This paper examines the positions of Coase and Pigou in regard to the problem of external effects (externalities). Assessing their two most important works, it appears that Coase has a more relevant preference for an evaluation of total efficiency, while Pigou, with some exceptions, is convinced that it is almost always socially desirable to reach marginal efficiency through taxes or liability. It is interesting that the economist of Chicago, who has elaborated on the renowned theorem, thinks that is not desirable to reach efficiency at the margin every time, and that it is often preferable to evaluate the total, which indicates the solution that is more welfare enhancing. A certain confusion in the work of Coase is noticeable. On one hand he criticizes Pigou for statements regarding the social desirability of relocating some industries away from the towns, and on the other hand, he suggests solutions that give an absolute right for an activity that is incompatible with the activity of another subject. In this way he eliminates the possibility of having a solution that is in accordance with Coase’s idea, which stresses that any external effect is reciprocal: The adjective “reciprocal” means that a damage to Y is the consequence of limiting the activity of Y in order to allow the activity of X, and the opposite is also true: A benefit for Y causes a damage to X. Beyond this criticism, Coase’s arguments against Pigou’s tools are represented by the famous theorem, according to which a public intervention is not necessary in order to obtain efficiency when transaction costs are low. However, the theorem is not an idea that can be used to say that Pigou’s methods are useless when transaction costs are high. Indeed, when transaction costs are high, efficiency cannot be reached through negotiations. Coase, nonetheless, rejects Pigou’s tools for every situation. Through a deep examination of the paragraphs of “The Problem of Social Costs,” it is understandable why Coase opposes Pigou’s tools. First of all, he considers that the remedy consisting in the compensation of the victim. To Pigou’s way of thinking, this is a strict liability rule. Coase states that the damage is caused by both parties, and, moreover, the amount of the damage depends on both parties. He understands that the compensation method described by Pigou can bring about moral hazards and, therefore, brings about new social costs.Since the article was written in 1960, Coase’s theory has been developed and has become a pillar of tort law and economics. Pigou proposed a tax as an alternative remedy for external effects, which does not bring about a behavior of moral hazard, because the victim bears the expected costs. However, Coase is diffident in regard to the tax. His idea was not developed by other scholars in the subsequent years. Coase understands that efficiency should require a tax on the victim, so that the victim considers the increase of the costs of precaution for the injurer due to creating the nuisance. In other words, Coase understands that the tax does not produce the socially optimal activity level of the parties if the costs of precaution of the other party are not considered as a component of the tax. Therefore, Coase‘s belief is that the tools of Pigou create so many problems as to make them inefficient.