I.	Para alcanzar un determinado nivel agregado de emisiones minimizando los costos totales de un programa basado en estándares, un regulador que no puede observar los costos de abatimiento de las empresas, ¿debe diseñar el programa de forma de permitir cierto nivel de transgresiones o debe diseñarlo de tal forma que haya cumplimiento perfecto?

I.1. Full information on abatement costs

We start by trying to answer the question in the case the regulator can observe the abatement costs of the firms.
In this case, the regulator has two possible penalty schemes: increasing or constant marginal penalties. We start by assuming the marginal penalty is increasing.

Individual choices under increasing marginal penalty

Penalty: 

Given all the relevant parameters, a firm i solves the following problem:

The Lagrangean of this problem is:

And the Kuhn – Tucker conditions:

From these, we know that the firm complies with the standard   
If this is not the case, the firm violates the standard, in which case  , and from KT condition 2),  λ = 0 and 
If we assume that  (we give a functional form to ), then, the above conditions is: 

From this expression we can get the firm´s reaction function:

Which gives the optimum violation () as a function of the abatement costs parameters, the enforcement parameters, and the level of the standard: 

The regulator jointly determines  and  to induce the desired level of emissions (and violations) to minimize expected costs of achieving E. It can be seen from this equation that, contrary to the case of emissions permits (Stranlund, 2007), in this case there is a trade off for the regulator between the level of the emission standard it sets and the corresponding level of the probability of inspection it has to commit to in order to induce a certain level of violation for plant i.

The regulatory choice of violations under increasing marginal penalty

Closed solution

Substituting for  and ,

And substituting for, 

Lagrange:

Condiciones de Kuhn Tucker

Assuming ,

From (1)

From (2)

General Characterization

Where μ is the dollar cost of an inspection and β is the per dollar cost of collecting penalties.