Chapter 35
Externalities
About the externalities
So far, we have implicitly assumed that forms bear al the costs and benefits associated with the production process
A production externality arises when this assumption does not hold
production externality: when the choice of one firm affect the production possibilities of another firm
Externalities can be negative if the effects on the other firm are bad or positive if the effects on the other firm are good
The steel firm and fishery example
If the firms emerged, there would be no externality!
We can also apply a tax based on pollution
In merged firm, 
The lefthand side is the reduction in cost to the steel form from an extra unit of x - can be interpreted as the marginal benefit of x
The righthand side is the marginal cost of pollution to the merged firm.
At the optimum, the marginal "benefit" of pollution equals its marginal cost
In the merged firm, pollution is only produced up to the point that marginal reduction in steel firm cost is positive
In the independent firm, pollution was produced by the steel firm up to the point at which marginal reduction in the steel form cost was 0
The merged firm produced less pollution than the independent steel firm
The first order condition gives
This is to say: the firm will produce pollution until the marginal "benefit" of pollution equals its cost (the tax rate)
To achieve the same level of x, the government can set
This is a Pigouvian tax - a tax on the externality calibrated to achieve the Pareto efficient output of the externality
Correcting the externality: creating a market
Suppose the government gives property rights over pollution to the fishery. In other words, government mandates that the fishery has the right to zero pollution
Then for the steel firm
for the fihery
One of the first order conditions gives
That is, px is chosen will be the same as the one chosen by the megred firm and will be Pareto efficient
If the property rights are instead given to the steel firm, how much would the fishery be willing to pay for pollution reduction
Suppose the government states that the steel firm has the right to produce x-bar units of pollution
for the steel firm
for the fishery
FOCs the same as when the property rights over pollution were held by the fishery
Coase Theorem
If property rights are well defined, then under certain conditions, a market for the externality will result in the Pareto effcient allocation of the externality regardless of who hold the property rights
Notice that while x* is the same regardless of who holds the property rights, π s and π f are not the same
Higher profits will be realised by the party that holds the property rights
The problem with externalities is the absence of a market for them
If property rights are defined by the government, a market can arise to correct the externality
Positive externalities
If firms are independent, the positive externality is underproduced relative to the efficient allocation
A Pigouvian subsidy can correct the problem
If property rights over the externality are well defined, a market can arise for the externality that can correct the problem