In this paper, we discuss some problems included in the Coase Theorem on externalities. Our results are summarized as follows, supposing that the externality involves two firms, an active injurer and a passive victim.
First, the Coase Theorem can be derived from two different kinds of model, i.e. a market model and a bargaining model. In the market model, however, the distribution of income is uniquely determined. It follows that the right is more strictly entitled in the market approach than in the bargaining approach from a distributional viewpoint.
Next, the externality problem essentially have multiple solutions, supposing that it is possible for a victim to live a parasite life. Therefore, the Coase Theorem has to be revised because the invariability of its solution is violated.
Thirdly, supposing that the right is not liability for damages but injunction, the Coase Theorem is not valid for the following reason. The theorem has to be true regardless of the entitlements. However, it holds true under the assumption of injunction only if we let the entitlement be at the efficient production. Thus, the liability for damages is preferable to the injunction because with the injunction the socially optimum distribution might not be obtained.
Lastly, we reconsider the choice between the property rule and the liability rule. We conclude that the liability rule is socially preferable to the property rule from both an allocational and a distributional viewpoints.