The famous Coase Theorem says that in the absence of transaction costs the initial allocation of resources does not matter because resources will end up with the users who can use them most efficiently.
To check if this reasoning works, let us carry a thought experiment.
Suppose that all the resources in the zero-transaction cost economy are allocated efficiently, except one plot of land, which is already a very stringent assumption. The owner of the land, John, is the most efficient user, except for just one person, Sam (stringent assumption 2).
John gets from the plot of land $1000 per year. If the title to the land plot were translated to Sam, he would get $2000 per year from it. Assume that these amounts are changeless (stringent assumption 3).
In line with the Coase Theorem, the land plot will be immediately transferred to Sam. But does this conclusion follow from the conditions described?
The first problem is that, since value is subjective, John may value the land plot not because or not just because it brings him money. In such situation the fact that someone may use the land plot more efficiently may just not bother him. Thus, in order to try to save the Coase Theorem, we need to assume that all that agents care about is maximization of monetary income (stringent assumption 4).
But does it save the theorem? Yes, Sam will increase the productivity of the land plot but how much will John value it? In other words, will he ask from Sam $1100 or $5000 or $30000?
Sam may offer John to pay him $1000+ for every year of John’s life remaining. But if we don’t eliminate time preference from the picture, that may not be enough.
Now, suppose that there is no time preference (stringent assumption 5), and John and Sam immediately strike a deal. There is still a problem for the Coase Theorem. For now, the monetary incomes of John and Sam will change. This may change relative prices in the economy and unsettle the rosy picture that had existed prior to the transfer where all other resources in the economy, except John’s land plot, had been efficiently allocated.
And not only has this changed. The increase in the productivity of the land plot by definition means that quantity of at least one good in the economy has increased or a new good has entered the market.
I don’t think that there is a need for carrying the logic further. It is clear that Coase Theorem does not hold even with the most stringent assumptions. And I can’t even think of an assumption that would solve the final problem I mentioned.