Mergers

One way to solve the problem posed by an externality is to "internalize" it by combining the involved parties. The market provides a strong incentive for firms involved to merge (horizontally or vertically) for reduction of negative external effects.

The resulting firm will maximize his profit (the two firms cumulated profit) so that the inefficiency will be removed. We obtain in this case Pareto optimum for both firms.

So, in the second space the external effects will disappear, but it still exists on the other spaces.

Social convention and education

Unlike firms, the peoples can not merge in order to internalize externalities. However, a number of social conventions - different from area to area - can be viewed as attempts to force people to take into accounts the externalities that they generate. For example, the golden rule "does unto others as you would have others do unto you," if it is applied, should conduce to internalize many externs’ negative effects, like hard noise or bad jokes. In effect these percepts correct for the absence of missing markets.

Bargaining

Another way to internalize the extern effects is to put together involved parties and to bargain the negative external effects and to obtain an efficient outcome. It is well known the Coase Theorem who demand that an efficient solution will be achieved independently of who is assigned the ownership rights, as long as someone is assigned those rights. So, as long as the involved parties will bargains, it is possible to obtain the social optimum, even if one part will obtain more like others.

However, by those three methods we can internalize only external effects that concern market space. For the other spaces we need the intervention of public authority to correct damages and to obtain Pareto optimum.

2.4 Public authority intervention for externalities internalization

In cases where individuals acting on their own cannot attain an efficient solution, there are several ways which government can intervene and correct the market inefficiency.

Regulation

In most countries (and especially in western countries) the main approach for dealing with environmental problems is regulation. Under regulation, each polluter is told to reduce pollution by certain amount or else face legal sanctions.

By regulation, we can also establish the maximum admitted levels for pollution factors.

Corrective Taxes

Another way to internalize externalities is to impose a tax system for pollution. These taxes are called "Pigouvian taxes", suggested by the British economist A.C. Pigou. A "Pigouvian tax" is a tax levied upon each unit of a polluter’s output in an amount just equal to the marginal damage it influents at the efficient level of output (see Figure 4).

Evidently, that is a coercive measure for imposing social optimum, but in some conditions this is the only way to reestablish the distorted equilibrium.

The main problem here is to establish the correct level of pigouvian tax, because is very difficult to evaluate social marginal cost.

As we shown above, the inefficiencies associated with externalities can be linked to the absence of pollutant market. Creating a pollutant market is possible only by public authority intervention. Under this scheme, the government announces that it will sell permits to spew y^* level of pollutants, that correspond to social optimum level of production Q^*. The government announces that it will auction off y^* pollution rights. Firms or association of consumers bid for the right to own these permissions to pollute, and the permissions go to the agents with the highest bid.

If the winner agent cannot use the entire amount of quantity of pollutant bid, then it is possible to sell a part of those rights.

The government for environment recovers or for rewarding the reduction emission effort can use the resulting moneys from these auctions.

Using one of another internalization methods depend on pollution or pollutant type, the environmental damages and on area importance.

In the first part of this paper we exposed the theoretical ways that we can internalize the extern effects. Afterwards, we show a general microeconomic model for externalities’ internalization.

In theirs activities the economic agents (and we consider the producers) maximize especially short-term profit. We expose two variants of model, respectively a short-term model (a static model) and a long-term model (a dynamic model).

3.1 The Static Model

In our short run model each firm will maximize the profit under some conditions.

The static model is:

The (3.1) relation indicates the profit level P ^t at moment t. These include the revenue (p Q ) minus total costs (CT) and plus the reword function for its reduction of pollution effort.

The total cost function includes the variable cost (CV) and fixed cost (CF). Supplementary, we include the expenses for pollution taxes (T y^t ), who depend on pollution level and the tax for each type of pollutant (T_i).

Remark.

The T function is not necessary constant depending on pollution level. We can use a tax system with a reduced level of taxes before a certain amount, and then an increasing tax system (linear or not linear) just on the maximum admitted level of pollution.

If the emission level is greater than the maximum admitted level (y > y^L), then the firm will pay a fixed penalty (A₁). This penalty will be included in cost function.

The last term in (3.1) indicates the public power reword for the firm effort to reduce the emission level. If ( y^t-1 - y^t ) is positive, then the government will rewords firm by reduction of profit tax with x percents. So, it exists an incentive for the firm to reduce her emission level.

