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: Q A = 5 – 0.5P Bob’s demand for widgets is given by: Q B = 6 – P The market demand for widgets = Anna’s demand + Bob’s demand = Q A + Q B = = 5 – 0.5P + 6 – P = 11 – 1.5P

The Demand for Private Goods

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 Q K = 2 – 0.5P Lilly’s demand is given by Q L = 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 Q K = 2 – 0.5P 0.5 P K = 2 – Q | x 2 P K = 4 – 2Q Lilly’s demand is given by Q L = 6 – 0.5P 0.5P L = 6 – Q | x 2 P L = 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

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?

fig The Prisoners’ dilemma Does not confessConfesses Does not confess Confesses John’s alternatives George’s alterantives Everyone gets 1 year Everyone gets 3 years George - 3 months John- 10 years George - 10 years John - 3 months

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 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. If one of them pays € 4 they are both better off. Pays Doesn’t Pay Pays(-1, -1)(-1, 3) Doesn’t Pay (3, -1)(0, 0) John’s alternatives George’s alternatives

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 Q dA = 6- P Q dB = 6- 2P Q dC = 10- 2P Q dD = 8- P Q dE = 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.