The Coase theorem and the initial assignment of property rights

The Coase theorem and the initial assignment of property rights

"Surveys and experiments reveal that people sometimes demand much more to give something up that they have than they would be willing to pay to acquire it.... The divergence between the buying and selling price is called an endowment effect because the price varies depending on the initial assignment of ownership." (Cooter and Ulen: 91)

The diagram to the right illustrates consumption for Kelty, who lives on the shore of a lake and derives utility from the water quality of the lake and from money income (measured in $1,000).
Initially, the water quality of the lake is high, and Kelty consumes at point a and enjoys utility Ua.

Now suppose a factory locates on the opposite shore of the lake. Its pollution reduces the water quality of the lake to Lo.
Step 1: Use the label 'b' to indicate Kelty's new consumption point in the diagram.

Kelty files a lawsuit to enjoin the factory from polluting the lake.

Case 1: Kelty wins the lawsuit and is awarded the right to a pollution-free lake.
Step 2: Use the label 'A' to indicate in the diagram the minimum amount of money that the factory must pay Kelty to get his permission to pollute the lake.

Case 2: Kelty loses the lawsuit, and the factory is awarded the right to pollute the lake.
Step 3: Use the label 'B' to indicate in the diagram the maximum amount of money that Kelty will pay the factory to stop its polluting.

Question: Does Kelty consider the water quality of the lake to be a normal or inferior good? How can you tell?

Exercise: In the lower right diagram, sketch Kelty's demand curve Db for water quality when utility is Ub and his demand curve Da for utility Ua. Use your demand curves to show how much more Kelty must be paid to give up Hi-Lo of water quality (Case 1) than he would be willing to pay to retain Hi-Lo of water quality (Case 2).

Coase Theorem corollary: The particular efficient outcome we get can depend on how property rights are assigned.