This paper presents a general equilibrium model to analyze the influence that a contaminating sector has on a natural system’s capacity of resilience, the provision of a public utility service and social welfare, in which the level and capacity to respond to resilience are uncertain, so a probability distribution for the growing loss of resilience with pollution going from a prudent state to an imprudent is defined. And examines first the incidence of expected Pigouvian taxes and finds that these taxes are not enough to maintain resilience because of the cumulative effect of pollution and also that society prefers a prudent tax. Furthermore, the transaction of Permits for Environmental Services (PES) between sector that provides the public utility service and the contaminating sector is allowed. This shows a redistribution of resources very much in favor of the contaminating sector, and there are no incentives to invest in these payments unless the affected have additional objectives for the maximization of private benefit.