There are 10 households living in a small town. Of these, 4 households are farmers and 6 work in other industries. A factory pollutes the river that runs through the town. The farmers incur damages of $11,000 from the pollution, and the other households incur damages of $500. The factory says that it can install equipment to clean up the pollution for a total of $40,000, but that the town must pay for the installation. The town mayor proposes that all households share the cost equally, and pay a tax of $4,000 each to cover the cost of the equipment. 1. Is this proposal a Pareto improvement? 2. Is this proposal a potential Pareto improvement? 3. Design a tax system that would fund the cost of the equipment and be a Pareto improvement. (Show that it is a Pareto improvement.)