***Below is how I answered. I am unsure how correct I am. Any critics are appreciated!

1.In the situation depicted below:

A.Which users (upstream or downstream) should get the property right (allowing them to have their interests protected) according to Coase's "theorem"?

Moving left to right emissions are increasing. Marginal benefit is B because it is producing earning profits in a low-cost way. If the upstream entity had to reduce emissions then B would become cost. The external cost to the downstream is A if downstream keeps producing at the cost, high emissions way and A is the social benefit if the upstream reduces its pollution, thereby reducing upstreams' marginal benefit. Upstream users get the property right according to the Coase's Theorem because they benefit most (shaded area A, Abetment) than downstream users benefit (shaded area B, Benefit)

B.Which property right (full liability or no liability) is more socially efficient?

No liability is more socially efficient because area A is smaller than area B.

C.Would a change from full liability to no liability be a Pareto improvement?

Pareto improvement can not be achieved in this case because either directional movement off switching liability makes either upstream or downstream worse off in case of one or the other benefiting.

D.Indicate in the graph the "net benefit" to society of a switch from full liability to no liability (be careful to label or indicate this answer clearly).

Net benefit to society for the switch from full liability to no liability is represented by the orange shading in the graph.