'Rescuing' the Coase Theorem, part II: Enforceable contracts penalty clauses
Another possibility for 'rescuing' the Coase Theorem in the three-party example is to follow Bernholz (1997) and Aivazian and Callen (2003) and introduce the concepts of enforceable contracts and penalty clauses. To understand the role of enforceable contracts and penalties, suppose that contracts, once written, cannot be breached without compensation to the affected parties. Then, in our example, once a contract between any two-player coalition has been agreed to, a party that wishes to break an agreement and negotiate with another party would face a financial cost.
Suppose, for example, that there is a rule of no liability, and that factory 1 signs an agreement with the residents to stop production. Then the residents must receive at least 24 from such an agreement, and factory 1 must receive at least 3, with the joint value equal to 31. Suppose the parties split the gains from trade, so that the residents receive 26 and factory 1 receives 5. Now suppose that the factory 1 wishes to breach this agreement and instead merge with factory 2 and jointly produce. Factory 1 must compensate the residents 26 if he breaches their agreement. But this is not possible, since the joint profits that can be gained from a merger between the factories are only equal to 15 in total, and factory 2 must get at least 8 of those in order for the merger to be worth his while. The gains from breaching the contract are simply not high enough to warrant factory 1 breaching the contract.
Similarly, suppose that the residents wished to breach their agreement with factory 1, and instead form an agreement with factory 2. The available gains are 36. Factory 1 would need to be compensated 5, and factory 2 needs to receive at least 8. So that leaves a maximum of 23 for the residents to enjoy after all compensation has been made. But the residents were already receiving 26 in their contract with factory 1. Therefore, with enforceable contracts in place, there is no incentive for the residents to breach their agreement either. But since neither factory 1 nor the residents want to breach the agreement, it must be stable. Both parties' only option is to then sign an agreement with factory 2, from which there are mutual benefits. Therefore, cycling does not occur and the invariance and efficiency versions of the Coase Theorem again hold.