The penalty ant the taxes are external for the firm because there are established by public power. The firm can choose the technology, the quantity and quality of inputs, and as result of maximization profit problem is production level. On short run on suppose technology unchanged, so the firm can choose only inputs.

The solution of model will indicate the type ("dirty" or "clean") and quantity of used inputs, the production level, the pollution level for each type of pollutant and the profit level on short run.

We must analyze separately the taxes' level. If this level is too large, then it is possible that the firm becomes not competitive on market, with all social and economical problems possible. For that this tax level must be reasonable for not generating a too great social cost.

The (3.2) equation represents the technology restriction (or production function). The production level cannot exceed installed production capacity or the market demand.

The (3.3) restriction indicates the emission level for each type of pollutant. This level depends on production level and inputs quality.

The (3.4) restrictions indicate the maximum input (capital, labor, inputs, etc.) available level.

The last group of restriction (3.5) is the nonnegative restrictions for our variables.

Remarks

1. In this model we not restricted the maximum level of pollution because the Romanian firms generally not respect these levels.

2. The (3.2) restrictions (the technology restriction) can be a subproblem of general problem and can be solved separately.

3. The model can be applied for every kind of firm, for every domain.

The model solution will indicate the optimum level of production depending on input's quantity and quality, taxes and penalties. Considering production we can establish the emission level.

For solving this model, first, we construct the Lagrangean function.

The first and the second order conditions assure the existence of solutions and his determination. The signification of Kuhn-Tucker and Lagrange multipliers attached to restrictions is very important:

- l ₁ represents the marginal profit of production;

- l ₂ represent the marginal profit of pollution reduction;

- l ₃ represent the marginal profit of inputs.

If these multipliers are zeros, then the profit level cannot be improved by any small change. If one of them is positive, then we can increase the profit level by increasing the associated variable. For example, if l ₂ > 0 then rice of pollution level can improve the profit level, despite the pollution tax and penalties.

If the Lagrange multipliers are negative, then every attached variable growth indicates a profit decrease.

3.2 The Dynamic Model

Last paragraph contains a static model (even if we have the time like indices, the variables are independently on time). The firm cannot modify the technology on short time, so its behavior is not depending on this variable. However, on long run the firm can modify his technology, and that will modify his behavior.

In our model for this case the firm maximizes his long run profit.

The model is:

The main differences between these two models are:

- for the first case, the firm will maximize his short term profit, and for the second case, the firm maximize his long term profit;

- for the first case the producer cannot improve his technology (there are no investments), and for the dynamic model the producer can modify his technology, improve his productivity and reduce the pollutant emission.

Evidently, for the initial periods the investment diminishes the profit level, but on long run the profit level can increase because of pollution cost reduction, profit reward and an increased productivity.

The solution of this model will indicate, the investment level, which is done by at moment that investment marginal cost on long run is equal on investment marginal cost.

The next problem we must solve is to determine the optimum level of taxes and penalties to protect environment and to encourage the economic growth.

Q^t represents the production level at t moment. It is a column vector Q^t = (Q₁^t,...,Q_n^t)^tr , with n the outputs number;

P^t is an price vector at t moment, P^t = (P₁^t,...,P_n^t);

y^t is the pollutant levels vector, y^t = (y₁^t ,...,y_N^t)^tr, with N the number of pollutants. This level depends on production level and input quality;

g(Q^t) is column vector of the pollution emission function;

A(y) is penalty vector for each pollutant that exceeds the maximum admitted level;

f(k^t) represent the production function, with k^t the used inputs;

T represents the tax function for each type of pollutant;

CT represents the total cost, which include:

CV - variable cost;

CF - the fixed cost;

T y^t - the cost level done by taxes and penalties;

x - is the percent of profit reward for reduction of emission levels;

h_i(k^t) - the inputs restrictions;

QC - demand function for outputs;

QI - maximum production done by installed capacity;

P ^t (Q^t ,T, A) - the profit level depending on production level, tax level and penalties;

y^L - is the maximum admitted level for each pollutant;

d - is discount parameter for the producer;

I^t - is the investment level;

- l ₁ represents the marginal profit of production;

- l ₂ represent the marginal profit of pollution reduction;

- l ₃ represent the marginal profit of inputs.