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Let us try to analyse the Fontainbleu case in the light of the Posnerian interpretation of Coase's theorem. Well, so viewed the social cost represented by the Eden Roc's no-longer sunny swimming pool was not imposed by the Fontainbleu alone, but by both parties: such is the reciprocal nature of the problem of allocating costs and goods. From this perspective we have to assume that it is always possible to modify the initial legal delimitation of rights by transactions in the market. And, of course, if market transactions are costless, such a rearrangement of rights will always take place if it leads to an increase in the value of production. So the ultimate result (i.e., that which maximizes the value of production) is independent of the legal position if the pricing system is assumed to work without costs.
All this would have the ring of truth, were there not a legal system enforcing distributed rights. Coase assumes that either the Eden Roc or the Fontainbleu should have to bargain; but each can refuse to bargain if it has a right and can stand in court to defend it. So the process is not independent from the assignment of rights. The payoff to the individual parties varies according to this assignment. It is just the net result for society which is independent.
But I would ask with Hayek, who is this being "Society"? Is it not but a ghost evoked by our primitive anthropological approach to social facts? Does "Society" exist? Does it have a welfare function? Does it snicker?
In a world with rights and courts to enforce them, Eden Roc, if it has a right to sun, can pay just $10,000 in costs to sue, and will prevail even if this means the Fontainbleu will be forbidden to "increase value" by $100,000. On the other hand, if Fontainbleu has a right to build on its property it could do so even if the expected income would be less than Eden Roc's losses. The only limit admitted by just about every theory of rights is that the 14-story tower must not be built with the exclusive intention of damaging Eden Roc, without any profit for Fontainbleu.
Not only does the ultimate result not depend, in a Posnerian world, on the initial assignment of rights, but the entire proposed bargaining process starts only if there is a particular assignment of rights, and will not start at all given certain assignments.
If Fontaibleu has a right to build on its property, it has no need to buy it from Eden Roc. On the other hand if Eden Roc has a right to sun Fontainbleu needs to acquire it, and so Eden Roc can be compensated for the loss, and it can even gain something bargaining for the higher price at which Fontaibleu would still add the tower.If Eden Roc has no right it just suffers a net loss. The parties' pay offs change dramatically. It is the net result for Society which never changes, just because this result is defined as the net balance of profits and losses ddistributed between the parties. The theorem just says that "x + or - y is equal to the algebric difference of x and y". It is not even a theorem but the same definition of algebric calculus. Is it a grat analytical result that the net balance does not change? By definition the net balance cannot change. It is trivial to observe that a theorem must be a tautology, but what it matters is that, as always, in Economics the problem is never the Theorem but the interpretation of the theorem. The problem is the interpretation of the theorem in terms of the "net balance" as the wealth of Society and in terms of the process of definition of rights and liabilities of the parties.
When Posnerian Coase speaks of rights and rearrangements of rights, I think he is in fact speaking of possessions and rearrangements of possessions. It is true that in a state of nature the ultimate result will not depend upon the initial assignment of possessions. But this is not true in a legal order. What I mean is that Posnerian Coase is plausible only in Lockean terms which explain also the peculiar approach to the reciprocal nature of the problem raised in the theorem. It seems to me that Coase assumes that the farmer and the herdsman have a title to what they possess (control), and that the farmer cannot simply shoot the herdsman's cows (probably the most convenient solution) nor the herdsman douse the farmer's cabin with fuel and burn it down. That would be a truly reciprocal problem of conflict. The only framework I know in which it is assumed that individuals have a title to their bodies  and to what they can thenceforth possess, in which it is assumed that there are contracts and property rights but no courts to enforce them, is that state of nature peculiarly shaped by Locke for his purposes. But does this State of Nature make sense as a paradigm? At any rate no one, not even Nozick, ever advanced a plausible reason for accepting this state as a starting point. Even Nozick assumes only that if we start from the Lockean state of nature, then certain consequences must be accepted.
I maintain that the Coase theorem as applied by Posner is valid only in a Lockean State of Nature. It is too narrow to serve as a justification for the decision-making of an appellate court. In addition, the Posnerian Coase creates the strange consortium of a Lockean framework linked with a totalitarian version of wealth maximization. If we believe in a theory of rights we cannot believe in the necessity of immolating those rights to maximize the wealth of society. And as I have said, I do not think it plausible in ontological terms to admit the existence of a discrete entity called "Society" which has a particular welfare function to maximize.
The plausibility of the Posnerian Coase theorem depends upon the assumption that, in a free market with no obstacles to bargaining between parties, voluntary exchange will allocate goods to their most valuable uses. But although this is true of goods (by which I mean property rights recognised in goods) which I can freely exchange, it may be not true of rules of liability and it is certainly not true of the definition of rights. Free exchange may allocate the right to build an addition to the Fontainbleu to whomever values that right most, but it has nothing to do with the process of deciding if that right exists in the first place, and if so, what its boundaries are.
I think that a great misunderstanding arises from the muddling up of two different levels of meaning: one of the exchange of rights, and the other of the bargaining between opposite parties about the definition of the rights to be exchanged. This is a distinction upon which the standard theory of social contract focused centuries before Posner construed Coase's theorem. It is a distinction one may easily find in all philosophers have written about this theory. The inconsistency between utilitarian and rights-based theories is made apparent as well by all scholars who have investigated utilitarian theories seriously. It is this strange consortium and misunderstanding which makes the theorem interesting (in the British sense of the word).
The well-known tenet, according to which parties can always reach a wealth-maximizing agreement in a world without transaction costs, may be read on two different levels.
In a Lockean State of Nature, where all have title to what they can possess, parties can, in the absence of transaction costs, come out of this state in a satisfactory way by means of agreement. This is plain old social contract theory.
When it is a question of the exchange of already-defined property rights, market forces can, in the absence of transaction costs, lead to an allocation of resources towards their most valued uses. This is plain old economics.
It is the muddling-up, the confusion between these two levels, that makes the theorem interesting but also leads to the untenable conclusion that inside a legal order, if parties seeking to use the same bit of land in two conflicting ways can bargain, the party who values his use most highly will always prevail. We shall see this in the next paragraph. But I maintain that Posnerian Coase is interesting precisely because of this confusion. Confusion, far more then clarity, is always intellectually exciting. It is like taking a draft by Kyd, the plot for a revenge play, and so complicating it as to transform it into Hamlet : an extremely charming and inconsistent drama.
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