As

The crucial term is the last one. This shows that the merged firm will take into account the effect of pollution on the marginal costs of both the steel firm and the fishery. When the steel division decides how much pollution to produce, it considers the effect of this action on the profits of the fish division; that is, it takes the social cost of its production plan into account.

What does this imply about the amount of pollution produced? When the steel firm acted independently, the amount of pollution was determined by the condition

Ax v

That is, the steel mill produced pollution until the marginal cost was zero:

In the merged firm, the amount of pollution is determined by the condition

L^JL LJxJL

That is, the merged firm produces pollution until the sum of the marginal cost to the steel mill and the marginal cost to the fishery is zero. This condition can also be written as

In this latter expression MCp{f,x) is positive, since more pollution increases the cost of producing a given amount of fish. Hence the merged firm will want to produce where — MCs(s,x) is positive; that is, it will want to produce less pollution than the independent steel firm. When the true social cost of the externality involved in the steel production is taken into account, the optimal production of pollution will be reduced.

When the steel firm considers minimizing its private costs of producing steel, it produces where the marginal cost of extra pollution equals zero;

but the Pareto efficient level of pollution requires minimizing the social costs of the pollution. At the Pareto efficient level of pollution, the sum of the two firm's marginal costs of pollution must be equal to zero.

This argument is illustrated in Figure 34.3. In this diagram —MCs measures the marginal cost to the steel firm from producing more pollution. The curve labeled MCp measures the marginal cost to the fishery of more pollution. The profit-maximizing steel firm produces pollution up to the point where its marginal cost from generating more pollution equals zero.

Social cost and private cost. The steel firm produces pollution up to the point where the marginal cost of extra pollution equals zero. But the Pareto efficient production of pollution is at the point where price equals marginal social cost, which includes the cost of pollution borne by the fishery.

But at the Pareto efficient level of pollution, the steel firm pollutes up to the point where the effect of a marginal increase in pollution is equal to the marginal social cost, which counts the impact of pollution on the costs of both firms. At the efficient level of pollution production, the amount that the steel firm is willing to pay for an extra unit of pollution should equal the social costs generated by that extra pollution—which include the costs it imposes on the fishery.

This is perfectly consistent with the efficiency arguments given in earlier

PRICE

QUANTITY OF POLLUTION

MCf chapters. There we assumed that there were no externalities, so that private costs and social costs coincided. In this case the free market will determine a Pareto efficient amount of output of each good. But if the private costs and the social costs diverge, the market alone may not be sufficient to achieve Pareto efficiency.

EXAMPLE: Pollution Vouchers

Everyone wants a clean environment ... as long as someone else pays for it. Even if we reach a consensus on how much we should reduce pollution, there is still the problem of determining the most cost-effective way to achieve the targeted reduction.

Take the case of nitrogen oxide emissions. One emitter may find it relatively inexpensive to reduce its emissions of this pollutant, whereas another may find it very expensive. Should they both be required to reduce their emission of pollutants by the same physical amount, by the same proportional amount, or by some other rule?

Let's look at a simple economic model. Suppose that there are only two firms. Firm I's emission quota is x\ and firm 2's is x2. The cost of achieving an emission quota x\ is c\(x{) and similarly for firm 2. The total amount of emission is fixed at some target level X. If we want to minimize the total costs of achieving the emissions target, subject to the aggregate constraint, we need to solve the following problem:

A by now standard economic argument shows that the marginal cost of emission control must be equalized across the firms. If one firm had a higher marginal cost of emission control than the other, then we could lower total costs by reducing its quota and increasing the quota of the other firm.

How can we achieve this outcome? If the government regulators had information on the cost of emissions for all firms, they could calculate the appropriate pattern of production and impose it on all the relevant parties. But the cost of gathering all this information, and keeping it up-to-date, is staggering. It is much easier to characterize the optimal solution than to actually implement it!

Many economists have argued that the best way to implement the efficient solution to the emission control problem is to use a market. It appears that such a market based emissions control system will soon be put into effect in Southern California. Here is how the California plan works.2

2 See Richard Stevenson, "Trying a Market Approach to Smog," New York Times,

Each of the 2700 largest polluters in Southern California is assigned a quota for their emissions of nitrogen oxide. This quota is initially set to be 8 percent less than their previous year's emission. If the firm exactly meets its emissions quota it faces no fines or penalties. However, if it reduces its emissions by more than its emissions quota, it can sell the extra "right to emit'1 on the open market.

Suppose that a firm's quota is 95 tons of nitrogen oxide emissions per year. If it manages to produce only 90 tons in a given year, then it can sell the right to emit 5 tons of nitrogen oxide to some other firm. Each firm can compare the market price of an emission credit to the cost of reducing its emissions and decide whether it was more cost-effective to reduce emissions further or purchase emission credits from other firms.

Firms that find it easy to reduce emissions will sell credits to firms that find it costly to reduce emissions. In equilibrium, the market price of the right to emit one ton of pollution should just equal the marginal cost of reducing emissions by one ton. But this is exactly the condition characterizing the optimal pattern of emissions! The market for emission permits produces the efficient pattern of emissions automatically.

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Project Management Made Easy

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