
3
0
0
1
2
3
4
5
0
1
2
3
4
5
Q
0
1
2
3
4
5
6
7
8
9
Q
Q
The Demand for Public Goods
• Nonrival consumption makes the derivation of
the demand for public goods a different story.
• Everyone can enjoy the benefits of a public good
simultaneously.
• The consumption by one person does not
prevent the consumption by another. Thus, the
value society receives from a public good is the
sum of the value received by all who enjoy the
benefits.
The Demand for Public Goods
• Example:
• There are two buyers of wadgets (public
goods): Katerina and Lilly
• Their individual demand curves present
the marginal benefit they derive from any
quantity of the good in consumption, or in
terms of market concepts: the price they
would be willing and able to pay for any
quantity of the good
The Demand for Public Goods
•
•
•
•
•
Katerina’s demand is given by
QK = 2 – 0.5P
Lilly’s demand is given by
QL = 6 – 0.5P
Market demand will present total benefit derived
from each quantity of wadgets
• Thus, we should present the individual demand
equations in their inverse form in order to reflect
the demand curves for a public good
The Demand for Public Goods
•
•
•
•
•
•
•
•
Katerina’s demand is given by
QK = 2 – 0.5P
0.5 PK = 2 – Q | x 2
PK = 4 – 2Q
Lilly’s demand is given by
QL = 6 – 0.5P
0.5PL = 6 – Q | x 2
PL = 12 – 2Q
The Demand for Public Goods
• Market demand for wadgets = Katerina’s
demand + Lilly’s demand = P = 4 – 2Q +
• 12 – 2Q = 16 – 4Q
• The market demand for the public good
(wadgets) will be the vertical summation of
the individual demand curves
The Demand for Public Goods
Katerina's demand
M B(P)
4
3
2
1
0
0
1
2
3
4
Q
Lilly's demand
P
11
10
9
8
7
6
5
4
3
2
1
0
0
1
2
3
4
5
Q
Market demand
P
12
11
10
9
8
7
6
5
4
3
2
1
0
0
1
2
3
Q
4
5
The Prisoners’ dilemma
Two suspects, John and George, are arrested by the police. The
police have insufficient evidence for a conviction, and, having
separated both prisoners, visit each of them to offer the same
deal: if one testifies for the prosecution against the other and the
other remains silent, the betrayer gets 3 months and the silent
accomplice receives the full 10-year sentence. If both stay silent,
both prisoners are sentenced to only 1 year in jail for a minor
charge. If each betrays the other, each receives a three-year
sentence. Each prisoner must make the choice of whether to
betray the other or to remain silent. However, neither prisoner
knows for sure what choice the other prisoner will make. So this
dilemma poses the question: How should the prisoners act?
The Prisoners’ dilemma
John’s alternatives
Does not confess
Does not confess
George’s
alterantives
Confesses
Everyone gets
1 year
George 3 months
John- 10 years
fig
Confesses
George 10 years
John 3 months
Everyone gets
3 years
The Prisoners’ dilemma
The Prisoners’ dilemma is the duopoly’s
dilemma. Prisoners cannot coordinate their
confessions. Even though they both would get
less if they do not confess, they betray the other
player, because of the greater payoff.
No matter what the other player does, one player
will always gain a greater payoff by playing
defect. Since in any situation playing defect is
more beneficial than cooperating, all rational
players will play defect.
Prisoners’ Dilemma in the public
goods provision
John’s alternatives
George’s alternatives
It costs €4 to provide a
clean street outside
John’s and George’s
houses.
Either John or George can
pay for it.
They both value clean
streets at €3.
Pays
Doesn’t
Pay
Pays
(-1, -1)
(-1, 3)
Doesn’t
Pay
(3, -1)
(0, 0)
If one of them pays € 4
they are both better off.
Private provision of public
goods
Does not work
• The free rider
problem
Works
• Some
individuals
might value the public
good much more than
the others and be
ready to pay for its
provision
• Cooperative
agreement among the
consumers
The problem of socially efficient quantity of
the public good – private, public, or mixed
provision
• Example:
• Due to changes in city planning, the
automobile traffic has been redirected
through a quite neighborhood and has
brought noise and dust to the inhabitants.
They found that one way to slow down the
traffic and reduce significantly the noise
and dust, was to install traffic lights.
The problem of socially efficient
quantity of the public good
There were 5 house owners
(A,B,C,D, and E)in the
neighborhood with the following
individual demand curves for
traffic lights
•
•
•
•
•
QdA = 6- P
QdB = 6- 2P
QdC = 10- 2P
QdD = 8- P
QdE = 9- P
The MC for installing a traffic light
is €3
•
•
•
Find the socially optimal
(allocatively efficient quantity of
traffic lights
Find the quantity of traffic lights
that would be installed if house
owners cooperate according to
their willingness to pay
Find the quantity of traffic lights if
the municipality subsidizes traffic
light installations by paying an
euro per traffic light
Public provision of public goods
•
•
•
•
•
•
Example
“Imported” goods are very expensive in a remote region, due to high
transportation costs.
The government is considering building a bridge which will lower the price of
these goods by 15%.
The price elasticity of demand for these goods is -0.3
The cost of the bridge should be paid by beneficiaries – the citizens of the
region.
Find the optimal income tax rate rise in order to justify the project.