Some of the mangos from your neighbor's mango tree drop into your yard. You don't like mangos and the fallen mangos make it harder to mow your lawn. Your neighbor values the tree at $300, and your cost of dealing with it is $500. If your neighbor has the legal right to keep the tree, what would be an efficient outcome according to the Coase theorem?

You pay your neighbor $400 to cut the tree down.

Explanation:

You pay your neighbor $400 to cut the tree down.

The amount paid to the neighbor is to be more than the value of the tree as your neighbour values and this will satisfy as per the Coase Theorem which states that amount paid for the damage caused due to negative externality should be more than the value that the person attaches to production of externality.Also, it is to be lower than the cost which the person has to bear because of mango production and thus as a result both gain $100 in the process.

You should pay your neighbor any amount higher than $300 and lower than $500 so that he cuts the tree down.

Explanation:

Under the Coase Theorem both parties will seek an economical solution without regarding the initial property rights.

This means that it doesn't matter if it's your neighbor's tree that bothers you, what matters is that you don't want to be bothered anymore. You value removing the tree at $500, and your neighbor values his tree at $300. So an economically optimal solution to this dispute would be for you to pay your neighbor more than $300 but less than $500.