Externalities & Public Goods

Question 1

Why are externalities a market failure?

Answer 1

They cause the FWT not to hold so the market will not come to a Pareto-efficient eqm

Question 2

What is a consumption and a production externality?

Answer 2

C: If one agent’s utility function depends directly on another’s consumption
P: If one firm’s cost or production function depends on another’s production

Question 3

When there are two producers and an externality (pollution), how would you expect the cost functions to behave?

Answer 3

The polluting firm’s cost should be strictly decreasing in pollution for low values of pollution and constant for higher values, the affected firm’s cost should be strictly increasing in pollution

Question 4

When there are two price taking producers (goods x and y) and an externality (pollution p), what problems would the producers solve?

Answer 4

X chooses x and p to maximise p_xx - c_X(x, p) and Y chooses y to maximise p_yy - c_Y(y, p)

Question 5

When there are two price taking producers (goods x and y) and an externality (pollution p), what would the solution be?

Answer 5

Assuming interior solutions, the FOCs show that both producers will produce where price = MC and the price of polluting for the polluter is zero which is a Pareto-inefficient outcome

Question 6

When there are two price taking producers (goods x and y) and an externality (pollution p), what are the three ways to solve the externality?

Answer 6

Merge the firms, maximise the sum of profits from the two firms, and use Pigouvian taxation
These all require the sum of marginal cost of pollution (social MC of pollution) to be zero which balances the cost to Y and the benefit to X of pollution which will reduce the amount of pollution and lead to a Pareto-efficient outcome

Question 7

How would Pigouvian taxation solve the problem of a polluting producer?

Answer 7

The government imposes a tax t per unit of production on the polluter which is equal to the MC of pollution for the affected firm at the socially optimal level of pollution so they will produce at the Pareto-efficient level

Question 8

What is an argument against Pigouvian taxation?

Answer 8

To set an appropriate tax, the government needs to know the socially optimal level pollution, in which case it might as well just restrict pollution to that level

Question 9

What is the missing market approach to externalities?

Answer 9

FWT requires all relevant goods to have a market and a market price so an externality (good or bad) should have a market

Question 10

What are the two forms of using property rights to address externalities?

Answer 10

Giving the polluter the right to pollute so the affected firm pays to reduce pollution and giving the affected firm the right to clean air so the polluter pays to pollute
Both would lead to the same FOCs as the other ways to solve externalities

Question 11

What is the Tragedy of the Commons?

Answer 11

When a common resource is over-used as ill-defined property right lead everyone to follow their own private interests which results in a worse outcome for everyone

Question 12

What is a model that illustrates the tragedy of the commons?

Answer 12

On some land, c cows (assumed to be many so it can be treated as continuous) generate f(c) revenue, f is increasing and strictly concave (diminishing marginal returns), a is MC of one extra cow
If there is a single landowner they will maximise f(c) - ac which will leave f’(c) = a (MR = MC where f(c) has same slope as ac)
If the land is common then each farmer would decide whether or not to add a cow at cost a and with revenue approximately f(c)/c (since c is large relative to the single additional cow) so he will add the cow if f(c) > ac so cows will be added until f(c) = ac which is a Pareto-inefficient amount of cows above the social optimum, if each farmer were restricted to the optimum then the proceeds could be shared equally to make everyone strictly better off because each farmer only considers private impacts
Pigouvian taxation could also be used

Question 13

What is the Coase Theorem?

Answer 13

As long as there is efficient bargaining (no transaction costs), agents will bargain to a Pareto-efficient outcome (but there usually are transaction costs both in the free market and in government intervention)
If preferences are quasilinear in wealth, the efficient amount of the good involved in the externality is independent of the distribution of property rights

Question 14

How can different approaches to externalities, for e.g. the case of a noisy agent and a noise-averse (quiet) agent, be represented on an Edgeworth box?

Answer 14

One set of axes for the noisy agent (bottom and left) and another for the quiet agent with the noise axes both having more noise on the same side of the box (top)
If the noisy agent has the right to make noise, the endowment will be on the more noise side of the box (top) and the quiet agent will pay to reduce noise, if the quiet agent has the right to quiet so A will pay to make noise, in either case a Pareto-efficient outcome is reached and the amount of noise depends on initial property rights
If the utility functions are quasilinear in wealth, the contract curve is a straight line so final allocation of noise is independent of property rights (same MRS between money and noise with no dependence on wealth)

Question 15

What is a public good?

Answer 15

A good which is non-rivalrous and non-excludable
More loosely, a good which is consumed in the same quantity by everyone
An impure public good has the characteristics of a public good to some degree

Question 16

What can be said generally about the provision of public goods?

Answer 16

Decentralised market provision is unlikely to be Pareto-efficient (usually under-supplied), collective provision may be inefficient because of the free-rider problem

Question 17

When is it Pareto-efficient to supply a discrete public good?

Answer 17

If the same of the consumers’ reservation values (the maximum amount the consumer is willing to pay for the good) is at least as high as the cost of supplying itWha

Question 18

What is the condition for Pareto-efficient supply of a continuous public good?

Answer 18

Samuelson rule: Σ|MRS| = |MRT|
if <, beneficial to increase G
MRS for each agent is -MU_G/MU_m and MRT is -c’(G) (negative marginal cost of the public good)
Decentralised (private) provision would be below the optimum (even if agents guess what the other will pay)

Question 19

What is the Groves-Clark scheme or Clarke tax for Pareto-efficient centralised provision of a discrete public good?

Answer 19

Each agent announces their net reservation value (reservation value - equally divided cost of good)
Buy the good iff sum of net reservation values is greater than zero
If an agent is pivotal, that agent also pays a tax equal to -(externality they impose) which is equal to -(sum of the other agents’ net reservation values)