Mihai Roman, Ph. D., Monica Roman

Academy of Economic Studies - Bucharest




This paper presents an important and actual problem of contemporary word, the externality problem. First, we introduce the basic of economic theory of externalities, a short classification and the theoretical ways for internalization. Second, we present a microeconomic model for externalities' internalization. The producers take optimal decisions based on this model – in static and dynamic variants – conditional on environmental public policies.

Key words: externalities, internalize, pollution, environmental policies, social costs, private costs, model, multipliers.



The world economic growth in the last century leads to an increasing production, a large diversity of services and products, and increasing welfare, especially in developed countries. Also, this leads to an irrational consumption of natural and human resources and damages for environment.

Based on this conclusions, starting on ’70-th years, entering world was concerned on environment protection and environment recovering after human activities damage. This damage is not necessary voluntary realized by people, but it is a result of his production or consumption activities.

For most of there activities, peoples demand satisfaction maximization on short run. For consumption this means more and better goods, for production is more profit. The short run maximization leads to negative effects on long run because of secondary effects of production and consumption.

We call externalities the effects (positive or negative) generated by an entity (person or firm) that directly affects the welfare of another in a way that is not transmitted by the market prices.

If the positive effects are good for economy and human life, the negative effects must be controlled and minimized.

Because of limited resources it need an increasing investment in environment protection, but also general public policies that join economic and environment problems.


2.1 Social cost versus private cost of human activities

In economic theory is well known the difference between "private cost" and "social cost" of activities. From any economy the social marginal cost is different from private marginal cost. So, it is no possible to realize Pareto efficiency without public or private intervention. However, the Fundamental Theorem of Welfare Economics suggests that to obtain efficiency, price should equal social marginal cost, which includes all the costs of production, including the external damages to another firms and people.

The contradiction between private and social cost is traditionally given by deficiency of free market mechanisms, and has not correspondence in cost terms.

Theoretically, creating propriety rights (private or public) can solve this problem.

For example, in pollution case, "the propriety right" can be a public one, and "pollution rent" should be used by public power for environment recovering and protection.

If this propriety right not exists, the difference between social marginal cost and private marginal cost is "external cost".

Creating this propriety right will internalize the external cost, respectively includes external cost into private cost, and obtain social cost (Pareto optimum).

In Figure 1. is represented the difference between social marginal cost and private marginal cost.

Externalities’ internalization conduct to social marginal cost equal with private marginal cost and with market price, respectively Pareto optimum.

In Figure 1 the horizontal axes means quantity of good, and the vertical means good price. Demand curve for a normal product (with a negative slope) intersect supply curve (traditionally represent by marginal cost curves). PMC is private marginal cost and SMC is social marginal cost.


Figure 1. Social marginal cost and private marginal cost

For private sector (without externalities) the equilibrium point is Ep, described by production Qp and price p1. Social equilibrium point (who includes external effects) is Es, described by quantity Qs and the price p2. We observe that quantity Qs is less than Qp and the price p2 is greater p1.

Evidently, for a free market situation, we can not expect to obtain the social optimum (Pareto optimum).

Figure 2 shows the same problem in cost-benefit terms. Moving from Ep to Es conducts to some costs and benefits.

The costs is represented by area (B + C), who represent the reduction of gross consumption benefits.

The benefits are represented by area (A + B + C), who represent the cost reduction for resource consumption (C area), the external cost reduction (B area), and increasing welfare for consumers done by reduction of external effects (A area).

Putting all together, the benefits of moving from Ep to Es are area (A + B + C), and the costs are area (B + C). The difference between them represent the net gain of society, the A area.



Figure 2 Cost - benefit analysis of externalities

For producers side costs are greater than benefits, but finally we have a net social gain because of external negative effect reduction.

Consequently, even at first looks the externalities internalization is generating a greater price and a smaller quantity like in free market situation, the total benefits obtained by internalization are greater like total costs. So, it is necessary the movement from private equilibrium to social equilibrium.

2.2 A classification of external effects

To complete understand what represent an "external effect" it is necessary to explain "what is extern in rapport with". In Figure 3 we are represented the necessary spaces for a good definition of external effects.

The first space, the interior one, represents the economic agent, producers or consumers. The second space is market space, which contains economic agents and relationships between them. The third space includes supplementary public goods, and the fourth one contains all economic activities and interpersonal relationships. The last space, the greater one, is the biosphere with all these components, including people and the relationships with environment.

The movement from agent space to market space (a) is made by intermediary of Marshallian effects, respectively economies and diseconomies (positive or negative). From agent space to market and public good space (b) it appears external cost financing by entire society (or apart of them, for collective goods).

Figure 3. A classification of external effects

From agent space to economic activities and interpersonal relationship space (c) we have the interpersonal external effects. (For example, the neighbor’s noise, the traffic noise or the lost time in traffic is interpersonal external effects.)

Finally, the relationships between economic agents and biosphere (d) are external effects on environment.

2.3 Private internalization of externalities


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.


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.


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).

Figure 4 Social optimum and Pigouvian Tax


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.

Creating a market

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:

or equivalent,

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 yt ), who depend on pollution level and the tax for each type of pollutant (Ti).


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 > yL), 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 ( yt-1 - yt ) 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.


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.

Annex The variable of model list

Qt represents the production level at t moment. It is a column vector Qt = (Q1t,...,Qnt)tr , with n the outputs number;

Pt is an price vector at t moment, Pt = (P1t,...,Pnt);

yt is the pollutant levels vector, yt = (y1t ,...,yNt)tr, with N the number of pollutants. This level depends on production level and input quality;

g(Qt) is column vector of the pollution emission function;

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

f(kt) represent the production function, with kt 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 yt - the cost level done by taxes and penalties;

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

hi(kt) - the inputs restrictions;

QC - demand function for outputs;

QI - maximum production done by installed capacity;

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

yL - is the maximum admitted level for each pollutant;

d - is discount parameter for the producer;

It - 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.



[1] Anderton,A., Economics, Causeway Press, Oxford, 1991

[2] Becker, S.G., Economic Theory, Alfred a Knapf Inc., New York,


[3] Carlton, D.W., Perloff, J.M., Modern Industrial Organization, Scott,

Foresman and Co., London, 1990

[4] Goldin, M.L., Rosen, H.S., The Economics of Sustainable

Development, Cambridge University Press, 1995

[5] Marin, D., T iga nescu, E., Oprescu, G., Microeconomie, Ed. Omnia

Uni SAST, Bras ov, 1995

[6] Roman, M., Roman, M., Integrarea mediului natural î n mecanismele

piet ei, working paper, Bucures ti, 1997