Week 9

• in real life, firms may be directly affected by the actions of other agents on the economy (externalities)
• with externalities,, competitive market solutions do not work, and policymakers may intervene to restore an efficient outcome
• in a consumption externality, the utility of one consumer is directly affected by the actions/ consumption of other consumers
• in a consumption externality, the consumer has preferences over their own consumption, and the actions of other consumers
• in a production externality, the production set of one firm is directly affected by the actions (input/ output choices) of another firm
• in a production externality, the optimal production level for a firm must be calculated factoring in the negative cost they have on the other firm
• socially optimal output levels should maximise total profit, so price* quantity, minus costs, minus externalities
• Pigouvian tax is a unit tax imposed on firm producing output
• a Pigouvian tax is used to create an efficient outcome when the unit tax, t, is equal to the marginal externality cost
• for an effective Pigouvian tax, the externality function e(x) must be known
• externalities do not have markets, so creating markets based on externalities can help manage them effectively
• by creating missing markets, like pollution permits, the firm producing the pollution sells the pollution for a negative price to the other firm to compensate for it
• when creating the missing markets for externalities, the price of the externality should be equal to the negative marginal cost of the externality; r = -e' (x)
• compensation mechanisms can enforce the efficient outcome when externalities are involved.
• compensation mechanisms involve a firm producing an externality paying the other firm money to compensate for the externality
• the compensation mechanism involves a 2 stage non-cooperative game theory to ensure compensation is at the right level
• the first stage of the compensation mechanism is announcement; where each firm simultaneously announces the penalty they want the other firm to pay on externalities
• in the first stage of the compensation mechanism, the penalty that the firms actually pay is the squared difference between the announced penalties
• the second stage of the compensation mechanism is the choice stage, where the firms decide how much of the externality to produce
• the solution of the compensation mechanism game is that t1 = t2 = e' (x), and that p= c' (x) + e' (x)
• in the compensation mechanism, if firm 1 thinks firm 2 will suggest a small compensation rate for them, then firm 1 will want 2 to have a high compensation rate, so firm 1 can produce more
• private goods are excludable and rival
• public goods are non-excludable and non-rival
• club goods are non-rival but excludable
• club goods are things like TV broadcasts
• market failure involves inefficient allocation of public goods
• an individual has an initial endowment, w, and decides how much to contribute to the public good, g, and how much to consume, x = w - g
• when there is a discrete public good, where it is either provided or not, it will be provided when the cost to provide it, c, is less than the total amount contributed toward it, g1 + g2
• the maximum willingness to pay for a public good is the reservation price, and is denoted as r
• it is pareto efficient to provide the public good when r1+ r2 > c
• free riding involves one player receiving the whole benefit of the public good without paying for it, leaving the other player paying the whole cost
• because of the free-riding problem, the dominant strategy for each player is to not buy it, which is not socially optimal
• the solution to free riding is to have the government intervene to take the money (tax) from everyone, and then use that tax to pay for the public good
• a continuous public good G = g1 + g2, and the utility of a individual is u1( g1 + g2, w1 - g1)
• efficient provision of a continuous public good is calculated by maximising a weighted sum of utilities
• the sum of the marginal rates of substitution for the public and private good should equal 1
• when the wealth of agent 1 is greater than the wealth of agent 2, agent 2 will free ride, so a solution to prevent this is needed
• the Lindahl allocation involves the government stepping in to price the public good at a level that allocation is efficient
• Voting involves providing the quantity and tax level for the public good that satisfies the median (average) voter