Legal rules in the Edgeworth Box

Different legal rules or property rights define different initial allocations in the Edgeworth Box. For example, suppose that the factory has the right to produce as much Q as it likes (that is, a rule of no liability), without being obligated to compensate the residents. Then the starting point for trading between the factory and the residents lies somewhere on the top edge of the Edgeworth Box, as is shown in Figure 3.4.1.

Possible initial allocations under a no liability rule in the Edgeworth Box

Figure 3.4.1 Possible initial allocations under a no liability rule in the Edgeworth Box

Possible initial allocations if the residents have the property right

Figure 3.4.2 Possible initial allocations if the residents have the property right

On the other hand, suppose that the residents have the right to prevent the factory from producing, and can demand a payment from the factory in exchange for granting them right to produce. Then, the starting point for trading between the factory and the residents would lie somewhere on the bottom edge of the Edgeworth Box, as is shown in Figure 3.4.2.

How do these different legal rules matter for the well-being of the factory and the residents, for efficiency, and for the production of Q? Is one legal rule better than another? If so, why? If not, why not?

We begin to answer these questions in this set-up by stating and proving the Coase Theorem. There are two versions to the Coase Theorem that we will explore:

  • 1. The Efficiency Version of the Coase Theorem: If transaction costs are sufficiently low, then the initial legal regime or assignment of property rights will not hinder the parties from reaching an agreement in which all possible gains from trade have been exhausted. In other words, from an efficiency point of view, if transaction costs are low, no legal rule is preferable to any other. Legal rules don't matter for efficiency.
  • 2. The Invariance Version of the Coase Theorem: If transaction costs are sufficiently low, then the bargaining will always lead to the same level of production of Q, irrespective of the initial legal regime or assignment of property rights. In other words, the legal rule has no relevance for determining the level of production of Q that will eventually be chosen by the factory.

These are quite remarkable propositions. Let us investigate them using the Edgeworth Box. Consider Figure 3.4.3 below. Throughout we hold the parties' initial amounts of money constant by assuming that, irrespective of the legal regime, the factory has an initial allocation of money, Mf, and the residents have an initial allocation of money, Mr.

 
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